Algebraic Construction of Exact Difference Equations from Symmetry of Equations

NASA Astrophysics Data System (ADS)

Itoh, Toshiaki

2009-09-01

Difference equations or exact numerical integrations, which have general solutions, are treated algebraically. Eliminating the symmetries of the equation, we can construct difference equations (DCE) or numerical integrations equivalent to some ODEs or PDEs that means both have the same solution functions. When arbitrary functions are given, whether we can construct numerical integrations that have solution functions equal to given function or not are treated in this work. Nowadays, Lie's symmetries solver for ODE and PDE has been implemented in many symbolic software. Using this solver we can construct algebraic DCEs or numerical integrations which are correspond to some ODEs or PDEs. In this work, we treated exact correspondence between ODE or PDE and DCE or numerical integration with Gröbner base and Janet base from the view of Lie's symmetries.

CPDES3: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in three dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on three-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES3 allows each spatial operator to have 7, 15, 19, or 27 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect induces which is vectorizable on some of the newer scientific computers.

CPDES2: A preconditioned conjugate gradient solver for linear asymmetric matrix equations arising from coupled partial differential equations in two dimensions

NASA Astrophysics Data System (ADS)

Anderson, D. V.; Koniges, A. E.; Shumaker, D. E.

1988-11-01

Many physical problems require the solution of coupled partial differential equations on two-dimensional domains. When the time scales of interest dictate an implicit discretization of the equations a rather complicated global matrix system needs solution. The exact form of the matrix depends on the choice of spatial grids and on the finite element or finite difference approximations employed. CPDES2 allows each spatial operator to have 5 or 9 point stencils and allows for general couplings between all of the component PDE's and it automatically generates the matrix structures needed to perform the algorithm. The resulting sparse matrix equation is solved by either the preconditioned conjugate gradient (CG) method or by the preconditioned biconjugate gradient (BCG) algorithm. An arbitrary number of component equations are permitted only limited by available memory. In the sub-band representation used, we generate an algorithm that is written compactly in terms of indirect indices which is vectorizable on some of the newer scientific computers.

A matrix-free implicit unstructured multigrid finite volume method for simulating structural dynamics and fluid structure interaction

NASA Astrophysics Data System (ADS)

Lv, X.; Zhao, Y.; Huang, X. Y.; Xia, G. H.; Su, X. H.

2007-07-01

A new three-dimensional (3D) matrix-free implicit unstructured multigrid finite volume (FV) solver for structural dynamics is presented in this paper. The solver is first validated using classical 2D and 3D cantilever problems. It is shown that very accurate predictions of the fundamental natural frequencies of the problems can be obtained by the solver with fast convergence rates. This method has been integrated into our existing FV compressible solver [X. Lv, Y. Zhao, et al., An efficient parallel/unstructured-multigrid preconditioned implicit method for simulating 3d unsteady compressible flows with moving objects, Journal of Computational Physics 215(2) (2006) 661-690] based on the immersed membrane method (IMM) [X. Lv, Y. Zhao, et al., as mentioned above]. Results for the interaction between the fluid and an immersed fixed-free cantilever are also presented to demonstrate the potential of this integrated fluid-structure interaction approach.

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

NASA Technical Reports Server (NTRS)

Moorthi, Shrinivas; Higgins, R. W.

1993-01-01

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Parameter investigation with line-implicit lower-upper symmetric Gauss-Seidel on 3D stretched grids

NASA Astrophysics Data System (ADS)

Otero, Evelyn; Eliasson, Peter

2015-03-01

An implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solver has been implemented as a multigrid smoother combined with a line-implicit method as an acceleration technique for Reynolds-averaged Navier-Stokes (RANS) simulation on stretched meshes. The computational fluid dynamics code concerned is Edge, an edge-based finite volume Navier-Stokes flow solver for structured and unstructured grids. The paper focuses on the investigation of the parameters related to our novel line-implicit LU-SGS solver for convergence acceleration on 3D RANS meshes. The LU-SGS parameters are defined as the Courant-Friedrichs-Lewy number, the left-hand side dissipation, and the convergence of iterative solution of the linear problem arising from the linearisation of the implicit scheme. The influence of these parameters on the overall convergence is presented and default values are defined for maximum convergence acceleration. The optimised settings are applied to 3D RANS computations for comparison with explicit and line-implicit Runge-Kutta smoothing. For most of the cases, a computing time acceleration of the order of 2 is found depending on the mesh type, namely the boundary layer and the magnitude of residual reduction.

Fast viscosity solutions for shape from shading under a more realistic imaging model

NASA Astrophysics Data System (ADS)

Wang, Guohui; Han, Jiuqiang; Jia, Honghai; Zhang, Xinman

2009-11-01

Shape from shading (SFS) has been a classical and important problem in the domain of computer vision. The goal of SFS is to reconstruct the 3-D shape of an object from its 2-D intensity image. To this end, an image irradiance equation describing the relation between the shape of a surface and its corresponding brightness variations is used. Then it is derived as an explicit partial differential equation (PDE). Using the nonlinear programming principle, we propose a detailed solution to Prados and Faugeras's implicit scheme for approximating the viscosity solution of the resulting PDE. Furthermore, by combining implicit and semi-implicit schemes, a new approximation scheme is presented. In order to accelerate the convergence speed, we adopt the Gauss-Seidel idea and alternating sweeping strategy to the approximation schemes. Experimental results on both synthetic and real images are performed to demonstrate that the proposed methods are fast and accurate.

A semi-Lagrangian approach to the shallow water equation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Mccormick, Stephen F.; Ruge, John; Sholl, David S.; Yavneh, Irad

1993-01-01

We present a formulation of the shallow water equations that emphasizes the conservation of potential vorticity. A locally conservative semi-Lagrangian time-stepping scheme is developed, which leads to a system of three coupled PDE's to be solved at each time level. We describe a smoothing analysis of these equations, on which an effective multigrid solver is constructed. Some results from applying this solver to the static version of these equations are presented.

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

DOE Office of Scientific and Technical Information (OSTI.GOV)

Garrett, C. Kristopher; Hauck, Cory D.

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

Advancing parabolic operators in thermodynamic MHD models: Explicit super time-stepping versus implicit schemes with Krylov solvers

NASA Astrophysics Data System (ADS)

Caplan, R. M.; Mikić, Z.; Linker, J. A.; Lionello, R.

2017-05-01

We explore the performance and advantages/disadvantages of using unconditionally stable explicit super time-stepping (STS) algorithms versus implicit schemes with Krylov solvers for integrating parabolic operators in thermodynamic MHD models of the solar corona. Specifically, we compare the second-order Runge-Kutta Legendre (RKL2) STS method with the implicit backward Euler scheme computed using the preconditioned conjugate gradient (PCG) solver with both a point-Jacobi and a non-overlapping domain decomposition ILU0 preconditioner. The algorithms are used to integrate anisotropic Spitzer thermal conduction and artificial kinematic viscosity at time-steps much larger than classic explicit stability criteria allow. A key component of the comparison is the use of an established MHD model (MAS) to compute a real-world simulation on a large HPC cluster. Special attention is placed on the parallel scaling of the algorithms. It is shown that, for a specific problem and model, the RKL2 method is comparable or surpasses the implicit method with PCG solvers in performance and scaling, but suffers from some accuracy limitations. These limitations, and the applicability of RKL methods are briefly discussed.

ASIS v1.0: an adaptive solver for the simulation of atmospheric chemistry

NASA Astrophysics Data System (ADS)

Cariolle, Daniel; Moinat, Philippe; Teyssèdre, Hubert; Giraud, Luc; Josse, Béatrice; Lefèvre, Franck

2017-04-01

This article reports on the development and tests of the adaptive semi-implicit scheme (ASIS) solver for the simulation of atmospheric chemistry. To solve the ordinary differential equation systems associated with the time evolution of the species concentrations, ASIS adopts a one-step linearized implicit scheme with specific treatments of the Jacobian of the chemical fluxes. It conserves mass and has a time-stepping module to control the accuracy of the numerical solution. In idealized box-model simulations, ASIS gives results similar to the higher-order implicit schemes derived from the Rosenbrock's and Gear's methods and requires less computation and run time at the moderate precision required for atmospheric applications. When implemented in the MOCAGE chemical transport model and the Laboratoire de Météorologie Dynamique Mars general circulation model, the ASIS solver performs well and reveals weaknesses and limitations of the original semi-implicit solvers used by these two models. ASIS can be easily adapted to various chemical schemes and further developments are foreseen to increase its computational efficiency, and to include the computation of the concentrations of the species in aqueous-phase in addition to gas-phase chemistry.

A Fast Solver for Implicit Integration of the Vlasov--Poisson System in the Eulerian Framework

DOE PAGES

Garrett, C. Kristopher; Hauck, Cory D.

2018-04-05

In this paper, we present a domain decomposition algorithm to accelerate the solution of Eulerian-type discretizations of the linear, steady-state Vlasov equation. The steady-state solver then forms a key component in the implementation of fully implicit or nearly fully implicit temporal integrators for the nonlinear Vlasov--Poisson system. The solver relies on a particular decomposition of phase space that enables the use of sweeping techniques commonly used in radiation transport applications. The original linear system for the phase space unknowns is then replaced by a smaller linear system involving only unknowns on the boundary between subdomains, which can then be solvedmore » efficiently with Krylov methods such as GMRES. Steady-state solves are combined to form an implicit Runge--Kutta time integrator, and the Vlasov equation is coupled self-consistently to the Poisson equation via a linearized procedure or a nonlinear fixed-point method for the electric field. Finally, numerical results for standard test problems demonstrate the efficiency of the domain decomposition approach when compared to the direct application of an iterative solver to the original linear system.« less

A semi-implicit augmented IIM for Navier–Stokes equations with open, traction, or free boundary conditions

PubMed Central

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2016-01-01

In this paper, a new Navier–Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier–Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented. PMID:27087702

A semi-implicit augmented IIM for Navier-Stokes equations with open, traction, or free boundary conditions.

PubMed

Li, Zhilin; Xiao, Li; Cai, Qin; Zhao, Hongkai; Luo, Ray

2015-08-15

In this paper, a new Navier-Stokes solver based on a finite difference approximation is proposed to solve incompressible flows on irregular domains with open, traction, and free boundary conditions, which can be applied to simulations of fluid structure interaction, implicit solvent model for biomolecular applications and other free boundary or interface problems. For some problems of this type, the projection method and the augmented immersed interface method (IIM) do not work well or does not work at all. The proposed new Navier-Stokes solver is based on the local pressure boundary method, and a semi-implicit augmented IIM. A fast Poisson solver can be used in our algorithm which gives us the potential for developing fast overall solvers in the future. The time discretization is based on a second order multi-step method. Numerical tests with exact solutions are presented to validate the accuracy of the method. Application to fluid structure interaction between an incompressible fluid and a compressible gas bubble is also presented.

Divergence-Free SPH for Incompressible and Viscous Fluids.

PubMed

Bender, Jan; Koschier, Dan

2017-03-01

In this paper we present a novel Smoothed Particle Hydrodynamics (SPH) method for the efficient and stable simulation of incompressible fluids. The most efficient SPH-based approaches enforce incompressibility either on position or velocity level. However, the continuity equation for incompressible flow demands to maintain a constant density and a divergence-free velocity field. We propose a combination of two novel implicit pressure solvers enforcing both a low volume compression as well as a divergence-free velocity field. While a compression-free fluid is essential for realistic physical behavior, a divergence-free velocity field drastically reduces the number of required solver iterations and increases the stability of the simulation significantly. Thanks to the improved stability, our method can handle larger time steps than previous approaches. This results in a substantial performance gain since the computationally expensive neighborhood search has to be performed less frequently. Moreover, we introduce a third optional implicit solver to simulate highly viscous fluids which seamlessly integrates into our solver framework. Our implicit viscosity solver produces realistic results while introducing almost no numerical damping. We demonstrate the efficiency, robustness and scalability of our method in a variety of complex simulations including scenarios with millions of turbulent particles or highly viscous materials.

PDE-based geophysical modelling using finite elements: examples from 3D resistivity and 2D magnetotellurics

NASA Astrophysics Data System (ADS)

Schaa, R.; Gross, L.; du Plessis, J.

2016-04-01

We present a general finite-element solver, escript, tailored to solve geophysical forward and inverse modeling problems in terms of partial differential equations (PDEs) with suitable boundary conditions. Escript’s abstract interface allows geoscientists to focus on solving the actual problem without being experts in numerical modeling. General-purpose finite element solvers have found wide use especially in engineering fields and find increasing application in the geophysical disciplines as these offer a single interface to tackle different geophysical problems. These solvers are useful for data interpretation and for research, but can also be a useful tool in educational settings. This paper serves as an introduction into PDE-based modeling with escript where we demonstrate in detail how escript is used to solve two different forward modeling problems from applied geophysics (3D DC resistivity and 2D magnetotellurics). Based on these two different cases, other geophysical modeling work can easily be realized. The escript package is implemented as a Python library and allows the solution of coupled, linear or non-linear, time-dependent PDEs. Parallel execution for both shared and distributed memory architectures is supported and can be used without modifications to the scripts.

Time integration algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Slack, David C.; Whitaker, D. L.; Walters, Robert W.

1994-01-01

Explicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.

Implicit integration methods for dislocation dynamics

DOE PAGES

Gardner, D. J.; Woodward, C. S.; Reynolds, D. R.; ...

2015-01-20

In dislocation dynamics simulations, strain hardening simulations require integrating stiff systems of ordinary differential equations in time with expensive force calculations, discontinuous topological events, and rapidly changing problem size. Current solvers in use often result in small time steps and long simulation times. Faster solvers may help dislocation dynamics simulations accumulate plastic strains at strain rates comparable to experimental observations. Here, this paper investigates the viability of high order implicit time integrators and robust nonlinear solvers to reduce simulation run times while maintaining the accuracy of the computed solution. In particular, implicit Runge-Kutta time integrators are explored as a waymore » of providing greater accuracy over a larger time step than is typically done with the standard second-order trapezoidal method. In addition, both accelerated fixed point and Newton's method are investigated to provide fast and effective solves for the nonlinear systems that must be resolved within each time step. Results show that integrators of third order are the most effective, while accelerated fixed point and Newton's method both improve solver performance over the standard fixed point method used for the solution of the nonlinear systems.« less

Implicit adaptive mesh refinement for 2D reduced resistive magnetohydrodynamics

NASA Astrophysics Data System (ADS)

Philip, Bobby; Chacón, Luis; Pernice, Michael

2008-10-01

An implicit structured adaptive mesh refinement (SAMR) solver for 2D reduced magnetohydrodynamics (MHD) is described. The time-implicit discretization is able to step over fast normal modes, while the spatial adaptivity resolves thin, dynamically evolving features. A Jacobian-free Newton-Krylov method is used for the nonlinear solver engine. For preconditioning, we have extended the optimal "physics-based" approach developed in [L. Chacón, D.A. Knoll, J.M. Finn, An implicit, nonlinear reduced resistive MHD solver, J. Comput. Phys. 178 (2002) 15-36] (which employed multigrid solver technology in the preconditioner for scalability) to SAMR grids using the well-known Fast Adaptive Composite grid (FAC) method [S. McCormick, Multilevel Adaptive Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1989]. A grid convergence study demonstrates that the solver performance is independent of the number of grid levels and only depends on the finest resolution considered, and that it scales well with grid refinement. The study of error generation and propagation in our SAMR implementation demonstrates that high-order (cubic) interpolation during regridding, combined with a robustly damping second-order temporal scheme such as BDF2, is required to minimize impact of grid errors at coarse-fine interfaces on the overall error of the computation for this MHD application. We also demonstrate that our implementation features the desired property that the overall numerical error is dependent only on the finest resolution level considered, and not on the base-grid resolution or on the number of refinement levels present during the simulation. We demonstrate the effectiveness of the tool on several challenging problems.

Solving Partial Differential Equations in a data-driven multiprocessor environment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

1988-12-31

Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

Development and Verification of the Charring Ablating Thermal Protection Implicit System Solver

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan D.; Kirk, Benjamin S.

2010-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method with first and second order implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton's method, while the fully implicit linear system is solved with the Generalized Minimal Residual method. Verification results from exact solutions and the Method of Manufactured Solutions are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

AQUASOL: An efficient solver for the dipolar Poisson–Boltzmann–Langevin equation

PubMed Central

Koehl, Patrice; Delarue, Marc

2010-01-01

The Poisson–Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson–Boltzmann–Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available. PMID:20151727

AQUASOL: An efficient solver for the dipolar Poisson-Boltzmann-Langevin equation.

PubMed

Koehl, Patrice; Delarue, Marc

2010-02-14

The Poisson-Boltzmann (PB) formalism is among the most popular approaches to modeling the solvation of molecules. It assumes a continuum model for water, leading to a dielectric permittivity that only depends on position in space. In contrast, the dipolar Poisson-Boltzmann-Langevin (DPBL) formalism represents the solvent as a collection of orientable dipoles with nonuniform concentration; this leads to a nonlinear permittivity function that depends both on the position and on the local electric field at that position. The differences in the assumptions underlying these two models lead to significant differences in the equations they generate. The PB equation is a second order, elliptic, nonlinear partial differential equation (PDE). Its response coefficients correspond to the dielectric permittivity and are therefore constant within each subdomain of the system considered (i.e., inside and outside of the molecules considered). While the DPBL equation is also a second order, elliptic, nonlinear PDE, its response coefficients are nonlinear functions of the electrostatic potential. Many solvers have been developed for the PB equation; to our knowledge, none of these can be directly applied to the DPBL equation. The methods they use may adapt to the difference; their implementations however are PBE specific. We adapted the PBE solver originally developed by Holst and Saied [J. Comput. Chem. 16, 337 (1995)] to the problem of solving the DPBL equation. This solver uses a truncated Newton method with a multigrid preconditioner. Numerical evidences suggest that it converges for the DPBL equation and that the convergence is superlinear. It is found however to be slow and greedy in memory requirement for problems commonly encountered in computational biology and computational chemistry. To circumvent these problems, we propose two variants, a quasi-Newton solver based on a simplified, inexact Jacobian and an iterative self-consistent solver that is based directly on the PBE solver. While both methods are not guaranteed to converge, numerical evidences suggest that they do and that their convergence is also superlinear. Both variants are significantly faster than the solver based on the exact Jacobian, with a much smaller memory footprint. All three methods have been implemented in a new code named AQUASOL, which is freely available.

An implicit higher-order spatially accurate scheme for solving time dependent flows on unstructured meshes

NASA Astrophysics Data System (ADS)

Tomaro, Robert F.

1998-07-01

The present research is aimed at developing a higher-order, spatially accurate scheme for both steady and unsteady flow simulations using unstructured meshes. The resulting scheme must work on a variety of general problems to ensure the creation of a flexible, reliable and accurate aerodynamic analysis tool. To calculate the flow around complex configurations, unstructured grids and the associated flow solvers have been developed. Efficient simulations require the minimum use of computer memory and computational times. Unstructured flow solvers typically require more computer memory than a structured flow solver due to the indirect addressing of the cells. The approach taken in the present research was to modify an existing three-dimensional unstructured flow solver to first decrease the computational time required for a solution and then to increase the spatial accuracy. The terms required to simulate flow involving non-stationary grids were also implemented. First, an implicit solution algorithm was implemented to replace the existing explicit procedure. Several test cases, including internal and external, inviscid and viscous, two-dimensional, three-dimensional and axi-symmetric problems, were simulated for comparison between the explicit and implicit solution procedures. The increased efficiency and robustness of modified code due to the implicit algorithm was demonstrated. Two unsteady test cases, a plunging airfoil and a wing undergoing bending and torsion, were simulated using the implicit algorithm modified to include the terms required for a moving and/or deforming grid. Secondly, a higher than second-order spatially accurate scheme was developed and implemented into the baseline code. Third- and fourth-order spatially accurate schemes were implemented and tested. The original dissipation was modified to include higher-order terms and modified near shock waves to limit pre- and post-shock oscillations. The unsteady cases were repeated using the higher-order spatially accurate code. The new solutions were compared with those obtained using the second-order spatially accurate scheme. Finally, the increased efficiency of using an implicit solution algorithm in a production Computational Fluid Dynamics flow solver was demonstrated for steady and unsteady flows. A third- and fourth-order spatially accurate scheme has been implemented creating a basis for a state-of-the-art aerodynamic analysis tool.

An Optimized Multicolor Point-Implicit Solver for Unstructured Grid Applications on Graphics Processing Units

NASA Technical Reports Server (NTRS)

Zubair, Mohammad; Nielsen, Eric; Luitjens, Justin; Hammond, Dana

2016-01-01

In the field of computational fluid dynamics, the Navier-Stokes equations are often solved using an unstructuredgrid approach to accommodate geometric complexity. Implicit solution methodologies for such spatial discretizations generally require frequent solution of large tightly-coupled systems of block-sparse linear equations. The multicolor point-implicit solver used in the current work typically requires a significant fraction of the overall application run time. In this work, an efficient implementation of the solver for graphics processing units is proposed. Several factors present unique challenges to achieving an efficient implementation in this environment. These include the variable amount of parallelism available in different kernel calls, indirect memory access patterns, low arithmetic intensity, and the requirement to support variable block sizes. In this work, the solver is reformulated to use standard sparse and dense Basic Linear Algebra Subprograms (BLAS) functions. However, numerical experiments show that the performance of the BLAS functions available in existing CUDA libraries is suboptimal for matrices representative of those encountered in actual simulations. Instead, optimized versions of these functions are developed. Depending on block size, the new implementations show performance gains of up to 7x over the existing CUDA library functions.

Effects of high-frequency damping on iterative convergence of implicit viscous solver

NASA Astrophysics Data System (ADS)

Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko

2017-11-01

This paper discusses effects of high-frequency damping on iterative convergence of an implicit defect-correction solver for viscous problems. The study targets a finite-volume discretization with a one parameter family of damped viscous schemes. The parameter α controls high-frequency damping: zero damping with α = 0, and larger damping for larger α (> 0). Convergence rates are predicted for a model diffusion equation by a Fourier analysis over a practical range of α. It is shown that the convergence rate attains its minimum at α = 1 on regular quadrilateral grids, and deteriorates for larger values of α. A similar behavior is observed for regular triangular grids. In both quadrilateral and triangular grids, the solver is predicted to diverge for α smaller than approximately 0.5. Numerical results are shown for the diffusion equation and the Navier-Stokes equations on regular and irregular grids. The study suggests that α = 1 and 4/3 are suitable values for robust and efficient computations, and α = 4 / 3 is recommended for the diffusion equation, which achieves higher-order accuracy on regular quadrilateral grids. Finally, a Jacobian-Free Newton-Krylov solver with the implicit solver (a low-order Jacobian approximately inverted by a multi-color Gauss-Seidel relaxation scheme) used as a variable preconditioner is recommended for practical computations, which provides robust and efficient convergence for a wide range of α.

Preconditioned conjugate gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1994-01-01

A preconditioned Krylov subspace method (GMRES) is used to solve the linear systems of equations formed at each time-integration step of the unsteady, two-dimensional, compressible Navier-Stokes equations of fluid flow. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux-split formulation. Several preconditioning techniques are investigated to enhance the efficiency and convergence rate of the implicit solver based on the GMRES algorithm. The superiority of the new solver is established by comparisons with a conventional implicit solver, namely line Gauss-Seidel relaxation (LGSR). Computational test results for low-speed (incompressible flow over a backward-facing step at Mach 0.1), transonic flow (trailing edge flow in a transonic turbine cascade), and hypersonic flow (shock-on-shock interactions on a cylindrical leading edge at Mach 6.0) are presented. For the Mach 0.1 case, overall speedup factors of up to 17 (in terms of time-steps) and 15 (in terms of CPU time on a CRAY-YMP/8) are found in favor of the preconditioned GMRES solver, when compared with the LGSR solver. The corresponding speedup factors for the transonic flow case are 17 and 23, respectively. The hypersonic flow case shows slightly lower speedup factors of 9 and 13, respectively. The study of preconditioners conducted in this research reveals that a new LUSGS-type preconditioner is much more efficient than a conventional incomplete LU-type preconditioner.

Parallelized CCHE2D flow model with CUDA Fortran on Graphics Process Units

USDA-ARS?s Scientific Manuscript database

This paper presents the CCHE2D implicit flow model parallelized using CUDA Fortran programming technique on Graphics Processing Units (GPUs). A parallelized implicit Alternating Direction Implicit (ADI) solver using Parallel Cyclic Reduction (PCR) algorithm on GPU is developed and tested. This solve...

On multigrid solution of the implicit equations of hydrodynamics. Experiments for the compressible Euler equations in general coordinates

NASA Astrophysics Data System (ADS)

Kifonidis, K.; Müller, E.

2012-08-01

Aims: We describe and study a family of new multigrid iterative solvers for the multidimensional, implicitly discretized equations of hydrodynamics. Schemes of this class are free of the Courant-Friedrichs-Lewy condition. They are intended for simulations in which widely differing wave propagation timescales are present. A preferred solver in this class is identified. Applications to some simple stiff test problems that are governed by the compressible Euler equations, are presented to evaluate the convergence behavior, and the stability properties of this solver. Algorithmic areas are determined where further work is required to make the method sufficiently efficient and robust for future application to difficult astrophysical flow problems. Methods: The basic equations are formulated and discretized on non-orthogonal, structured curvilinear meshes. Roe's approximate Riemann solver and a second-order accurate reconstruction scheme are used for spatial discretization. Implicit Runge-Kutta (ESDIRK) schemes are employed for temporal discretization. The resulting discrete equations are solved with a full-coarsening, non-linear multigrid method. Smoothing is performed with multistage-implicit smoothers. These are applied here to the time-dependent equations by means of dual time stepping. Results: For steady-state problems, our results show that the efficiency of the present approach is comparable to the best implicit solvers for conservative discretizations of the compressible Euler equations that can be found in the literature. The use of red-black as opposed to symmetric Gauss-Seidel iteration in the multistage-smoother is found to have only a minor impact on multigrid convergence. This should enable scalable parallelization without having to seriously compromise the method's algorithmic efficiency. For time-dependent test problems, our results reveal that the multigrid convergence rate degrades with increasing Courant numbers (i.e. time step sizes). Beyond a Courant number of nine thousand, even complete multigrid breakdown is observed. Local Fourier analysis indicates that the degradation of the convergence rate is associated with the coarse-grid correction algorithm. An implicit scheme for the Euler equations that makes use of the present method was, nevertheless, able to outperform a standard explicit scheme on a time-dependent problem with a Courant number of order 1000. Conclusions: For steady-state problems, the described approach enables the construction of parallelizable, efficient, and robust implicit hydrodynamics solvers. The applicability of the method to time-dependent problems is presently restricted to cases with moderately high Courant numbers. This is due to an insufficient coarse-grid correction of the employed multigrid algorithm for large time steps. Further research will be required to help us to understand and overcome the observed multigrid convergence difficulties for time-dependent problems.

A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives with Target Redemption Features

NASA Astrophysics Data System (ADS)

Christara, Christina C.; Minh Dang, Duy; Jackson, Kenneth R.; Lakhany, Asif

2010-09-01

We propose a general framework for efficient pricing via a partial differential equation (PDE) approach for exotic cross-currency interest rate (IR) derivatives, with strong emphasis on long-dated foreign exchange (FX) IR hybrids, namely Power Reverse Dual Currency (PRDC) swaps with a FX Target Redemption (FX-TARN) provision. The FX-TARN provision provides a cap on the FX-linked PRDC coupon amounts, and once the accumulated coupon amount reaches this cap, the underlying PRDC swap terminates. Our PDE pricing framework is based on an auxiliary state variable to keep track of the total accumulated PRDC coupon amount. Finite differences on uniform grids and the Alternating Direction Implicit (ADI) method are used for the spatial and time discretizations, respectively, of the model-dependent PDE corresponding to each discretized value of the auxiliary variable. Numerical examples illustrating the convergence properties of the numerical methods are provided.

Algorithmically scalable block preconditioner for fully implicit shallow-water equations in CAM-SE

DOE PAGES

Lott, P. Aaron; Woodward, Carol S.; Evans, Katherine J.

2014-10-19

Performing accurate and efficient numerical simulation of global atmospheric climate models is challenging due to the disparate length and time scales over which physical processes interact. Implicit solvers enable the physical system to be integrated with a time step commensurate with processes being studied. The dominant cost of an implicit time step is the ancillary linear system solves, so we have developed a preconditioner aimed at improving the efficiency of these linear system solves. Our preconditioner is based on an approximate block factorization of the linearized shallow-water equations and has been implemented within the spectral element dynamical core within themore » Community Atmospheric Model (CAM-SE). Furthermore, in this paper we discuss the development and scalability of the preconditioner for a suite of test cases with the implicit shallow-water solver within CAM-SE.« less

Xyce

DOE Office of Scientific and Technical Information (OSTI.GOV)

Thomquist, Heidi K.; Fixel, Deborah A.; Fett, David Brian

The Xyce Parallel Electronic Simulator simulates electronic circuit behavior in DC, AC, HB, MPDE and transient mode using standard analog (DAE) and/or device (PDE) device models including several age and radiation aware devices. It supports a variety of computing platforms (both serial and parallel) computers. Lastly, it uses a variety of modern solution algorithms dynamic parallel load-balancing and iterative solvers.

Implicit-explicit (IMEX) Runge-Kutta methods for non-hydrostatic atmospheric models

NASA Astrophysics Data System (ADS)

Gardner, David J.; Guerra, Jorge E.; Hamon, François P.; Reynolds, Daniel R.; Ullrich, Paul A.; Woodward, Carol S.

2018-04-01

The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit-explicit (IMEX) additive Runge-Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit - vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly. In each case, the impact of solving nonlinear systems in each implicit ARK stage in a linearly implicit fashion is also explored. The accuracy and efficiency of the IMEX splittings, ARK methods, and solver options are evaluated on a gravity wave and baroclinic wave test case. HEVI splittings that treat some vertical dynamics explicitly do not show a benefit in solution quality or run time over the most implicit HEVI formulation. While splittings that implicitly evolve some horizontal dynamics increase the maximum stable step size of a method, the gains are insufficient to overcome the additional cost of solving a globally coupled system. Solving implicit stage systems in a linearly implicit manner limits the solver cost but this is offset by a reduction in step size to achieve the desired accuracy for some methods. Overall, the third-order ARS343 and ARK324 methods performed the best, followed by the second-order ARS232 and ARK232 methods.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lott, P. Aaron; Woodward, Carol S.; Evans, Katherine J.

Performing accurate and efficient numerical simulation of global atmospheric climate models is challenging due to the disparate length and time scales over which physical processes interact. Implicit solvers enable the physical system to be integrated with a time step commensurate with processes being studied. The dominant cost of an implicit time step is the ancillary linear system solves, so we have developed a preconditioner aimed at improving the efficiency of these linear system solves. Our preconditioner is based on an approximate block factorization of the linearized shallow-water equations and has been implemented within the spectral element dynamical core within themore » Community Atmospheric Model (CAM-SE). Furthermore, in this paper we discuss the development and scalability of the preconditioner for a suite of test cases with the implicit shallow-water solver within CAM-SE.« less

Application of an unstructured grid flow solver to planes, trains and automobiles

NASA Technical Reports Server (NTRS)

Spragle, Gregory S.; Smith, Wayne A.; Yadlin, Yoram

1993-01-01

Rampant, an unstructured flow solver developed at Fluent Inc., is used to compute three-dimensional, viscous, turbulent, compressible flow fields within complex solution domains. Rampant is an explicit, finite-volume flow solver capable of computing flow fields using either triangular (2d) or tetrahedral (3d) unstructured grids. Local time stepping, implicit residual smoothing, and multigrid techniques are used to accelerate the convergence of the explicit scheme. The paper describes the Rampant flow solver and presents flow field solutions about a plane, train, and automobile.

Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models

DOE PAGES

Gardner, David J.; Guerra, Jorge E.; Hamon, François P.; ...

2018-04-17

The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit–explicit (IMEX) additive Runge–Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit – vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly. In each case, the impact of solving nonlinear systems in each implicit ARK stage in a linearly implicit fashion is also explored.The accuracymore » and efficiency of the IMEX splittings, ARK methods, and solver options are evaluated on a gravity wave and baroclinic wave test case. HEVI splittings that treat some vertical dynamics explicitly do not show a benefit in solution quality or run time over the most implicit HEVI formulation. While splittings that implicitly evolve some horizontal dynamics increase the maximum stable step size of a method, the gains are insufficient to overcome the additional cost of solving a globally coupled system. Solving implicit stage systems in a linearly implicit manner limits the solver cost but this is offset by a reduction in step size to achieve the desired accuracy for some methods. Overall, the third-order ARS343 and ARK324 methods performed the best, followed by the second-order ARS232 and ARK232 methods.« less

Implicit–explicit (IMEX) Runge–Kutta methods for non-hydrostatic atmospheric models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gardner, David J.; Guerra, Jorge E.; Hamon, François P.

The efficient simulation of non-hydrostatic atmospheric dynamics requires time integration methods capable of overcoming the explicit stability constraints on time step size arising from acoustic waves. In this work, we investigate various implicit–explicit (IMEX) additive Runge–Kutta (ARK) methods for evolving acoustic waves implicitly to enable larger time step sizes in a global non-hydrostatic atmospheric model. The IMEX formulations considered include horizontally explicit – vertically implicit (HEVI) approaches as well as splittings that treat some horizontal dynamics implicitly. In each case, the impact of solving nonlinear systems in each implicit ARK stage in a linearly implicit fashion is also explored.The accuracymore » and efficiency of the IMEX splittings, ARK methods, and solver options are evaluated on a gravity wave and baroclinic wave test case. HEVI splittings that treat some vertical dynamics explicitly do not show a benefit in solution quality or run time over the most implicit HEVI formulation. While splittings that implicitly evolve some horizontal dynamics increase the maximum stable step size of a method, the gains are insufficient to overcome the additional cost of solving a globally coupled system. Solving implicit stage systems in a linearly implicit manner limits the solver cost but this is offset by a reduction in step size to achieve the desired accuracy for some methods. Overall, the third-order ARS343 and ARK324 methods performed the best, followed by the second-order ARS232 and ARK232 methods.« less

IGA-ADS: Isogeometric analysis FEM using ADS solver

NASA Astrophysics Data System (ADS)

Łoś, Marcin M.; Woźniak, Maciej; Paszyński, Maciej; Lenharth, Andrew; Hassaan, Muhamm Amber; Pingali, Keshav

2017-08-01

In this paper we present a fast explicit solver for solution of non-stationary problems using L2 projections with isogeometric finite element method. The solver has been implemented within GALOIS framework. It enables parallel multi-core simulations of different time-dependent problems, in 1D, 2D, or 3D. We have prepared the solver framework in a way that enables direct implementation of the selected PDE and corresponding boundary conditions. In this paper we describe the installation, implementation of exemplary three PDEs, and execution of the simulations on multi-core Linux cluster nodes. We consider three case studies, including heat transfer, linear elasticity, as well as non-linear flow in heterogeneous media. The presented package generates output suitable for interfacing with Gnuplot and ParaView visualization software. The exemplary simulations show near perfect scalability on Gilbert shared-memory node with four Intel® Xeon® CPU E7-4860 processors, each possessing 10 physical cores (for a total of 40 cores).

Efficiency and flexibility using implicit methods within atmosphere dycores

NASA Astrophysics Data System (ADS)

Evans, K. J.; Archibald, R.; Norman, M. R.; Gardner, D. J.; Woodward, C. S.; Worley, P.; Taylor, M.

2016-12-01

A suite of explicit and implicit methods are evaluated for a range of configurations of the shallow water dynamical core within the spectral-element Community Atmosphere Model (CAM-SE) to explore their relative computational performance. The configurations are designed to explore the attributes of each method under different but relevant model usage scenarios including varied spectral order within an element, static regional refinement, and scaling to large problem sizes. The limitations and benefits of using explicit versus implicit, with different discretizations and parameters, are discussed in light of trade-offs such as MPI communication, memory, and inherent efficiency bottlenecks. For the regionally refined shallow water configurations, the implicit BDF2 method is about the same efficiency as an explicit Runge-Kutta method, without including a preconditioner. Performance of the implicit methods with the residual function executed on a GPU is also presented; there is speed up for the residual relative to a CPU, but overwhelming transfer costs motivate moving more of the solver to the device. Given the performance behavior of implicit methods within the shallow water dynamical core, the recommendation for future work using implicit solvers is conditional based on scale separation and the stiffness of the problem. The strong growth of linear iterations with increasing resolution or time step size is the main bottleneck to computational efficiency. Within the hydrostatic dynamical core, of CAM-SE, we present results utilizing approximate block factorization preconditioners implemented using the Trilinos library of solvers. They reduce the cost of linear system solves and improve parallel scalability. We provide a summary of the remaining efficiency considerations within the preconditioner and utilization of the GPU, as well as a discussion about the benefits of a time stepping method that provides converged and stable solutions for a much wider range of time step sizes. As more complex model components, for example new physics and aerosols, are connected in the model, having flexibility in the time stepping will enable more options for combining and resolving multiple scales of behavior.

Computational Electromagnetics

DTIC Science & Technology

2011-02-20

finite differences use the continuation method instead, and have been shown to lead to unconditionally stable numerics for a wide range of realistic PDE...best previous solvers were restricted to two-dimensional (range and height) refractive index variations. The numerical method we introduced...however, is such that even its solution on the basis of Rytov’s method gives rise to extremely high computational costs. We thus resort to

Multi-Dimensional Quantum Tunneling and Transport Using the Density-Gradient Model

NASA Technical Reports Server (NTRS)

Biegel, Bryan A.; Yu, Zhi-Ping; Ancona, Mario; Rafferty, Conor; Saini, Subhash (Technical Monitor)

1999-01-01

We show that quantum effects are likely to significantly degrade the performance of MOSFETs (metal oxide semiconductor field effect transistor) as these devices are scaled below 100 nm channel length and 2 nm oxide thickness over the next decade. A general and computationally efficient electronic device model including quantum effects would allow us to monitor and mitigate these effects. Full quantum models are too expensive in multi-dimensions. Using a general but efficient PDE solver called PROPHET, we implemented the density-gradient (DG) quantum correction to the industry-dominant classical drift-diffusion (DD) model. The DG model efficiently includes quantum carrier profile smoothing and tunneling in multi-dimensions and for any electronic device structure. We show that the DG model reduces DD model error from as much as 50% down to a few percent in comparison to thin oxide MOS capacitance measurements. We also show the first DG simulations of gate oxide tunneling and transverse current flow in ultra-scaled MOSFETs. The advantages of rapid model implementation using the PDE solver approach will be demonstrated, as well as the applicability of the DG model to any electronic device structure.

Design of a Variational Multiscale Method for Turbulent Compressible Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo Tibor; Murman, Scott M.

2013-01-01

A spectral-element framework is presented for the simulation of subsonic compressible high-Reynolds-number flows. The focus of the work is maximizing the efficiency of the computational schemes to enable unsteady simulations with a large number of spatial and temporal degrees of freedom. A collocation scheme is combined with optimized computational kernels to provide a residual evaluation with computational cost independent of order of accuracy up to 16th order. The optimized residual routines are used to develop a low-memory implicit scheme based on a matrix-free Newton-Krylov method. A preconditioner based on the finite-difference diagonalized ADI scheme is developed which maintains the low memory of the matrix-free implicit solver, while providing improved convergence properties. Emphasis on low memory usage throughout the solver development is leveraged to implement a coupled space-time DG solver which may offer further efficiency gains through adaptivity in both space and time.

Creating Weather System Ensembles Through Synergistic Process Modeling and Machine Learning

NASA Astrophysics Data System (ADS)

Chen, B.; Posselt, D. J.; Nguyen, H.; Wu, L.; Su, H.; Braverman, A. J.

2017-12-01

Earth's weather and climate are sensitive to a variety of control factors (e.g., initial state, forcing functions, etc). Characterizing the response of the atmosphere to a change in initial conditions or model forcing is critical for weather forecasting (ensemble prediction) and climate change assessment. Input - response relationships can be quantified by generating an ensemble of multiple (100s to 1000s) realistic realizations of weather and climate states. Atmospheric numerical models generate simulated data through discretized numerical approximation of the partial differential equations (PDEs) governing the underlying physics. However, the computational expense of running high resolution atmospheric state models makes generation of more than a few simulations infeasible. Here, we discuss an experiment wherein we approximate the numerical PDE solver within the Weather Research and Forecasting (WRF) Model using neural networks trained on a subset of model run outputs. Once trained, these neural nets can produce large number of realization of weather states from a small number of deterministic simulations with speeds that are orders of magnitude faster than the underlying PDE solver. Our neural network architecture is inspired by the governing partial differential equations. These equations are location-invariant, and consist of first and second derivations. As such, we use a 3x3 lon-lat grid of atmospheric profiles as the predictor in the neural net to provide the network the information necessary to compute the first and second moments. Results indicate that the neural network algorithm can approximate the PDE outputs with high degree of accuracy (less than 1% error), and that this error increases as a function of the prediction time lag.

A comparison of viscous-plastic sea ice solvers with and without replacement pressure

NASA Astrophysics Data System (ADS)

Kimmritz, Madlen; Losch, Martin; Danilov, Sergey

2017-07-01

Recent developments of the explicit elastic-viscous-plastic (EVP) solvers call for a new comparison with implicit solvers for the equations of viscous-plastic sea ice dynamics. In Arctic sea ice simulations, the modified and the adaptive EVP solvers, and the implicit Jacobian-free Newton-Krylov (JFNK) solver are compared against each other. The adaptive EVP method shows convergence rates that are generally similar or even better than those of the modified EVP method, but the convergence of the EVP methods is found to depend dramatically on the use of the replacement pressure (RP). Apparently, using the RP can affect the pseudo-elastic waves in the EVP methods by introducing extra non-physical oscillations so that, in the extreme case, convergence to the VP solution can be lost altogether. The JFNK solver also suffers from higher failure rates with RP implying that with RP the momentum equations are stiffer and more difficult to solve. For practical purposes, both EVP methods can be used efficiently with an unexpectedly low number of sub-cycling steps without compromising the solutions. The differences between the RP solutions and the NoRP solutions (when the RP is not being used) can be reduced with lower thresholds of viscous regularization at the cost of increasing stiffness of the equations, and hence the computational costs of solving them.

Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods

NASA Astrophysics Data System (ADS)

Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco

2015-04-01

The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface resistivity. The Hessian of the regularization term is used as preconditioner which requires an additional PDE solution in each iteration step. As it turns out, the relevant PDEs are naturally formulated in the finite element framework. Using the domain decomposition method provided in Escript, the inversion scheme has been parallelized for distributed memory computers with multi-core shared memory nodes. We show numerical examples from simple layered models to complex 3D models and compare with the results from other methods. The inversion scheme is furthermore tested on a field data example to characterise localised freshwater discharge in a coastal environment.. References: L. Gross and C. Kemp (2013) Large Scale Joint Inversion of Geophysical Data using the Finite Element Method in escript. ASEG Extended Abstracts 2013, http://dx.doi.org/10.1071/ASEG2013ab306

Three-Dimensional High-Lift Analysis Using a Parallel Unstructured Multigrid Solver

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1998-01-01

A directional implicit unstructured agglomeration multigrid solver is ported to shared and distributed memory massively parallel machines using the explicit domain-decomposition and message-passing approach. Because the algorithm operates on local implicit lines in the unstructured mesh, special care is required in partitioning the problem for parallel computing. A weighted partitioning strategy is described which avoids breaking the implicit lines across processor boundaries, while incurring minimal additional communication overhead. Good scalability is demonstrated on a 128 processor SGI Origin 2000 machine and on a 512 processor CRAY T3E machine for reasonably fine grids. The feasibility of performing large-scale unstructured grid calculations with the parallel multigrid algorithm is demonstrated by computing the flow over a partial-span flap wing high-lift geometry on a highly resolved grid of 13.5 million points in approximately 4 hours of wall clock time on the CRAY T3E.

Implicit and explicit subgrid-scale modeling in discontinuous Galerkin methods for large-eddy simulation

NASA Astrophysics Data System (ADS)

Fernandez, Pablo; Nguyen, Ngoc-Cuong; Peraire, Jaime

2017-11-01

Over the past few years, high-order discontinuous Galerkin (DG) methods for Large-Eddy Simulation (LES) have emerged as a promising approach to solve complex turbulent flows. Despite the significant research investment, the relation between the discretization scheme, the Riemann flux, the subgrid-scale (SGS) model and the accuracy of the resulting LES solver remains unclear. In this talk, we investigate the role of the Riemann solver and the SGS model in the ability to predict a variety of flow regimes, including transition to turbulence, wall-free turbulence, wall-bounded turbulence, and turbulence decay. The Taylor-Green vortex problem and the turbulent channel flow at various Reynolds numbers are considered. Numerical results show that DG methods implicitly introduce numerical dissipation in under-resolved turbulence simulations and, even in the high Reynolds number limit, this implicit dissipation provides a more accurate representation of the actual subgrid-scale dissipation than that by explicit models.

Steady potential solver for unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Dan

1994-01-01

Development of a steady flow solver for use with LINFLO was the objective of this report. The solver must be compatible with LINFLO, be composed of composite mesh, and have transonic capability. The approaches used were: (1) steady flow potential equations written in nonconservative form; (2) Newton's Method; (3) implicit, least-squares, interpolation method to obtain finite difference equations; and (4) matrix inversion routines from LINFLO. This report was given during the NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.

Convergence Acceleration of a Navier-Stokes Solver for Efficient Static Aeroelastic Computations

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru; Guruswamy, Guru P.

1995-01-01

New capabilities have been developed for a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is based on a combination of the lower-upper factored symmetric Gauss-Seidel implicit method and the modified Harten-Lax-van Leer-Einfeldt upwind scheme. A numerically stable and efficient pseudo-time-marching method is also developed for computing steady flows over flexible wings. Results are demonstrated for transonic flows over rigid and flexible wings.

Shape reanalysis and sensitivities utilizing preconditioned iterative boundary solvers

NASA Technical Reports Server (NTRS)

Guru Prasad, K.; Kane, J. H.

1992-01-01

The computational advantages associated with the utilization of preconditined iterative equation solvers are quantified for the reanalysis of perturbed shapes using continuum structural boundary element analysis (BEA). Both single- and multi-zone three-dimensional problems are examined. Significant reductions in computer time are obtained by making use of previously computed solution vectors and preconditioners in subsequent analyses. The effectiveness of this technique is demonstrated for the computation of shape response sensitivities required in shape optimization. Computer times and accuracies achieved using the preconditioned iterative solvers are compared with those obtained via direct solvers and implicit differentiation of the boundary integral equations. It is concluded that this approach employing preconditioned iterative equation solvers in reanalysis and sensitivity analysis can be competitive with if not superior to those involving direct solvers.

Parallel performance investigations of an unstructured mesh Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

2000-01-01

A Reynolds-averaged Navier-Stokes solver based on unstructured mesh techniques for analysis of high-lift configurations is described. The method makes use of an agglomeration multigrid solver for convergence acceleration. Implicit line-smoothing is employed to relieve the stiffness associated with highly stretched meshes. A GMRES technique is also implemented to speed convergence at the expense of additional memory usage. The solver is cache efficient and fully vectorizable, and is parallelized using a two-level hybrid MPI-OpenMP implementation suitable for shared and/or distributed memory architectures, as well as clusters of shared memory machines. Convergence and scalability results are illustrated for various high-lift cases.

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Rossow, C.-C.

2008-01-01

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Implicit schemes and parallel computing in unstructured grid CFD

NASA Technical Reports Server (NTRS)

Venkatakrishnam, V.

1995-01-01

The development of implicit schemes for obtaining steady state solutions to the Euler and Navier-Stokes equations on unstructured grids is outlined. Applications are presented that compare the convergence characteristics of various implicit methods. Next, the development of explicit and implicit schemes to compute unsteady flows on unstructured grids is discussed. Next, the issues involved in parallelizing finite volume schemes on unstructured meshes in an MIMD (multiple instruction/multiple data stream) fashion are outlined. Techniques for partitioning unstructured grids among processors and for extracting parallelism in explicit and implicit solvers are discussed. Finally, some dynamic load balancing ideas, which are useful in adaptive transient computations, are presented.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 1: One-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

An algorithm for solving a large class of two- and three-dimensional nonseparable elliptic partial differential equations (PDE's) is developed and tested. It uses a modified D'Yakanov-Gunn iterative procedure in which the relaxation factor is grid-point dependent. It is easy to implement and applicable to a variety of boundary conditions. It is also computationally efficient, as indicated by the results of numerical comparisons with other established methods. Furthermore, the current algorithm has the advantage of possessing two important properties which the traditional iterative methods lack; that is: (1) the convergence rate is relatively insensitive to grid-cell size and aspect ratio, and (2) the convergence rate can be easily estimated by using the coefficient of the PDE being solved.

Explicit and implicit springback simulation in sheet metal forming using fully coupled ductile damage and distortional hardening model

NASA Astrophysics Data System (ADS)

Yetna n'jock, M.; Houssem, B.; Labergere, C.; Saanouni, K.; Zhenming, Y.

2018-05-01

The springback is an important phenomenon which accompanies the forming of metallic sheets especially for high strength materials. A quantitative prediction of springback becomes very important for newly developed material with high mechanical characteristics. In this work, a numerical methodology is developed to quantify this undesirable phenomenon. This methodoly is based on the use of both explicit and implicit finite element solvers of Abaqus®. The most important ingredient of this methodology consists on the use of highly predictive mechanical model. A thermodynamically-consistent, non-associative and fully anisotropic elastoplastic constitutive model strongly coupled with isotropic ductile damage and accounting for distortional hardening is then used. An algorithm for local integration of the complete set of the constitutive equations is developed. This algorithm considers the rotated frame formulation (RFF) to ensure the incremental objectivity of the model in the framework of finite strains. This algorithm is implemented in both explicit (Abaqus/Explicit®) and implicit (Abaqus/Standard®) solvers of Abaqus® through the users routine VUMAT and UMAT respectively. The implicit solver of Abaqus® has been used to study spingback as it is generally a quasi-static unloading. In order to compare the methods `efficiency, the explicit method (Dynamic Relaxation Method) proposed by Rayleigh has been also used for springback prediction. The results obtained within U draw/bending benchmark are studied, discussed and compared with experimental results as reference. Finally, the purpose of this work is to evaluate the reliability of different methods predict efficiently springback in sheet metal forming.

Geometric multigrid for an implicit-time immersed boundary method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Guy, Robert D.; Philip, Bobby; Griffith, Boyce E.

2014-10-12

The immersed boundary (IB) method is an approach to fluid-structure interaction that uses Lagrangian variables to describe the deformations and resulting forces of the structure and Eulerian variables to describe the motion and forces of the fluid. Explicit time stepping schemes for the IB method require solvers only for Eulerian equations, for which fast Cartesian grid solution methods are available. Such methods are relatively straightforward to develop and are widely used in practice but often require very small time steps to maintain stability. Implicit-time IB methods permit the stable use of large time steps, but efficient implementations of such methodsmore » require significantly more complex solvers that effectively treat both Lagrangian and Eulerian variables simultaneously. Moreover, several different approaches to solving the coupled Lagrangian-Eulerian equations have been proposed, but a complete understanding of this problem is still emerging. This paper presents a geometric multigrid method for an implicit-time discretization of the IB equations. This multigrid scheme uses a generalization of box relaxation that is shown to handle problems in which the physical stiffness of the structure is very large. Numerical examples are provided to illustrate the effectiveness and efficiency of the algorithms described herein. Finally, these tests show that using multigrid as a preconditioner for a Krylov method yields improvements in both robustness and efficiency as compared to using multigrid as a solver. They also demonstrate that with a time step 100–1000 times larger than that permitted by an explicit IB method, the multigrid-preconditioned implicit IB method is approximately 50–200 times more efficient than the explicit method.« less

Three-dimensional unstructured grid Euler computations using a fully-implicit, upwind method

NASA Technical Reports Server (NTRS)

Whitaker, David L.

1993-01-01

A method has been developed to solve the Euler equations on a three-dimensional unstructured grid composed of tetrahedra. The method uses an upwind flow solver with a linearized, backward-Euler time integration scheme. Each time step results in a sparse linear system of equations which is solved by an iterative, sparse matrix solver. Local-time stepping, switched evolution relaxation (SER), preconditioning and reuse of the Jacobian are employed to accelerate the convergence rate. Implicit boundary conditions were found to be extremely important for fast convergence. Numerical experiments have shown that convergence rates comparable to that of a multigrid, central-difference scheme are achievable on the same mesh. Results are presented for several grids about an ONERA M6 wing.

On the development of OpenFOAM solvers based on explicit and implicit high-order Runge-Kutta schemes for incompressible flows with heat transfer

NASA Astrophysics Data System (ADS)

D'Alessandro, Valerio; Binci, Lorenzo; Montelpare, Sergio; Ricci, Renato

2018-01-01

Open-source CFD codes provide suitable environments for implementing and testing low-dissipative algorithms typically used to simulate turbulence. In this research work we developed CFD solvers for incompressible flows based on high-order explicit and diagonally implicit Runge-Kutta (RK) schemes for time integration. In particular, an iterated PISO-like procedure based on Rhie-Chow correction was used to handle pressure-velocity coupling within each implicit RK stage. For the explicit approach, a projected scheme was used to avoid the "checker-board" effect. The above-mentioned approaches were also extended to flow problems involving heat transfer. It is worth noting that the numerical technology available in the OpenFOAM library was used for space discretization. In this work, we additionally explore the reliability and effectiveness of the proposed implementations by computing several unsteady flow benchmarks; we also show that the numerical diffusion due to the time integration approach is completely canceled using the solution techniques proposed here.

Predictive Flow Control to Minimize Convective Time Delays

DTIC Science & Technology

2013-08-19

simulation. The CFO solver used is Cobalt, an unstructured finite-volume code developed for the solution of the compress- ible Navier-Stokes...cell-centered fin ite volume approach applicable to arbitrary cell topologies (e.g, hexahedra, prisms, tetrahedra). The spatial operator uses a Riemann ... solver , least squares gradient calculations using QR factorizati on to provide second order accuracy in space. A point implicit method using

An efficient mixed-precision, hybrid CPU-GPU implementation of a nonlinearly implicit one-dimensional particle-in-cell algorithm

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Guangye; Chacon, Luis; Barnes, Daniel C

2012-01-01

Recently, a fully implicit, energy- and charge-conserving particle-in-cell method has been developed for multi-scale, full-f kinetic simulations [G. Chen, et al., J. Comput. Phys. 230, 18 (2011)]. The method employs a Jacobian-free Newton-Krylov (JFNK) solver and is capable of using very large timesteps without loss of numerical stability or accuracy. A fundamental feature of the method is the segregation of particle orbit integrations from the field solver, while remaining fully self-consistent. This provides great flexibility, and dramatically improves the solver efficiency by reducing the degrees of freedom of the associated nonlinear system. However, it requires a particle push per nonlinearmore » residual evaluation, which makes the particle push the most time-consuming operation in the algorithm. This paper describes a very efficient mixed-precision, hybrid CPU-GPU implementation of the implicit PIC algorithm. The JFNK solver is kept on the CPU (in double precision), while the inherent data parallelism of the particle mover is exploited by implementing it in single-precision on a graphics processing unit (GPU) using CUDA. Performance-oriented optimizations, with the aid of an analytical performance model, the roofline model, are employed. Despite being highly dynamic, the adaptive, charge-conserving particle mover algorithm achieves up to 300 400 GOp/s (including single-precision floating-point, integer, and logic operations) on a Nvidia GeForce GTX580, corresponding to 20 25% absolute GPU efficiency (against the peak theoretical performance) and 50-70% intrinsic efficiency (against the algorithm s maximum operational throughput, which neglects all latencies). This is about 200-300 times faster than an equivalent serial CPU implementation. When the single-precision GPU particle mover is combined with a double-precision CPU JFNK field solver, overall performance gains 100 vs. the double-precision CPU-only serial version are obtained, with no apparent loss of robustness or accuracy when applied to a challenging long-time scale ion acoustic wave simulation.« less

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

Generalized conjugate-gradient methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1991-01-01

A generalized conjugate-gradient method is used to solve the two-dimensional, compressible Navier-Stokes equations of fluid flow. The equations are discretized with an implicit, upwind finite-volume formulation. Preconditioning techniques are incorporated into the new solver to accelerate convergence of the overall iterative method. The superiority of the new solver is demonstrated by comparisons with a conventional line Gauss-Siedel Relaxation solver. Computational test results for transonic flow (trailing edge flow in a transonic turbine cascade) and hypersonic flow (M = 6.0 shock-on-shock phenoena on a cylindrical leading edge) are presented. When applied to the transonic cascade case, the new solver is 4.4 times faster in terms of number of iterations and 3.1 times faster in terms of CPU time than the Relaxation solver. For the hypersonic shock case, the new solver is 3.0 times faster in terms of number of iterations and 2.2 times faster in terms of CPU time than the Relaxation solver.

Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers

NASA Technical Reports Server (NTRS)

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Implementation of Implicit Adaptive Mesh Refinement in an Unstructured Finite-Volume Flow Solver

NASA Technical Reports Server (NTRS)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2013-01-01

This paper explores the implementation of adaptive mesh refinement in an unstructured, finite-volume solver. Unsteady and steady problems are considered. The effect on the recovery of high-order numerics is explored and the results are favorable. Important to this work is the ability to provide a path for efficient, implicit time advancement. A method using a simple refinement sensor based on undivided differences is discussed and applied to a practical problem: a shock-shock interaction on a hypersonic, inviscid double-wedge. Cases are compared to uniform grids without the use of adapted meshes in order to assess error and computational expense. Discussion of difficulties, advances, and future work prepare this method for additional research. The potential for this method in more complicated flows is described.

Progress report on PIXIE3D, a fully implicit 3D extended MHD solver

NASA Astrophysics Data System (ADS)

Chacon, Luis

2008-11-01

Recently, invited talk at DPP07 an optimal, massively parallel implicit algorithm for 3D resistive magnetohydrodynamics (PIXIE3D) was demonstrated. Excellent algorithmic and parallel results were obtained with up to 4096 processors and 138 million unknowns. While this is a remarkable result, further developments are still needed for PIXIE3D to become a 3D extended MHD production code in general geometries. In this poster, we present an update on the status of PIXIE3D on several fronts. On the physics side, we will describe our progress towards the full Braginskii model, including: electron Hall terms, anisotropic heat conduction, and gyroviscous corrections. Algorithmically, we will discuss progress towards a robust, optimal, nonlinear solver for arbitrary geometries, including preconditioning for the new physical effects described, the implementation of a coarse processor-grid solver (to maintain optimal algorithmic performance for an arbitrarily large number of processors in massively parallel computations), and of a multiblock capability to deal with complicated geometries. L. Chac'on, Phys. Plasmas 15, 056103 (2008);

Oasis: A high-level/high-performance open source Navier-Stokes solver

NASA Astrophysics Data System (ADS)

Mortensen, Mikael; Valen-Sendstad, Kristian

2015-03-01

Oasis is a high-level/high-performance finite element Navier-Stokes solver written from scratch in Python using building blocks from the FEniCS project (fenicsproject.org). The solver is unstructured and targets large-scale applications in complex geometries on massively parallel clusters. Oasis utilizes MPI and interfaces, through FEniCS, to the linear algebra backend PETSc. Oasis advocates a high-level, programmable user interface through the creation of highly flexible Python modules for new problems. Through the high-level Python interface the user is placed in complete control of every aspect of the solver. A version of the solver, that is using piecewise linear elements for both velocity and pressure, is shown to reproduce very well the classical, spectral, turbulent channel simulations of Moser et al. (1999). The computational speed is strongly dominated by the iterative solvers provided by the linear algebra backend, which is arguably the best performance any similar implicit solver using PETSc may hope for. Higher order accuracy is also demonstrated and new solvers may be easily added within the same framework.

Array-based Hierarchical Mesh Generation in Parallel

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2015-11-03

In this paper, we describe an array-based hierarchical mesh generation capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial mesh that can be used for a number of purposes such as multi-level methods to generating large meshes. The capability is developed under the parallel mesh framework “Mesh Oriented dAtaBase” a.k.a MOAB. We describe the underlying data structures and algorithms to generate such hierarchies and present numerical results for computational efficiency and mesh quality. Inmore » conclusion, we also present results to demonstrate the applicability of the developed capability to a multigrid finite-element solver.« less

Workload Characterization of CFD Applications Using Partial Differential Equation Solvers

NASA Technical Reports Server (NTRS)

Waheed, Abdul; Yan, Jerry; Saini, Subhash (Technical Monitor)

1998-01-01

Workload characterization is used for modeling and evaluating of computing systems at different levels of detail. We present workload characterization for a class of Computational Fluid Dynamics (CFD) applications that solve Partial Differential Equations (PDEs). This workload characterization focuses on three high performance computing platforms: SGI Origin2000, EBM SP-2, a cluster of Intel Pentium Pro bases PCs. We execute extensive measurement-based experiments on these platforms to gather statistics of system resource usage, which results in workload characterization. Our workload characterization approach yields a coarse-grain resource utilization behavior that is being applied for performance modeling and evaluation of distributed high performance metacomputing systems. In addition, this study enhances our understanding of interactions between PDE solver workloads and high performance computing platforms and is useful for tuning these applications.

Final Report for "Implimentation and Evaluation of Multigrid Linear Solvers into Extended Magnetohydrodynamic Codes for Petascale Computing"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Srinath Vadlamani; Scott Kruger; Travis Austin

Extended magnetohydrodynamic (MHD) codes are used to model the large, slow-growing instabilities that are projected to limit the performance of International Thermonuclear Experimental Reactor (ITER). The multiscale nature of the extended MHD equations requires an implicit approach. The current linear solvers needed for the implicit algorithm scale poorly because the resultant matrices are so ill-conditioned. A new solver is needed, especially one that scales to the petascale. The most successful scalable parallel processor solvers to date are multigrid solvers. Applying multigrid techniques to a set of equations whose fundamental modes are dispersive waves is a promising solution to CEMM problems.more » For the Phase 1, we implemented multigrid preconditioners from the HYPRE project of the Center for Applied Scientific Computing at LLNL via PETSc of the DOE SciDAC TOPS for the real matrix systems of the extended MHD code NIMROD which is a one of the primary modeling codes of the OFES-funded Center for Extended Magnetohydrodynamic Modeling (CEMM) SciDAC. We implemented the multigrid solvers on the fusion test problem that allows for real matrix systems with success, and in the process learned about the details of NIMROD data structures and the difficulties of inverting NIMROD operators. The further success of this project will allow for efficient usage of future petascale computers at the National Leadership Facilities: Oak Ridge National Laboratory, Argonne National Laboratory, and National Energy Research Scientific Computing Center. The project will be a collaborative effort between computational plasma physicists and applied mathematicians at Tech-X Corporation, applied mathematicians Front Range Scientific Computations, Inc. (who are collaborators on the HYPRE project), and other computational plasma physicists involved with the CEMM project.« less

An interior penalty stabilised incompressible discontinuous Galerkin-Fourier solver for implicit large eddy simulations

NASA Astrophysics Data System (ADS)

Ferrer, Esteban

2017-11-01

We present an implicit Large Eddy Simulation (iLES) h / p high order (≥2) unstructured Discontinuous Galerkin-Fourier solver with sliding meshes. The solver extends the laminar version of Ferrer and Willden, 2012 [34], to enable the simulation of turbulent flows at moderately high Reynolds numbers in the incompressible regime. This solver allows accurate flow solutions of the laminar and turbulent 3D incompressible Navier-Stokes equations on moving and static regions coupled through a high order sliding interface. The spatial discretisation is provided by the Symmetric Interior Penalty Discontinuous Galerkin (IP-DG) method in the x-y plane coupled with a purely spectral method that uses Fourier series and allows efficient computation of spanwise periodic three-dimensional flows. Since high order methods (e.g. discontinuous Galerkin and Fourier) are unable to provide enough numerical dissipation to enable under-resolved high Reynolds computations (i.e. as necessary in the iLES approach), we adapt the laminar version of the solver to increase (controllably) the dissipation and enhance the stability in under-resolved simulations. The novel stabilisation relies on increasing the penalty parameter included in the DG interior penalty (IP) formulation. The latter penalty term is included when discretising the linear viscous terms in the incompressible Navier-Stokes equations. These viscous penalty fluxes substitute the stabilising effect of non-linear fluxes, which has been the main trend in implicit LES discontinuous Galerkin approaches. The IP-DG penalty term provides energy dissipation, which is controlled by the numerical jumps at element interfaces (e.g. large in under-resolved regions) such as to stabilise under-resolved high Reynolds number flows. This dissipative term has minimal impact in well resolved regions and its implicit treatment does not restrict the use of large time steps, thus providing an efficient stabilization mechanism for iLES. The IP-DG stabilisation is complemented with a Spectral Vanishing Viscosity (SVV) method, in the z-direction, to enhance stability in the continuous Fourier space. The coupling between the numerical viscosity in the DG plane and the SVV damping, provides an efficient approach to stabilise high order methods at moderately high Reynolds numbers. We validate the formulation for three turbulent flow cases: a circular cylinder at Re = 3900, a static and pitch oscillating NACA 0012 airfoil at Re = 10000 and finally a rotating vertical-axis turbine at Re = 40000, with Reynolds based on the circular diameter, airfoil chord and turbine diameter, respectively. All our results compare favourably with published direct numerical simulations, large eddy simulations or experimental data. We conclude that the DG-Fourier high order solver, with IP-SVV stabilisation, proves to be a valuable tool to predict turbulent flows and associated statistics for both static and rotating machinery.

Implicit Coupling Approach for Simulation of Charring Carbon Ablators

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Gokcen, Tahir

2013-01-01

This study demonstrates that coupling of a material thermal response code and a flow solver with nonequilibrium gas/surface interaction for simulation of charring carbon ablators can be performed using an implicit approach. The material thermal response code used in this study is the three-dimensional version of Fully Implicit Ablation and Thermal response program, which predicts charring material thermal response and shape change on hypersonic space vehicles. The flow code solves the reacting Navier-Stokes equations using Data Parallel Line Relaxation method. Coupling between the material response and flow codes is performed by solving the surface mass balance in flow solver and the surface energy balance in material response code. Thus, the material surface recession is predicted in flow code, and the surface temperature and pyrolysis gas injection rate are computed in material response code. It is demonstrated that the time-lagged explicit approach is sufficient for simulations at low surface heating conditions, in which the surface ablation rate is not a strong function of the surface temperature. At elevated surface heating conditions, the implicit approach has to be taken, because the carbon ablation rate becomes a stiff function of the surface temperature, and thus the explicit approach appears to be inappropriate resulting in severe numerical oscillations of predicted surface temperature. Implicit coupling for simulation of arc-jet models is performed, and the predictions are compared with measured data. Implicit coupling for trajectory based simulation of Stardust fore-body heat shield is also conducted. The predicted stagnation point total recession is compared with that predicted using the chemical equilibrium surface assumption

Performance Benchmark for a Prismatic Flow Solver

DTIC Science & Technology

2007-03-26

Gauss- Seidel (LU-SGS) implicit method is used for time integration to reduce the computational time. A one-equation turbulence model by Goldberg and...numerical flux computations. The Lower-Upper-Symmetric Gauss- Seidel (LU-SGS) implicit method [1] is used for time integration to reduce the...Sharov, D. and Nakahashi, K., “Reordering of Hybrid Unstructured Grids for Lower-Upper Symmetric Gauss- Seidel Computations,” AIAA Journal, Vol. 36

Dynamic one-dimensional modeling of secondary settling tanks and system robustness evaluation.

PubMed

Li, Ben; Stenstrom, M K

2014-01-01

One-dimensional secondary settling tank models are widely used in current engineering practice for design and optimization, and usually can be expressed as a nonlinear hyperbolic or nonlinear strongly degenerate parabolic partial differential equation (PDE). Reliable numerical methods are needed to produce approximate solutions that converge to the exact analytical solutions. In this study, we introduced a reliable numerical technique, the Yee-Roe-Davis (YRD) method as the governing PDE solver, and compared its reliability with the prevalent Stenstrom-Vitasovic-Takács (SVT) method by assessing their simulation results at various operating conditions. The YRD method also produced a similar solution to the previously developed Method G and Enquist-Osher method. The YRD and SVT methods were also used for a time-to-failure evaluation, and the results show that the choice of numerical method can greatly impact the solution. Reliable numerical methods, such as the YRD method, are strongly recommended.

Fast Euler solver for transonic airfoils. I - Theory. II - Applications

NASA Technical Reports Server (NTRS)

Dadone, Andrea; Moretti, Gino

1988-01-01

Equations written in terms of generalized Riemann variables are presently integrated by inverting six bidiagonal matrices and two tridiagonal matrices, using an implicit Euler solver that is based on the lambda-formulation. The solution is found on a C-grid whose boundaries are very close to the airfoil. The fast solver is then applied to the computation of several flowfields on a NACA 0012 airfoil at various Mach number and alpha values, yielding results that are primarily concerned with transonic flows. The effects of grid fineness and boundary distances are analyzed; the code is found to be robust and accurate, as well as fast.

Benchmarking Defmod, an open source FEM code for modeling episodic fault rupture

NASA Astrophysics Data System (ADS)

Meng, Chunfang

2017-03-01

We present Defmod, an open source (linear) finite element code that enables us to efficiently model the crustal deformation due to (quasi-)static and dynamic loadings, poroelastic flow, viscoelastic flow and frictional fault slip. Ali (2015) provides the original code introducing an implicit solver for (quasi-)static problem, and an explicit solver for dynamic problem. The fault constraint is implemented via Lagrange Multiplier. Meng (2015) combines these two solvers into a hybrid solver that uses failure criteria and friction laws to adaptively switch between the (quasi-)static state and dynamic state. The code is capable of modeling episodic fault rupture driven by quasi-static loadings, e.g. due to reservoir fluid withdraw or injection. Here, we focus on benchmarking the Defmod results against some establish results.

Low-storage implicit/explicit Runge-Kutta schemes for the simulation of stiff high-dimensional ODE systems

NASA Astrophysics Data System (ADS)

Cavaglieri, Daniele; Bewley, Thomas

2015-04-01

Implicit/explicit (IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storage RK schemes are especially effective for time-marching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop and characterize eight new low-storage implicit/explicit RK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep.

Cpu/gpu Computing for AN Implicit Multi-Block Compressible Navier-Stokes Solver on Heterogeneous Platform

NASA Astrophysics Data System (ADS)

Deng, Liang; Bai, Hanli; Wang, Fang; Xu, Qingxin

2016-06-01

CPU/GPU computing allows scientists to tremendously accelerate their numerical codes. In this paper, we port and optimize a double precision alternating direction implicit (ADI) solver for three-dimensional compressible Navier-Stokes equations from our in-house Computational Fluid Dynamics (CFD) software on heterogeneous platform. First, we implement a full GPU version of the ADI solver to remove a lot of redundant data transfers between CPU and GPU, and then design two fine-grain schemes, namely “one-thread-one-point” and “one-thread-one-line”, to maximize the performance. Second, we present a dual-level parallelization scheme using the CPU/GPU collaborative model to exploit the computational resources of both multi-core CPUs and many-core GPUs within the heterogeneous platform. Finally, considering the fact that memory on a single node becomes inadequate when the simulation size grows, we present a tri-level hybrid programming pattern MPI-OpenMP-CUDA that merges fine-grain parallelism using OpenMP and CUDA threads with coarse-grain parallelism using MPI for inter-node communication. We also propose a strategy to overlap the computation with communication using the advanced features of CUDA and MPI programming. We obtain speedups of 6.0 for the ADI solver on one Tesla M2050 GPU in contrast to two Xeon X5670 CPUs. Scalability tests show that our implementation can offer significant performance improvement on heterogeneous platform.

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

NASA Technical Reports Server (NTRS)

Chang, S. C.

1986-01-01

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

ICASE Semiannual Report 1 October 1991 - 31 March 1992

DTIC Science & Technology

1992-05-01

who have resident appointments for limited periods of time as well as by visiting and resident consultants. Members of NASA’s research staff may also...performed showing that the full optimization problem can be solved with a computational cost which is only a few times more than that of solving the PDE...The goal is to obtain a solution of the optimization problem in a computational cost which is just a few times (2-3) that of the flow solver. Such a

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

DOE PAGES

Osborn, Sarah; Zulian, Patrick; Benson, Thomas; ...

2018-01-30

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less

Scalable hierarchical PDE sampler for generating spatially correlated random fields using nonmatching meshes: Scalable hierarchical PDE sampler using nonmatching meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Osborn, Sarah; Zulian, Patrick; Benson, Thomas

This work describes a domain embedding technique between two nonmatching meshes used for generating realizations of spatially correlated random fields with applications to large-scale sampling-based uncertainty quantification. The goal is to apply the multilevel Monte Carlo (MLMC) method for the quantification of output uncertainties of PDEs with random input coefficients on general and unstructured computational domains. We propose a highly scalable, hierarchical sampling method to generate realizations of a Gaussian random field on a given unstructured mesh by solving a reaction–diffusion PDE with a stochastic right-hand side. The stochastic PDE is discretized using the mixed finite element method on anmore » embedded domain with a structured mesh, and then, the solution is projected onto the unstructured mesh. This work describes implementation details on how to efficiently transfer data from the structured and unstructured meshes at coarse levels, assuming that this can be done efficiently on the finest level. We investigate the efficiency and parallel scalability of the technique for the scalable generation of Gaussian random fields in three dimensions. An application of the MLMC method is presented for quantifying uncertainties of subsurface flow problems. Here, we demonstrate the scalability of the sampling method with nonmatching mesh embedding, coupled with a parallel forward model problem solver, for large-scale 3D MLMC simulations with up to 1.9·109 unknowns.« less

A two-dimensional Riemann solver with self-similar sub-structure - Alternative formulation based on least squares projection

NASA Astrophysics Data System (ADS)

Balsara, Dinshaw S.; Vides, Jeaniffer; Gurski, Katharine; Nkonga, Boniface; Dumbser, Michael; Garain, Sudip; Audit, Edouard

2016-01-01

Just as the quality of a one-dimensional approximate Riemann solver is improved by the inclusion of internal sub-structure, the quality of a multidimensional Riemann solver is also similarly improved. Such multidimensional Riemann problems arise when multiple states come together at the vertex of a mesh. The interaction of the resulting one-dimensional Riemann problems gives rise to a strongly-interacting state. We wish to endow this strongly-interacting state with physically-motivated sub-structure. The self-similar formulation of Balsara [16] proves especially useful for this purpose. While that work is based on a Galerkin projection, in this paper we present an analogous self-similar formulation that is based on a different interpretation. In the present formulation, we interpret the shock jumps at the boundary of the strongly-interacting state quite literally. The enforcement of the shock jump conditions is done with a least squares projection (Vides, Nkonga and Audit [67]). With that interpretation, we again show that the multidimensional Riemann solver can be endowed with sub-structure. However, we find that the most efficient implementation arises when we use a flux vector splitting and a least squares projection. An alternative formulation that is based on the full characteristic matrices is also presented. The multidimensional Riemann solvers that are demonstrated here use one-dimensional HLLC Riemann solvers as building blocks. Several stringent test problems drawn from hydrodynamics and MHD are presented to show that the method works. Results from structured and unstructured meshes demonstrate the versatility of our method. The reader is also invited to watch a video introduction to multidimensional Riemann solvers on http://www.nd.edu/ dbalsara/Numerical-PDE-Course.

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

NASA Technical Reports Server (NTRS)

Batina, John T.

1990-01-01

Improved algorithms for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration shceme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. The paper presents a description of the Euler solvers along with results and comparisons which assess the capability.

Accuracy of an unstructured-grid upwind-Euler algorithm for the ONERA M6 wing

NASA Technical Reports Server (NTRS)

Batina, John T.

1991-01-01

Improved algorithms for the solution of the three-dimensional, time-dependent Euler equations are presented for aerodynamic analysis involving unstructured dynamic meshes. The improvements have been developed recently to the spatial and temporal discretizations used by unstructured-grid flow solvers. The spatial discretization involves a flux-split approach that is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves either an explicit time-integration scheme using a multistage Runge-Kutta procedure or an implicit time-integration scheme using a Gauss-Seidel relaxation procedure, which is computationally efficient for either steady or unsteady flow problems. With the implicit Gauss-Seidel procedure, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady flow results are presented for both the NACA 0012 airfoil and the Office National d'Etudes et de Recherches Aerospatiales M6 wing to demonstrate applications of the new Euler solvers. The paper presents a description of the Euler solvers along with results and comparisons that assess the capability.

Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes

NASA Technical Reports Server (NTRS)

Batina, John T.

1990-01-01

Improved algorithm for the solution of the time-dependent Euler equations are presented for unsteady aerodynamic analysis involving unstructured dynamic meshes. The improvements were developed recently to the spatial and temporal discretizations used by unstructured grid flow solvers. The spatial discretization involves a flux-split approach which is naturally dissipative and captures shock waves sharply with at most one grid point within the shock structure. The temporal discretization involves an implicit time-integration scheme using a Gauss-Seidel relaxation procedure which is computationally efficient for either steady or unsteady flow problems. For example, very large time steps may be used for rapid convergence to steady state, and the step size for unsteady cases may be selected for temporal accuracy rather than for numerical stability. Steady and unsteady flow results are presented for the NACA 0012 airfoil to demonstrate applications of the new Euler solvers. The unsteady results were obtained for the airfoil pitching harmonically about the quarter chord. The resulting instantaneous pressure distributions and lift and moment coefficients during a cycle of motion compare well with experimental data. A description of the Euler solvers is presented along with results and comparisons which assess the capability.

An implicit numerical scheme for the simulation of internal viscous flows on unstructured grids

NASA Technical Reports Server (NTRS)

Jorgenson, Philip C. E.; Pletcher, Richard H.

1994-01-01

The Navier-Stokes equations are solved numerically for two-dimensional steady viscous laminar flows. The grids are generated based on the method of Delaunay triangulation. A finite-volume approach is used to discretize the conservation law form of the compressible flow equations written in terms of primitive variables. A preconditioning matrix is added to the equations so that low Mach number flows can be solved economically. The equations are time marched using either an implicit Gauss-Seidel iterative procedure or a solver based on a conjugate gradient like method. A four color scheme is employed to vectorize the block Gauss-Seidel relaxation procedure. This increases the memory requirements minimally and decreases the computer time spent solving the resulting system of equations substantially. A factor of 7.6 speed up in the matrix solver is typical for the viscous equations. Numerical results are obtained for inviscid flow over a bump in a channel at subsonic and transonic conditions for validation with structured solvers. Viscous results are computed for developing flow in a channel, a symmetric sudden expansion, periodic tandem cylinders in a cross-flow, and a four-port valve. Comparisons are made with available results obtained by other investigators.

The Method of Space-time Conservation Element and Solution Element: Development of a New Implicit Solver

NASA Technical Reports Server (NTRS)

Chang, S. C.; Wang, X. Y.; Chow, C. Y.; Himansu, A.

1995-01-01

The method of space-time conservation element and solution element is a nontraditional numerical method designed from a physicist's perspective, i.e., its development is based more on physics than numerics. It uses only the simplest approximation techniques and yet is capable of generating nearly perfect solutions for a 2-D shock reflection problem used by Helen Yee and others. In addition to providing an overall view of the new method, we introduce a new concept in the design of implicit schemes, and use it to construct a highly accurate solver for a convection-diffusion equation. It is shown that, in the inviscid case, this new scheme becomes explicit and its amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, its principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Nonlinear study of the parallel velocity/tearing instability using an implicit, nonlinear resistive MHD solver

NASA Astrophysics Data System (ADS)

Chacon, L.; Finn, J. M.; Knoll, D. A.

2000-10-01

Recently, a new parallel velocity instability has been found.(J. M. Finn, Phys. Plasmas), 2, 12 (1995) This mode is a tearing mode driven unstable by curvature effects and sound wave coupling in the presence of parallel velocity shear. Under such conditions, linear theory predicts that tearing instabilities will grow even in situations in which the classical tearing mode is stable. This could then be a viable seed mechanism for the neoclassical tearing mode, and hence a non-linear study is of interest. Here, the linear and non-linear stages of this instability are explored using a fully implicit, fully nonlinear 2D reduced resistive MHD code,(L. Chacon et al), ``Implicit, Jacobian-free Newton-Krylov 2D reduced resistive MHD nonlinear solver,'' submitted to J. Comput. Phys. (2000) including viscosity and particle transport effects. The nonlinear implicit time integration is performed using the Newton-Raphson iterative algorithm. Krylov iterative techniques are employed for the required algebraic matrix inversions, implemented Jacobian-free (i.e., without ever forming and storing the Jacobian matrix), and preconditioned with a ``physics-based'' preconditioner. Nonlinear results indicate that, for large total plasma beta and large parallel velocity shear, the instability results in the generation of large poloidal shear flows and large magnetic islands even in regimes when the classical tearing mode is absolutely stable. For small viscosity, the time asymptotic state can be turbulent.

TDIGG - TWO-DIMENSIONAL, INTERACTIVE GRID GENERATION CODE

NASA Technical Reports Server (NTRS)

Vu, B. T.

1994-01-01

TDIGG is a fast and versatile program for generating two-dimensional computational grids for use with finite-difference flow-solvers. Both algebraic and elliptic grid generation systems are included. The method for grid generation by algebraic transformation is based on an interpolation algorithm and the elliptic grid generation is established by solving the partial differential equation (PDE). Non-uniform grid distributions are carried out using a hyperbolic tangent stretching function. For algebraic grid systems, interpolations in one direction (univariate) and two directions (bivariate) are considered. These interpolations are associated with linear or cubic Lagrangian/Hermite/Bezier polynomial functions. The algebraic grids can subsequently be smoothed using an elliptic solver. For elliptic grid systems, the PDE can be in the form of Laplace (zero forcing function) or Poisson. The forcing functions in the Poisson equation come from the boundary or the entire domain of the initial algebraic grids. A graphics interface procedure using the Silicon Graphics (GL) Library is included to allow users to visualize the grid variations at each iteration. This will allow users to interactively modify the grid to match their applications. TDIGG is written in FORTRAN 77 for Silicon Graphics IRIS series computers running IRIX. This package requires either MIT's X Window System, Version 11 Revision 4 or SGI (Motif) Window System. A sample executable is provided on the distribution medium. It requires 148K of RAM for execution. The standard distribution medium is a .25 inch streaming magnetic IRIX tape cartridge in UNIX tar format. This program was developed in 1992.

IRMHD: an implicit radiative and magnetohydrodynamical solver for self-gravitating systems

NASA Astrophysics Data System (ADS)

Hujeirat, A.

1998-07-01

The 2D implicit hydrodynamical solver developed by Hujeirat & Rannacher is now modified to include the effects of radiation, magnetic fields and self-gravity in different geometries. The underlying numerical concept is based on the operator splitting approach, and the resulting 2D matrices are inverted using different efficient preconditionings such as ADI (alternating direction implicit), the approximate factorization method and Line-Gauss-Seidel or similar iteration procedures. Second-order finite volume with third-order upwinding and second-order time discretization is used. To speed up convergence and enhance efficiency we have incorporated an adaptive time-step control and monotonic multilevel grid distributions as well as vectorizing the code. Test calculations had shown that it requires only 38 per cent more computational effort than its explicit counterpart, whereas its range of application to astrophysical problems is much larger. For example, strongly time-dependent, quasi-stationary and steady-state solutions for the set of Euler and Navier-Stokes equations can now be sought on a non-linearly distributed and strongly stretched mesh. As most of the numerical techniques used to build up this algorithm have been described by Hujeirat & Rannacher in an earlier paper, we focus in this paper on the inclusion of self-gravity, radiation and magnetic fields. Strategies for satisfying the condition ∇.B=0 in the implicit evolution of MHD flows are given. A new discretization strategy for the vector potential which allows alternating use of the direct method is prescribed. We investigate the efficiencies of several 2D solvers for a Poisson-like equation and compare their convergence rates. We provide a splitting approach for the radiative flux within the FLD (flux-limited diffusion) approximation to enhance consistency and accuracy between regions of different optical depths. The results of some test problems are presented to demonstrate the accuracy and robustness of the code.

Numerical solution of 3D Navier-Stokes equations with upwind implicit schemes

NASA Technical Reports Server (NTRS)

Marx, Yves P.

1990-01-01

An upwind MUSCL type implicit scheme for the three-dimensional Navier-Stokes equations is presented. Comparison between different approximate Riemann solvers (Roe and Osher) are performed and the influence of the reconstructions schemes on the accuracy of the solution as well as on the convergence of the method is studied. A new limiter is introduced in order to remove the problems usually associated with non-linear upwind schemes. The implementation of a diagonal upwind implicit operator for the three-dimensional Navier-Stokes equations is also discussed. Finally the turbulence modeling is assessed. Good prediction of separated flows are demonstrated if a non-equilibrium turbulence model is used.

Implicit filtered P{sub N} for high-energy density thermal radiation transport using discontinuous Galerkin finite elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Laboure, Vincent M., E-mail: vincent.laboure@tamu.edu; McClarren, Ryan G., E-mail: rgm@tamu.edu; Hauck, Cory D., E-mail: hauckc@ornl.gov

2016-09-15

In this work, we provide a fully-implicit implementation of the time-dependent, filtered spherical harmonics (FP{sub N}) equations for non-linear, thermal radiative transfer. We investigate local filtering strategies and analyze the effect of the filter on the conditioning of the system, showing in particular that the filter improves the convergence properties of the iterative solver. We also investigate numerically the rigorous error estimates derived in the linear setting, to determine whether they hold also for the non-linear case. Finally, we simulate a standard test problem on an unstructured mesh and make comparisons with implicit Monte Carlo (IMC) calculations.

A Comparison of PETSC Library and HPF Implementations of an Archetypal PDE Computation

NASA Technical Reports Server (NTRS)

Hayder, M. Ehtesham; Keyes, David E.; Mehrotra, Piyush

1997-01-01

Two paradigms for distributed-memory parallel computation that free the application programmer from the details of message passing are compared for an archetypal structured scientific computation a nonlinear, structured-grid partial differential equation boundary value problem using the same algorithm on the same hardware. Both paradigms, parallel libraries represented by Argonne's PETSC, and parallel languages represented by the Portland Group's HPF, are found to be easy to use for this problem class, and both are reasonably effective in exploiting concurrency after a short learning curve. The level of involvement required by the application programmer under either paradigm includes specification of the data partitioning (corresponding to a geometrically simple decomposition of the domain of the PDE). Programming in SPAM style for the PETSC library requires writing the routines that discretize the PDE and its Jacobian, managing subdomain-to-processor mappings (affine global- to-local index mappings), and interfacing to library solver routines. Programming for HPF requires a complete sequential implementation of the same algorithm, introducing concurrency through subdomain blocking (an effort similar to the index mapping), and modest experimentation with rewriting loops to elucidate to the compiler the latent concurrency. Correctness and scalability are cross-validated on up to 32 nodes of an IBM SP2.

Multiscale solvers and systematic upscaling in computational physics

NASA Astrophysics Data System (ADS)

Brandt, A.

2005-07-01

Multiscale algorithms can overcome the scale-born bottlenecks that plague most computations in physics. These algorithms employ separate processing at each scale of the physical space, combined with interscale iterative interactions, in ways which use finer scales very sparingly. Having been developed first and well known as multigrid solvers for partial differential equations, highly efficient multiscale techniques have more recently been developed for many other types of computational tasks, including: inverse PDE problems; highly indefinite (e.g., standing wave) equations; Dirac equations in disordered gauge fields; fast computation and updating of large determinants (as needed in QCD); fast integral transforms; integral equations; astrophysics; molecular dynamics of macromolecules and fluids; many-atom electronic structures; global and discrete-state optimization; practical graph problems; image segmentation and recognition; tomography (medical imaging); fast Monte-Carlo sampling in statistical physics; and general, systematic methods of upscaling (accurate numerical derivation of large-scale equations from microscopic laws).

Adaptive Implicit Non-Equilibrium Radiation Diffusion

DOE Office of Scientific and Technical Information (OSTI.GOV)

Philip, Bobby; Wang, Zhen; Berrill, Mark A

2013-01-01

We describe methods for accurate and efficient long term time integra- tion of non-equilibrium radiation diffusion systems: implicit time integration for effi- cient long term time integration of stiff multiphysics systems, local control theory based step size control to minimize the required global number of time steps while control- ling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

LLNL contributions to ANL Report ANL/NE-16/6 "Sharp User Manual"

DOE Office of Scientific and Technical Information (OSTI.GOV)

Solberg, J. M.

Diablo is a Multiphysics implicit finite element code with an emphasis on coupled structural/thermal analysis. In the SHARP framework, it is used as the structural solver, and may also be used as the mesh smoother.

Probabilistic numerical methods for PDE-constrained Bayesian inverse problems

NASA Astrophysics Data System (ADS)

Cockayne, Jon; Oates, Chris; Sullivan, Tim; Girolami, Mark

2017-06-01

This paper develops meshless methods for probabilistically describing discretisation error in the numerical solution of partial differential equations. This construction enables the solution of Bayesian inverse problems while accounting for the impact of the discretisation of the forward problem. In particular, this drives statistical inferences to be more conservative in the presence of significant solver error. Theoretical results are presented describing rates of convergence for the posteriors in both the forward and inverse problems. This method is tested on a challenging inverse problem with a nonlinear forward model.

Development of a High-Order Navier-Stokes Solver Using Flux Reconstruction to Simulate Three-Dimensional Vortex Structures in a Curved Artery Model

NASA Astrophysics Data System (ADS)

Cox, Christopher

Low-order numerical methods are widespread in academic solvers and ubiquitous in industrial solvers due to their robustness and usability. High-order methods are less robust and more complicated to implement; however, they exhibit low numerical dissipation and have the potential to improve the accuracy of flow simulations at a lower computational cost when compared to low-order methods. This motivates our development of a high-order compact method using Huynh's flux reconstruction scheme for solving unsteady incompressible flow on unstructured grids. We use Chorin's classic artificial compressibility formulation with dual time stepping to solve unsteady flow problems. In 2D, an implicit non-linear lower-upper symmetric Gauss-Seidel scheme with backward Euler discretization is used to efficiently march the solution in pseudo time, while a second-order backward Euler discretization is used to march in physical time. We verify and validate implementation of the high-order method coupled with our implicit time stepping scheme using both steady and unsteady incompressible flow problems. The current implicit time stepping scheme is proven effective in satisfying the divergence-free constraint on the velocity field in the artificial compressibility formulation. The high-order solver is extended to 3D and parallelized using MPI. Due to its simplicity, time marching for 3D problems is done explicitly. The feasibility of using the current implicit time stepping scheme for large scale three-dimensional problems with high-order polynomial basis still remains to be seen. We directly use the aforementioned numerical solver to simulate pulsatile flow of a Newtonian blood-analog fluid through a rigid 180-degree curved artery model. One of the most physiologically relevant forces within the cardiovascular system is the wall shear stress. This force is important because atherosclerotic regions are strongly correlated with curvature and branching in the human vasculature, where the shear stress is both oscillatory and multidirectional. Also, the combined effect of curvature and pulsatility in cardiovascular flows produces unsteady vortices. The aim of this research as it relates to cardiovascular fluid dynamics is to predict the spatial and temporal evolution of vortical structures generated by secondary flows, as well as to assess the correlation between multiple vortex pairs and wall shear stress. We use a physiologically (pulsatile) relevant flow rate and generate results using both fully developed and uniform entrance conditions, the latter being motivated by the fact that flow upstream of a curved artery may not have sufficient straight entrance length to become fully developed. Under the two pulsatile inflow conditions, we characterize the morphology and evolution of various vortex pairs and their subsequent effect on relevant haemodynamic wall shear stress metrics.

Adagio 4.20 User’s Guide

DOE Office of Scientific and Technical Information (OSTI.GOV)

Spencer, Benjamin Whiting; Crane, Nathan K.; Heinstein, Martin W.

2011-03-01

Adagio is a Lagrangian, three-dimensional, implicit code for the analysis of solids and structures. It uses a multi-level iterative solver, which enables it to solve problems with large deformations, nonlinear material behavior, and contact. It also has a versatile library of continuum and structural elements, and an extensive library of material models. Adagio is written for parallel computing environments, and its solvers allow for scalable solutions of very large problems. Adagio uses the SIERRA Framework, which allows for coupling with other SIERRA mechanics codes. This document describes the functionality and input structure for Adagio.

Parallel Cartesian grid refinement for 3D complex flow simulations

NASA Astrophysics Data System (ADS)

Angelidis, Dionysios; Sotiropoulos, Fotis

2013-11-01

A second order accurate method for discretizing the Navier-Stokes equations on 3D unstructured Cartesian grids is presented. Although the grid generator is based on the oct-tree hierarchical method, fully unstructured data-structure is adopted enabling robust calculations for incompressible flows, avoiding both the need of synchronization of the solution between different levels of refinement and usage of prolongation/restriction operators. The current solver implements a hybrid staggered/non-staggered grid layout, employing the implicit fractional step method to satisfy the continuity equation. The pressure-Poisson equation is discretized by using a novel second order fully implicit scheme for unstructured Cartesian grids and solved using an efficient Krylov subspace solver. The momentum equation is also discretized with second order accuracy and the high performance Newton-Krylov method is used for integrating them in time. Neumann and Dirichlet conditions are used to validate the Poisson solver against analytical functions and grid refinement results to a significant reduction of the solution error. The effectiveness of the fractional step method results in the stability of the overall algorithm and enables the performance of accurate multi-resolution real life simulations. This material is based upon work supported by the Department of Energy under Award Number DE-EE0005482.

Solving groundwater flow problems by conjugate-gradient methods and the strongly implicit procedure

USGS Publications Warehouse

Hill, Mary C.

1990-01-01

The performance of the preconditioned conjugate-gradient method with three preconditioners is compared with the strongly implicit procedure (SIP) using a scalar computer. The preconditioners considered are the incomplete Cholesky (ICCG) and the modified incomplete Cholesky (MICCG), which require the same computer storage as SIP as programmed for a problem with a symmetric matrix, and a polynomial preconditioner (POLCG), which requires less computer storage than SIP. Although POLCG is usually used on vector computers, it is included here because of its small storage requirements. In this paper, published comparisons of the solvers are evaluated, all four solvers are compared for the first time, and new test cases are presented to provide a more complete basis by which the solvers can be judged for typical groundwater flow problems. Based on nine test cases, the following conclusions are reached: (1) SIP is actually as efficient as ICCG for some of the published, linear, two-dimensional test cases that were reportedly solved much more efficiently by ICCG; (2) SIP is more efficient than other published comparisons would indicate when common convergence criteria are used; and (3) for problems that are three-dimensional, nonlinear, or both, and for which common convergence criteria are used, SIP is often more efficient than ICCG, and is sometimes more efficient than MICCG.

A consistent modelling methodology for secondary settling tanks in wastewater treatment.

PubMed

Bürger, Raimund; Diehl, Stefan; Nopens, Ingmar

2011-03-01

The aim of this contribution is partly to build consensus on a consistent modelling methodology (CMM) of complex real processes in wastewater treatment by combining classical concepts with results from applied mathematics, and partly to apply it to the clarification-thickening process in the secondary settling tank. In the CMM, the real process should be approximated by a mathematical model (process model; ordinary or partial differential equation (ODE or PDE)), which in turn is approximated by a simulation model (numerical method) implemented on a computer. These steps have often not been carried out in a correct way. The secondary settling tank was chosen as a case since this is one of the most complex processes in a wastewater treatment plant and simulation models developed decades ago have no guarantee of satisfying fundamental mathematical and physical properties. Nevertheless, such methods are still used in commercial tools to date. This particularly becomes of interest as the state-of-the-art practice is moving towards plant-wide modelling. Then all submodels interact and errors propagate through the model and severely hamper any calibration effort and, hence, the predictive purpose of the model. The CMM is described by applying it first to a simple conversion process in the biological reactor yielding an ODE solver, and then to the solid-liquid separation in the secondary settling tank, yielding a PDE solver. Time has come to incorporate established mathematical techniques into environmental engineering, and wastewater treatment modelling in particular, and to use proven reliable and consistent simulation models. Copyright © 2011 Elsevier Ltd. All rights reserved.

Computational aeroelasticity using a pressure-based solver

NASA Astrophysics Data System (ADS)

Kamakoti, Ramji

A computational methodology for performing fluid-structure interaction computations for three-dimensional elastic wing geometries is presented. The flow solver used is based on an unsteady Reynolds-Averaged Navier-Stokes (RANS) model. A well validated k-ε turbulence model with wall function treatment for near wall region was used to perform turbulent flow calculations. Relative merits of alternative flow solvers were investigated. The predictor-corrector-based Pressure Implicit Splitting of Operators (PISO) algorithm was found to be computationally economic for unsteady flow computations. Wing structure was modeled using Bernoulli-Euler beam theory. A fully implicit time-marching scheme (using the Newmark integration method) was used to integrate the equations of motion for structure. Bilinear interpolation and linear extrapolation techniques were used to transfer necessary information between fluid and structure solvers. Geometry deformation was accounted for by using a moving boundary module. The moving grid capability was based on a master/slave concept and transfinite interpolation techniques. Since computations were performed on a moving mesh system, the geometric conservation law must be preserved. This is achieved by appropriately evaluating the Jacobian values associated with each cell. Accurate computation of contravariant velocities for unsteady flows using the momentum interpolation method on collocated, curvilinear grids was also addressed. Flutter computations were performed for the AGARD 445.6 wing at subsonic, transonic and supersonic Mach numbers. Unsteady computations were performed at various dynamic pressures to predict the flutter boundary. Results showed favorable agreement of experiment and previous numerical results. The computational methodology exhibited capabilities to predict both qualitative and quantitative features of aeroelasticity.

A Nonlinear Multigrid Solver for an Atmospheric General Circulation Model Based on Semi-Implicit Semi-Lagrangian Advection of Potential Vorticity

NASA Technical Reports Server (NTRS)

McCormick, S.; Ruge, John W.

1998-01-01

This work represents a part of a project to develop an atmospheric general circulation model based on the semi-Lagrangian advection of potential vorticity (PC) with divergence as the companion prognostic variable.

CASTRO: A NEW COMPRESSIBLE ASTROPHYSICAL SOLVER. II. GRAY RADIATION HYDRODYNAMICS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, W.; Almgren, A.; Bell, J.

We describe the development of a flux-limited gray radiation solver for the compressible astrophysics code, CASTRO. CASTRO uses an Eulerian grid with block-structured adaptive mesh refinement based on a nested hierarchy of logically rectangular variable-sized grids with simultaneous refinement in both space and time. The gray radiation solver is based on a mixed-frame formulation of radiation hydrodynamics. In our approach, the system is split into two parts, one part that couples the radiation and fluid in a hyperbolic subsystem, and another parabolic part that evolves radiation diffusion and source-sink terms. The hyperbolic subsystem is solved explicitly with a high-order Godunovmore » scheme, whereas the parabolic part is solved implicitly with a first-order backward Euler method.« less

Preconditioned conjugate-gradient methods for low-speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations is integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the Lower-Upper Successive Symmetric Over-Relaxation iterative scheme is more efficient than a preconditioner based on Incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional Line Gauss-Seidel Relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Preconditioned Conjugate Gradient methods for low speed flow calculations

NASA Technical Reports Server (NTRS)

Ajmani, Kumud; Ng, Wing-Fai; Liou, Meng-Sing

1993-01-01

An investigation is conducted into the viability of using a generalized Conjugate Gradient-like method as an iterative solver to obtain steady-state solutions of very low-speed fluid flow problems. Low-speed flow at Mach 0.1 over a backward-facing step is chosen as a representative test problem. The unsteady form of the two dimensional, compressible Navier-Stokes equations are integrated in time using discrete time-steps. The Navier-Stokes equations are cast in an implicit, upwind finite-volume, flux split formulation. The new iterative solver is used to solve a linear system of equations at each step of the time-integration. Preconditioning techniques are used with the new solver to enhance the stability and the convergence rate of the solver and are found to be critical to the overall success of the solver. A study of various preconditioners reveals that a preconditioner based on the lower-upper (L-U)-successive symmetric over-relaxation iterative scheme is more efficient than a preconditioner based on incomplete L-U factorizations of the iteration matrix. The performance of the new preconditioned solver is compared with a conventional line Gauss-Seidel relaxation (LGSR) solver. Overall speed-up factors of 28 (in terms of global time-steps required to converge to a steady-state solution) and 20 (in terms of total CPU time on one processor of a CRAY-YMP) are found in favor of the new preconditioned solver, when compared with the LGSR solver.

Thermal mathematical modeling of a multicell common pressure vessel nickel-hydrogen battery

NASA Technical Reports Server (NTRS)

Kim, Junbom; Nguyen, T. V.; White, R. E.

1992-01-01

A two-dimensional and time-dependent thermal model of a multicell common pressure vessel (CPV) nickel-hydrogen battery was developed. A finite element solver called PDE/Protran was used to solve this model. The model was used to investigate the effects of various design parameters on the temperature profile within the cell. The results were used to help find a design that will yield an acceptable temperature gradient inside a multicell CPV nickel-hydrogen battery. Steady-state and unsteady-state cases with a constant heat generation rate and a time-dependent heat generation rate were solved.

BOOK REVIEW: Advanced Topics in Computational Partial Differential Equations: Numerical Methods and Diffpack Programming

NASA Astrophysics Data System (ADS)

Katsaounis, T. D.

2005-02-01

The scope of this book is to present well known simple and advanced numerical methods for solving partial differential equations (PDEs) and how to implement these methods using the programming environment of the software package Diffpack. A basic background in PDEs and numerical methods is required by the potential reader. Further, a basic knowledge of the finite element method and its implementation in one and two space dimensions is required. The authors claim that no prior knowledge of the package Diffpack is required, which is true, but the reader should be at least familiar with an object oriented programming language like C++ in order to better comprehend the programming environment of Diffpack. Certainly, a prior knowledge or usage of Diffpack would be a great advantage to the reader. The book consists of 15 chapters, each one written by one or more authors. Each chapter is basically divided into two parts: the first part is about mathematical models described by PDEs and numerical methods to solve these models and the second part describes how to implement the numerical methods using the programming environment of Diffpack. Each chapter closes with a list of references on its subject. The first nine chapters cover well known numerical methods for solving the basic types of PDEs. Further, programming techniques on the serial as well as on the parallel implementation of numerical methods are also included in these chapters. The last five chapters are dedicated to applications, modelled by PDEs, in a variety of fields. The first chapter is an introduction to parallel processing. It covers fundamentals of parallel processing in a simple and concrete way and no prior knowledge of the subject is required. Examples of parallel implementation of basic linear algebra operations are presented using the Message Passing Interface (MPI) programming environment. Here, some knowledge of MPI routines is required by the reader. Examples solving in parallel simple PDEs using Diffpack and MPI are also presented. Chapter 2 presents the overlapping domain decomposition method for solving PDEs. It is well known that these methods are suitable for parallel processing. The first part of the chapter covers the mathematical formulation of the method as well as algorithmic and implementational issues. The second part presents a serial and a parallel implementational framework within the programming environment of Diffpack. The chapter closes by showing how to solve two application examples with the overlapping domain decomposition method using Diffpack. Chapter 3 is a tutorial about how to incorporate the multigrid solver in Diffpack. The method is illustrated by examples such as a Poisson solver, a general elliptic problem with various types of boundary conditions and a nonlinear Poisson type problem. In chapter 4 the mixed finite element is introduced. Technical issues concerning the practical implementation of the method are also presented. The main difficulties of the efficient implementation of the method, especially in two and three space dimensions on unstructured grids, are presented and addressed in the framework of Diffpack. The implementational process is illustrated by two examples, namely the system formulation of the Poisson problem and the Stokes problem. Chapter 5 is closely related to chapter 4 and addresses the problem of how to solve efficiently the linear systems arising by the application of the mixed finite element method. The proposed method is block preconditioning. Efficient techniques for implementing the method within Diffpack are presented. Optimal block preconditioners are used to solve the system formulation of the Poisson problem, the Stokes problem and the bidomain model for the electrical activity in the heart. The subject of chapter 6 is systems of PDEs. Linear and nonlinear systems are discussed. Fully implicit and operator splitting methods are presented. Special attention is paid to how existing solvers for scalar equations in Diffpack can be used to derive fully implicit solvers for systems. The proposed techniques are illustrated in terms of two applications, namely a system of PDEs modelling pipeflow and a two-phase porous media flow. Stochastic PDEs is the topic of chapter 7. The first part of the chapter is a simple introduction to stochastic PDEs; basic analytical properties are presented for simple models like transport phenomena and viscous drag forces. The second part considers the numerical solution of stochastic PDEs. Two basic techniques are presented, namely Monte Carlo and perturbation methods. The last part explains how to implement and incorporate these solvers into Diffpack. Chapter 8 describes how to operate Diffpack from Python scripts. The main goal here is to provide all the programming and technical details in order to glue the programming environment of Diffpack with visualization packages through Python and in general take advantage of the Python interfaces. Chapter 9 attempts to show how to use numerical experiments to measure the performance of various PDE solvers. The authors gathered a rather impressive list, a total of 14 PDE solvers. Solvers for problems like Poisson, Navier--Stokes, elasticity, two-phase flows and methods such as finite difference, finite element, multigrid, and gradient type methods are presented. The authors provide a series of numerical results combining various solvers with various methods in order to gain insight into their computational performance and efficiency. In Chapter 10 the authors consider a computationally challenging problem, namely the computation of the electrical activity of the human heart. After a brief introduction on the biology of the problem the authors present the mathematical models involved and a numerical method for solving them within the framework of Diffpack. Chapter 11 and 12 are closely related; actually they could have been combined in a single chapter. Chapter 11 introduces several mathematical models used in finance, based on the Black--Scholes equation. Chapter 12 considers several numerical methods like Monte Carlo, lattice methods, finite difference and finite element methods. Implementation of these methods within Diffpack is presented in the last part of the chapter. Chapter 13 presents how the finite element method is used for the modelling and analysis of elastic structures. The authors describe the structural elements of Diffpack which include popular elements such as beams and plates and examples are presented on how to use them to simulate elastic structures. Chapter 14 describes an application problem, namely the extrusion of aluminum. This is a rather\\endcolumn complicated process which involves non-Newtonian flow, heat transfer and elasticity. The authors describe the systems of PDEs modelling the underlying process and use a finite element method to obtain a numerical solution. The implementation of the numerical method in Diffpack is presented along with some applications. The last chapter, chapter 15, focuses on mathematical and numerical models of systems of PDEs governing geological processes in sedimentary basins. The underlying mathematical model is solved using the finite element method within a fully implicit scheme. The authors discuss the implementational issues involved within Diffpack and they present results from several examples. In summary, the book focuses on the computational and implementational issues involved in solving partial differential equations. The potential reader should have a basic knowledge of PDEs and the finite difference and finite element methods. The examples presented are solved within the programming framework of Diffpack and the reader should have prior experience with the particular software in order to take full advantage of the book. Overall the book is well written, the subject of each chapter is well presented and can serve as a reference for graduate students, researchers and engineers who are interested in the numerical solution of partial differential equations modelling various applications.

Development of the Semi-implicit Time Integration in KIM-SH

NASA Astrophysics Data System (ADS)

NAM, H.

2015-12-01

The Korea Institute of Atmospheric Prediction Systems (KIAPS) was founded in 2011 by the Korea Meteorological Administration (KMA) to develop Korea's own global Numerical Weather Prediction (NWP) system as nine year (2011-2019) project. The KIM-SH is a KIAPS integrated model-spectral element based in the HOMME. In KIM-SH, the explicit schemes are employed. We introduce the three- and two-time-level semi-implicit scheme in KIM-SH as the time integration. Explicit schemes however have a tendancy to be unstable and require very small timesteps while semi-implicit schemes are very stable and can have much larger timesteps.We define the linear and reference values, then by definition of semi-implicit scheme, we apply the linear solver as GMRES. The numerical results from experiments will be introduced with the current development status of the time integration in KIM-SH. Several numerical examples are shown to confirm the efficiency and reliability of the proposed schemes.

High Performance Radiation Transport Simulations on TITAN

DOE Office of Scientific and Technical Information (OSTI.GOV)

Baker, Christopher G; Davidson, Gregory G; Evans, Thomas M

2012-01-01

In this paper we describe the Denovo code system. Denovo solves the six-dimensional, steady-state, linear Boltzmann transport equation, of central importance to nuclear technology applications such as reactor core analysis (neutronics), radiation shielding, nuclear forensics and radiation detection. The code features multiple spatial differencing schemes, state-of-the-art linear solvers, the Koch-Baker-Alcouffe (KBA) parallel-wavefront sweep algorithm for inverting the transport operator, a new multilevel energy decomposition method scaling to hundreds of thousands of processing cores, and a modern, novel code architecture that supports straightforward integration of new features. In this paper we discuss the performance of Denovo on the 10--20 petaflop ORNLmore » GPU-based system, Titan. We describe algorithms and techniques used to exploit the capabilities of Titan's heterogeneous compute node architecture and the challenges of obtaining good parallel performance for this sparse hyperbolic PDE solver containing inherently sequential computations. Numerical results demonstrating Denovo performance on early Titan hardware are presented.« less

An assessment of unstructured grid technology for timely CFD analysis

NASA Technical Reports Server (NTRS)

Kinard, Tom A.; Schabowski, Deanne M.

1995-01-01

An assessment of two unstructured methods is presented in this paper. A tetrahedral unstructured method USM3D, developed at NASA Langley Research Center is compared to a Cartesian unstructured method, SPLITFLOW, developed at Lockheed Fort Worth Company. USM3D is an upwind finite volume solver that accepts grids generated primarily from the Vgrid grid generator. SPLITFLOW combines an unstructured grid generator with an implicit flow solver in one package. Both methods are exercised on three test cases, a wing, and a wing body, and a fully expanded nozzle. The results for the first two runs are included here and compared to the structured grid method TEAM and to available test data. On each test case, the set up procedure are described, including any difficulties that were encountered. Detailed descriptions of the solvers are not included in this paper.

CFD analysis of a twin scroll radial turbine

NASA Astrophysics Data System (ADS)

Fürst, Jiří; Žák, Zdenĕk

2018-06-01

The contribution deals with the application of coupled implicit solver for compressible flows to CFD analysis of a twin scroll radial turbine. The solver is based on the finite volume method, convective terms are approximated using AUSM+up scheme, viscous terms use central approximation and the time evolution is achieved with lower-upper symmetric Gauss-Seidel (LU-SGS) method. The solver allows steady simulation with the so called frozen rotor approach as well as the fully unsteady solution. Both approaches are at first validated for the case of ERCOFTAC pump [1]. Then the CFD analysis of the flow through a twin scroll radial turbine and the predictions of the efficiency and turbine power is performed and the results are compared to experimental data obtained in the framework of Josef Božek - Competence Centre for Automotive Industry.

Application of a compressible flow solver and barotropic cavitation model for the evaluation of the suction head in a low specific speed centrifugal pump impeller channel

NASA Astrophysics Data System (ADS)

Limbach, P.; Müller, T.; Skoda, R.

2015-12-01

Commonly, for the simulation of cavitation in centrifugal pumps incompressible flow solvers with VOF kind cavitation models are applied. Since the source/sink terms of the void fraction transport equation are based on simplified bubble dynamics, empirical parameters may need to be adjusted to the particular pump operating point. In the present study a barotropic cavitation model, which is based solely on thermodynamic fluid properties and does not include any empirical parameters, is applied on a single flow channel of a pump impeller in combination with a time-explicit viscous compressible flow solver. The suction head curves (head drop) are compared to the results of an incompressible implicit standard industrial CFD tool and are predicted qualitatively correct by the barotropic model.

A SEMI-LAGRANGIAN TWO-LEVEL PRECONDITIONED NEWTON-KRYLOV SOLVER FOR CONSTRAINED DIFFEOMORPHIC IMAGE REGISTRATION.

PubMed

Mang, Andreas; Biros, George

2017-01-01

We propose an efficient numerical algorithm for the solution of diffeomorphic image registration problems. We use a variational formulation constrained by a partial differential equation (PDE), where the constraints are a scalar transport equation. We use a pseudospectral discretization in space and second-order accurate semi-Lagrangian time stepping scheme for the transport equations. We solve for a stationary velocity field using a preconditioned, globalized, matrix-free Newton-Krylov scheme. We propose and test a two-level Hessian preconditioner. We consider two strategies for inverting the preconditioner on the coarse grid: a nested preconditioned conjugate gradient method (exact solve) and a nested Chebyshev iterative method (inexact solve) with a fixed number of iterations. We test the performance of our solver in different synthetic and real-world two-dimensional application scenarios. We study grid convergence and computational efficiency of our new scheme. We compare the performance of our solver against our initial implementation that uses the same spatial discretization but a standard, explicit, second-order Runge-Kutta scheme for the numerical time integration of the transport equations and a single-level preconditioner. Our improved scheme delivers significant speedups over our original implementation. As a highlight, we observe a 20 × speedup for a two dimensional, real world multi-subject medical image registration problem.

Covert Shifts of Attention Function as an Implicit Aid to Insight

ERIC Educational Resources Information Center

Thomas, Laura E.; Lleras, Alejandro

2009-01-01

Previous research shows that directed actions can unconsciously influence higher-order cognitive processing, helping learners to retain knowledge and guiding problem solvers to useful insights (e.g. Cook, S. W., Mitchell, Z., & Goldin-Meadow, S. (2008). Gesturing makes learning last. "Cognition," 106, 1047-1058; Thomas, L. E., & Lleras, A. (2007).…

Parallel computational fluid dynamics '91; Conference Proceedings, Stuttgart, Germany, Jun. 10-12, 1991

NASA Technical Reports Server (NTRS)

Reinsch, K. G. (Editor); Schmidt, W. (Editor); Ecer, A. (Editor); Haeuser, Jochem (Editor); Periaux, J. (Editor)

1992-01-01

A conference was held on parallel computational fluid dynamics and produced related papers. Topics discussed in these papers include: parallel implicit and explicit solvers for compressible flow, parallel computational techniques for Euler and Navier-Stokes equations, grid generation techniques for parallel computers, and aerodynamic simulation om massively parallel systems.

Development and Verification of the Charring, Ablating Thermal Protection Implicit System Simulator

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Calvert, Nathan; Kirk, Benjamin S.

2011-01-01

The development and verification of the Charring Ablating Thermal Protection Implicit System Solver (CATPISS) is presented. This work concentrates on the derivation and verification of the stationary grid terms in the equations that govern three-dimensional heat and mass transfer for charring thermal protection systems including pyrolysis gas flow through the porous char layer. The governing equations are discretized according to the Galerkin finite element method (FEM) with first and second order fully implicit time integrators. The governing equations are fully coupled and are solved in parallel via Newton s method, while the linear system is solved via the Generalized Minimum Residual method (GMRES). Verification results from exact solutions and Method of Manufactured Solutions (MMS) are presented to show spatial and temporal orders of accuracy as well as nonlinear convergence rates.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less

A High-Order Low-Order Algorithm with Exponentially Convergent Monte Carlo for Thermal Radiative Transfer

DOE PAGES

Bolding, Simon R.; Cleveland, Mathew Allen; Morel, Jim E.

2016-10-21

In this paper, we have implemented a new high-order low-order (HOLO) algorithm for solving thermal radiative transfer problems. The low-order (LO) system is based on the spatial and angular moments of the transport equation and a linear-discontinuous finite-element spatial representation, producing equations similar to the standard S 2 equations. The LO solver is fully implicit in time and efficiently resolves the nonlinear temperature dependence at each time step. The high-order (HO) solver utilizes exponentially convergent Monte Carlo (ECMC) to give a globally accurate solution for the angular intensity to a fixed-source pure-absorber transport problem. This global solution is used tomore » compute consistency terms, which require the HO and LO solutions to converge toward the same solution. The use of ECMC allows for the efficient reduction of statistical noise in the Monte Carlo solution, reducing inaccuracies introduced through the LO consistency terms. Finally, we compare results with an implicit Monte Carlo code for one-dimensional gray test problems and demonstrate the efficiency of ECMC over standard Monte Carlo in this HOLO algorithm.« less

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

DOE PAGES

Carlberg, Kevin; Ray, Jaideep; van Bloemen Waanders, Bart

2015-02-14

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equationsmore » at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.« less

Incompressible viscous flow simulations of the NFAC wind tunnel

NASA Technical Reports Server (NTRS)

Champney, Joelle Milene

1986-01-01

The capabilities of an existing 3-D incompressible Navier-Stokes flow solver, INS3D, are extended and improved to solve turbulent flows through the incorporation of zero- and two-equation turbulence models. The two-equation model equations are solved in their high Reynolds number form and utilize wall functions in the treatment of solid wall boundary conditions. The implicit approximate factorization scheme is modified to improve the stability of the two-equation solver. Applications to the 3-D viscous flow inside the 80 by 120 feet open return wind tunnel of the National Full Scale Aerodynamics Complex (NFAC) are discussed and described.

Parallelization of Unsteady Adaptive Mesh Refinement for Unstructured Navier-Stokes Solvers

NASA Technical Reports Server (NTRS)

Schwing, Alan M.; Nompelis, Ioannis; Candler, Graham V.

2014-01-01

This paper explores the implementation of the MPI parallelization in a Navier-Stokes solver using adaptive mesh re nement. Viscous and inviscid test problems are considered for the purpose of benchmarking, as are implicit and explicit time advancement methods. The main test problem for comparison includes e ects from boundary layers and other viscous features and requires a large number of grid points for accurate computation. Ex- perimental validation against double cone experiments in hypersonic ow are shown. The adaptive mesh re nement shows promise for a staple test problem in the hypersonic com- munity. Extension to more advanced techniques for more complicated ows is described.

Spillover, nonlinearity, and flexible structures

NASA Technical Reports Server (NTRS)

Bass, Robert W.; Zes, Dean

1991-01-01

Many systems whose evolution in time is governed by Partial Differential Equations (PDEs) are linearized around a known equilibrium before Computer Aided Control Engineering (CACE) is considered. In this case, there are infinitely many independent vibrational modes, and it is intuitively evident on physical grounds that infinitely many actuators would be needed in order to control all modes. A more precise, general formulation of this grave difficulty (spillover problem) is due to A.V. Balakrishnan. A possible route to circumvention of this difficulty lies in leaving the PDE in its original nonlinear form, and adding the essentially finite dimensional control action prior to linearization. One possibly applicable technique is the Liapunov Schmidt rigorous reduction of singular infinite dimensional implicit function problems to finite dimensional implicit function problems. Omitting details of Banach space rigor, the formalities of this approach are given.

Toward an optimal solver for time-spectral fluid-dynamic and aeroelastic solutions on unstructured meshes

NASA Astrophysics Data System (ADS)

Mundis, Nathan L.; Mavriplis, Dimitri J.

2017-09-01

The time-spectral method applied to the Euler and coupled aeroelastic equations theoretically offers significant computational savings for purely periodic problems when compared to standard time-implicit methods. However, attaining superior efficiency with time-spectral methods over traditional time-implicit methods hinges on the ability rapidly to solve the large non-linear system resulting from time-spectral discretizations which become larger and stiffer as more time instances are employed or the period of the flow becomes especially short (i.e. the maximum resolvable wave-number increases). In order to increase the efficiency of these solvers, and to improve robustness, particularly for large numbers of time instances, the Generalized Minimal Residual Method (GMRES) is used to solve the implicit linear system over all coupled time instances. The use of GMRES as the linear solver makes time-spectral methods more robust, allows them to be applied to a far greater subset of time-accurate problems, including those with a broad range of harmonic content, and vastly improves the efficiency of time-spectral methods. In previous work, a wave-number independent preconditioner that mitigates the increased stiffness of the time-spectral method when applied to problems with large resolvable wave numbers has been developed. This preconditioner, however, directly inverts a large matrix whose size increases in proportion to the number of time instances. As a result, the computational time of this method scales as the cube of the number of time instances. In the present work, this preconditioner has been reworked to take advantage of an approximate-factorization approach that effectively decouples the spatial and temporal systems. Once decoupled, the time-spectral matrix can be inverted in frequency space, where it has entries only on the main diagonal and therefore can be inverted quite efficiently. This new GMRES/preconditioner combination is shown to be over an order of magnitude more efficient than the previous wave-number independent preconditioner for problems with large numbers of time instances and/or large reduced frequencies.

Compatible Spatial Discretizations for Partial Differential Equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arnold, Douglas, N, ed.

From May 11--15, 2004, the Institute for Mathematics and its Applications held a hot topics workshop on Compatible Spatial Discretizations for Partial Differential Equations. The numerical solution of partial differential equations (PDE) is a fundamental task in science and engineering. The goal of the workshop was to bring together a spectrum of scientists at the forefront of the research in the numerical solution of PDEs to discuss compatible spatial discretizations. We define compatible spatial discretizations as those that inherit or mimic fundamental properties of the PDE such as topology, conservation, symmetries, and positivity structures and maximum principles. A wide varietymore » of discretization methods applied across a wide range of scientific and engineering applications have been designed to or found to inherit or mimic intrinsic spatial structure and reproduce fundamental properties of the solution of the continuous PDE model at the finite dimensional level. A profusion of such methods and concepts relevant to understanding them have been developed and explored: mixed finite element methods, mimetic finite differences, support operator methods, control volume methods, discrete differential forms, Whitney forms, conservative differencing, discrete Hodge operators, discrete Helmholtz decomposition, finite integration techniques, staggered grid and dual grid methods, etc. This workshop seeks to foster communication among the diverse groups of researchers designing, applying, and studying such methods as well as researchers involved in practical solution of large scale problems that may benefit from advancements in such discretizations; to help elucidate the relations between the different methods and concepts; and to generally advance our understanding in the area of compatible spatial discretization methods for PDE. Particular points of emphasis included: + Identification of intrinsic properties of PDE models that are critical for the fidelity of numerical simulations. + Identification and design of compatible spatial discretizations of PDEs, their classification, analysis, and relations. + Relationships between different compatible spatial discretization methods and concepts which have been developed; + Impact of compatible spatial discretizations upon physical fidelity, verification and validation of simulations, especially in large-scale, multiphysics settings. + How solvers address the demands placed upon them by compatible spatial discretizations. This report provides information about the program and abstracts of all the presentations.« less

Development of a steady potential solver for use with linearized, unsteady aerodynamic analyses

NASA Technical Reports Server (NTRS)

Hoyniak, Daniel; Verdon, Joseph M.

1991-01-01

A full potential steady flow solver (SFLOW) developed explicitly for use with an inviscid unsteady aerodynamic analysis (LINFLO) is described. The steady solver uses the nonconservative form of the nonlinear potential flow equations together with an implicit, least squares, finite difference approximation to solve for the steady flow field. The difference equations were developed on a composite mesh which consists of a C grid embedded in a rectilinear (H grid) cascade mesh. The composite mesh is capable of resolving blade to blade and far field phenomena on the H grid, while accurately resolving local phenomena on the C grid. The resulting system of algebraic equations is arranged in matrix form using a sparse matrix package and solved by Newton's method. Steady and unsteady results are presented for two cascade configurations: a high speed compressor and a turbine with high exit Mach number.

An implicit scheme with memory reduction technique for steady state solutions of DVBE in all flow regimes

NASA Astrophysics Data System (ADS)

Yang, L. M.; Shu, C.; Yang, W. M.; Wu, J.

2018-04-01

High consumption of memory and computational effort is the major barrier to prevent the widespread use of the discrete velocity method (DVM) in the simulation of flows in all flow regimes. To overcome this drawback, an implicit DVM with a memory reduction technique for solving a steady discrete velocity Boltzmann equation (DVBE) is presented in this work. In the method, the distribution functions in the whole discrete velocity space do not need to be stored, and they are calculated from the macroscopic flow variables. As a result, its memory requirement is in the same order as the conventional Euler/Navier-Stokes solver. In the meantime, it is more efficient than the explicit DVM for the simulation of various flows. To make the method efficient for solving flow problems in all flow regimes, a prediction step is introduced to estimate the local equilibrium state of the DVBE. In the prediction step, the distribution function at the cell interface is calculated by the local solution of DVBE. For the flow simulation, when the cell size is less than the mean free path, the prediction step has almost no effect on the solution. However, when the cell size is much larger than the mean free path, the prediction step dominates the solution so as to provide reasonable results in such a flow regime. In addition, to further improve the computational efficiency of the developed scheme in the continuum flow regime, the implicit technique is also introduced into the prediction step. Numerical results showed that the proposed implicit scheme can provide reasonable results in all flow regimes and increase significantly the computational efficiency in the continuum flow regime as compared with the existing DVM solvers.

Adaptive [theta]-methods for pricing American options

NASA Astrophysics Data System (ADS)

Khaliq, Abdul Q. M.; Voss, David A.; Kazmi, Kamran

2008-12-01

We develop adaptive [theta]-methods for solving the Black-Scholes PDE for American options. By adding a small, continuous term, the Black-Scholes PDE becomes an advection-diffusion-reaction equation on a fixed spatial domain. Standard implementation of [theta]-methods would require a Newton-type iterative procedure at each time step thereby increasing the computational complexity of the methods. Our linearly implicit approach avoids such complications. We establish a general framework under which [theta]-methods satisfy a discrete version of the positivity constraint characteristic of American options, and numerically demonstrate the sensitivity of the constraint. The positivity results are established for the single-asset and independent two-asset models. In addition, we have incorporated and analyzed an adaptive time-step control strategy to increase the computational efficiency. Numerical experiments are presented for one- and two-asset American options, using adaptive exponential splitting for two-asset problems. The approach is compared with an iterative solution of the two-asset problem in terms of computational efficiency.

Computational strategies for three-dimensional flow simulations on distributed computer systems

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Weed, Richard A.

1995-01-01

This research effort is directed towards an examination of issues involved in porting large computational fluid dynamics codes in use within the industry to a distributed computing environment. This effort addresses strategies for implementing the distributed computing in a device independent fashion and load balancing. A flow solver called TEAM presently in use at Lockheed Aeronautical Systems Company was acquired to start this effort. The following tasks were completed: (1) The TEAM code was ported to a number of distributed computing platforms including a cluster of HP workstations located in the School of Aerospace Engineering at Georgia Tech; a cluster of DEC Alpha Workstations in the Graphics visualization lab located at Georgia Tech; a cluster of SGI workstations located at NASA Ames Research Center; and an IBM SP-2 system located at NASA ARC. (2) A number of communication strategies were implemented. Specifically, the manager-worker strategy and the worker-worker strategy were tested. (3) A variety of load balancing strategies were investigated. Specifically, the static load balancing, task queue balancing and the Crutchfield algorithm were coded and evaluated. (4) The classical explicit Runge-Kutta scheme in the TEAM solver was replaced with an LU implicit scheme. And (5) the implicit TEAM-PVM solver was extensively validated through studies of unsteady transonic flow over an F-5 wing, undergoing combined bending and torsional motion. These investigations are documented in extensive detail in the dissertation, 'Computational Strategies for Three-Dimensional Flow Simulations on Distributed Computing Systems', enclosed as an appendix.

Computational strategies for three-dimensional flow simulations on distributed computer systems

NASA Astrophysics Data System (ADS)

Sankar, Lakshmi N.; Weed, Richard A.

1995-08-01

This research effort is directed towards an examination of issues involved in porting large computational fluid dynamics codes in use within the industry to a distributed computing environment. This effort addresses strategies for implementing the distributed computing in a device independent fashion and load balancing. A flow solver called TEAM presently in use at Lockheed Aeronautical Systems Company was acquired to start this effort. The following tasks were completed: (1) The TEAM code was ported to a number of distributed computing platforms including a cluster of HP workstations located in the School of Aerospace Engineering at Georgia Tech; a cluster of DEC Alpha Workstations in the Graphics visualization lab located at Georgia Tech; a cluster of SGI workstations located at NASA Ames Research Center; and an IBM SP-2 system located at NASA ARC. (2) A number of communication strategies were implemented. Specifically, the manager-worker strategy and the worker-worker strategy were tested. (3) A variety of load balancing strategies were investigated. Specifically, the static load balancing, task queue balancing and the Crutchfield algorithm were coded and evaluated. (4) The classical explicit Runge-Kutta scheme in the TEAM solver was replaced with an LU implicit scheme. And (5) the implicit TEAM-PVM solver was extensively validated through studies of unsteady transonic flow over an F-5 wing, undergoing combined bending and torsional motion. These investigations are documented in extensive detail in the dissertation, 'Computational Strategies for Three-Dimensional Flow Simulations on Distributed Computing Systems', enclosed as an appendix.

Modelling atmospheric flows with adaptive moving meshes

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Smolarkiewicz, Piotr K.; Dörnbrack, Andreas

2012-04-01

An anelastic atmospheric flow solver has been developed that combines semi-implicit non-oscillatory forward-in-time numerics with a solution-adaptive mesh capability. A key feature of the solver is the unification of a mesh adaptation apparatus, based on moving mesh partial differential equations (PDEs), with the rigorous formulation of the governing anelastic PDEs in generalised time-dependent curvilinear coordinates. The solver development includes an enhancement of the flux-form multidimensional positive definite advection transport algorithm (MPDATA) - employed in the integration of the underlying anelastic PDEs - that ensures full compatibility with mass continuity under moving meshes. In addition, to satisfy the geometric conservation law (GCL) tensor identity under general moving meshes, a diagnostic approach is proposed based on the treatment of the GCL as an elliptic problem. The benefits of the solution-adaptive moving mesh technique for the simulation of multiscale atmospheric flows are demonstrated. The developed solver is verified for two idealised flow problems with distinct levels of complexity: passive scalar advection in a prescribed deformational flow, and the life cycle of a large-scale atmospheric baroclinic wave instability showing fine-scale phenomena of fronts and internal gravity waves.

A Numerical Approach to Solving the Hall MHD Equations Including Diamagnetic Drift (Preprint)

DTIC Science & Technology

2008-02-19

SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON Dr. Jean-Luc Cambier a. REPORT...1997. [3] L. Chacon and D.A. Knoll. A 2d high-beta hall mhd implicit nonlinear solver. Journal of Computational Physics, 188:573–592, 2003. [4] Tony F

Using hybrid implicit Monte Carlo diffusion to simulate gray radiation hydrodynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cleveland, Mathew A., E-mail: cleveland7@llnl.gov; Gentile, Nick

This work describes how to couple a hybrid Implicit Monte Carlo Diffusion (HIMCD) method with a Lagrangian hydrodynamics code to evaluate the coupled radiation hydrodynamics equations. This HIMCD method dynamically applies Implicit Monte Carlo Diffusion (IMD) [1] to regions of a problem that are opaque and diffusive while applying standard Implicit Monte Carlo (IMC) [2] to regions where the diffusion approximation is invalid. We show that this method significantly improves the computational efficiency as compared to a standard IMC/Hydrodynamics solver, when optically thick diffusive material is present, while maintaining accuracy. Two test cases are used to demonstrate the accuracy andmore » performance of HIMCD as compared to IMC and IMD. The first is the Lowrie semi-analytic diffusive shock [3]. The second is a simple test case where the source radiation streams through optically thin material and heats a thick diffusive region of material causing it to rapidly expand. We found that HIMCD proves to be accurate, robust, and computationally efficient for these test problems.« less

Implicit Multibody Penalty-BasedDistributed Contact.

PubMed

Xu, Hongyi; Zhao, Yili; Barbic, Jernej

2014-09-01

The penalty method is a simple and popular approach to resolving contact in computer graphics and robotics. Penalty-based contact, however, suffers from stability problems due to the highly variable and unpredictable net stiffness, and this is particularly pronounced in simulations with time-varying distributed geometrically complex contact. We employ semi-implicit integration, exact analytical contact gradients, symbolic Gaussian elimination and a SVD solver to simulate stable penalty-based frictional contact with large, time-varying contact areas, involving many rigid objects and articulated rigid objects in complex conforming contact and self-contact. We also derive implicit proportional-derivative control forces for real-time control of articulated structures with loops. We present challenging contact scenarios such as screwing a hexbolt into a hole, bowls stacked in perfectly conforming configurations, and manipulating many objects using actively controlled articulated mechanisms in real time.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods for unstructured mesh computations are developed and tested. The approximate system which arises from the Newton-linearization of the nonlinear evolution operator is solved by using the preconditioned generalized minimum residual technique. These different preconditioners are investigated: the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over-relaxation (SSOR). The preconditioners have been optimized to have good vectorization properties. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also investigated. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Aerodynamic optimization studies on advanced architecture computers

NASA Technical Reports Server (NTRS)

Chawla, Kalpana

1995-01-01

The approach to carrying out multi-discipline aerospace design studies in the future, especially in massively parallel computing environments, comprises of choosing (1) suitable solvers to compute solutions to equations characterizing a discipline, and (2) efficient optimization methods. In addition, for aerodynamic optimization problems, (3) smart methodologies must be selected to modify the surface shape. In this research effort, a 'direct' optimization method is implemented on the Cray C-90 to improve aerodynamic design. It is coupled with an existing implicit Navier-Stokes solver, OVERFLOW, to compute flow solutions. The optimization method is chosen such that it can accomodate multi-discipline optimization in future computations. In the work , however, only single discipline aerodynamic optimization will be included.

Computing approximate solutions of the protein structure determination problem using global constraints on discrete crystal lattices.

PubMed

Dal Palù, Alessandro; Dovier, Agostino; Pontelli, Enrico

2010-01-01

Crystal lattices are discrete models of the three-dimensional space that have been effectively employed to facilitate the task of determining proteins' natural conformation. This paper investigates alternative global constraints that can be introduced in a constraint solver over discrete crystal lattices. The objective is to enhance the efficiency of lattice solvers in dealing with the construction of approximate solutions of the protein structure determination problem. Some of them (e.g., self-avoiding-walk) have been explicitly or implicitly already used in previous approaches, while others (e.g., the density constraint) are new. The intrinsic complexities of all of them are studied and preliminary experimental results are discussed.

Physically-enhanced data visualisation: towards real time solution of Partial Differential Equations in 3D domains

NASA Astrophysics Data System (ADS)

Zlotnik, Sergio

2017-04-01

Information provided by visualisation environments can be largely increased if the data shown is combined with some relevant physical processes and the used is allowed to interact with those processes. This is particularly interesting in VR environments where the user has a deep interplay with the data. For example, a geological seismic line in a 3D "cave" shows information of the geological structure of the subsoil. The available information could be enhanced with the thermal state of the region under study, with water-flow patterns in porous rocks or with rock displacements under some stress conditions. The information added by the physical processes is usually the output of some numerical technique applied to solve a Partial Differential Equation (PDE) that describes the underlying physics. Many techniques are available to obtain numerical solutions of PDE (e.g. Finite Elements, Finite Volumes, Finite Differences, etc). Although, all these traditional techniques require very large computational resources (particularly in 3D), making them useless in a real time visualization environment -such as VR- because the time required to compute a solution is measured in minutes or even in hours. We present here a novel alternative for the resolution of PDE-based problems that is able to provide a 3D solutions for a very large family of problems in real time. That is, the solution is evaluated in a one thousands of a second, making the solver ideal to be embedded into VR environments. Based on Model Order Reduction ideas, the proposed technique divides the computational work in to a computationally intensive "offline" phase, that is run only once in a life time, and an "online" phase that allow the real time evaluation of any solution within a family of problems. Preliminary examples of real time solutions of complex PDE-based problems will be presented, including thermal problems, flow problems, wave problems and some simple coupled problems.

Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes

DOE PAGES

Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin; ...

2016-08-18

In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used tomore » project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.« less

Architecting the Finite Element Method Pipeline for the GPU.

PubMed

Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T

2014-02-01

The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.

Application of PDSLin to the magnetic reconnection problem

NASA Astrophysics Data System (ADS)

Yuan, Xuefei; Li, Xiaoye S.; Yamazaki, Ichitaro; Jardin, Stephen C.; Koniges, Alice E.; Keyes, David E.

2013-01-01

Magnetic reconnection is a fundamental process in a magnetized plasma at both low and high magnetic Lundquist numbers (the ratio of the resistive diffusion time to the Alfvén wave transit time), which occurs in a wide variety of laboratory and space plasmas, e.g. magnetic fusion experiments, the solar corona and the Earth's magnetotail. An implicit time advance for the two-fluid magnetic reconnection problem is known to be difficult because of the large condition number of the associated matrix. This is especially troublesome when the collisionless ion skin depth is large so that the Whistler waves, which cause the fast reconnection, dominate the physics (Yuan et al 2012 J. Comput. Phys. 231 5822-53). For small system sizes, a direct solver such as SuperLU can be employed to obtain an accurate solution as long as the condition number is bounded by the reciprocal of the floating-point machine precision. However, SuperLU scales effectively only to hundreds of processors or less. For larger system sizes, it has been shown that physics-based (Chacón and Knoll 2003 J. Comput. Phys. 188 573-92) or other preconditioners can be applied to provide adequate solver performance. In recent years, we have been developing a new algebraic hybrid linear solver, PDSLin (Parallel Domain decomposition Schur complement-based Linear solver) (Yamazaki and Li 2010 Proc. VECPAR pp 421-34 and Yamazaki et al 2011 Technical Report). In this work, we compare numerical results from a direct solver and the proposed hybrid solver for the magnetic reconnection problem and demonstrate that the new hybrid solver is scalable to thousands of processors while maintaining the same robustness as a direct solver.

Pseudo-time methods for constrained optimization problems governed by PDE

NASA Technical Reports Server (NTRS)

Taasan, Shlomo

1995-01-01

In this paper we present a novel method for solving optimization problems governed by partial differential equations. Existing methods are gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurfaces while improving the residuals of the design equations per each iteration. In contrast, the method presented here march on the design hypersurface and at each iteration improve the residuals of the state and costate equations. The new method is usually much less expensive per iteration step since, in most problems of practical interest, the design equation involves much less unknowns that that of either the state or costate equations. Convergence is shown using energy estimates for the evolution equations governing the iterative process. Numerical tests show that the new method allows the solution of the optimization problem in a cost of solving the analysis problems just a few times, independent of the number of design parameters. The method can be applied using single grid iterations as well as with multigrid solvers.

WARP3D-Release 10.8: Dynamic Nonlinear Analysis of Solids using a Preconditioned Conjugate Gradient Software Architecture

NASA Technical Reports Server (NTRS)

Koppenhoefer, Kyle C.; Gullerud, Arne S.; Ruggieri, Claudio; Dodds, Robert H., Jr.; Healy, Brian E.

1998-01-01

This report describes theoretical background material and commands necessary to use the WARP3D finite element code. WARP3D is under continuing development as a research code for the solution of very large-scale, 3-D solid models subjected to static and dynamic loads. Specific features in the code oriented toward the investigation of ductile fracture in metals include a robust finite strain formulation, a general J-integral computation facility (with inertia, face loading), an element extinction facility to model crack growth, nonlinear material models including viscoplastic effects, and the Gurson-Tver-gaard dilatant plasticity model for void growth. The nonlinear, dynamic equilibrium equations are solved using an incremental-iterative, implicit formulation with full Newton iterations to eliminate residual nodal forces. The history integration of the nonlinear equations of motion is accomplished with Newmarks Beta method. A central feature of WARP3D involves the use of a linear-preconditioned conjugate gradient (LPCG) solver implemented in an element-by-element format to replace a conventional direct linear equation solver. This software architecture dramatically reduces both the memory requirements and CPU time for very large, nonlinear solid models since formation of the assembled (dynamic) stiffness matrix is avoided. Analyses thus exhibit the numerical stability for large time (load) steps provided by the implicit formulation coupled with the low memory requirements characteristic of an explicit code. In addition to the much lower memory requirements of the LPCG solver, the CPU time required for solution of the linear equations during each Newton iteration is generally one-half or less of the CPU time required for a traditional direct solver. All other computational aspects of the code (element stiffnesses, element strains, stress updating, element internal forces) are implemented in the element-by- element, blocked architecture. This greatly improves vectorization of the code on uni-processor hardware and enables straightforward parallel-vector processing of element blocks on multi-processor hardware.

Impact of implicit effects on uncertainties and sensitivities of the Doppler coefficient of a LWR pin cell

NASA Astrophysics Data System (ADS)

Hursin, Mathieu; Leray, Olivier; Perret, Gregory; Pautz, Andreas; Bostelmann, Friederike; Aures, Alexander; Zwermann, Winfried

2017-09-01

In the present work, PSI and GRS sensitivity analysis (SA) and uncertainty quantification (UQ) methods, SHARK-X and XSUSA respectively, are compared for reactivity coefficient calculation; for reference the results of the TSUNAMI and SAMPLER modules of the SCALE code package are also provided. The main objective of paper is to assess the impact of the implicit effect, e.g., considering the effect of cross section perturbation on the self-shielding calculation, on the Doppler coefficient SA and UQ. Analyses are done for a Light Water Reactor (LWR) pin cell based on Phase I of the UAM LWR benchmark. The negligence of implicit effects in XSUSA and TSUNAMI leads to deviations of a few percent between the sensitivity profiles compared to SAMPLER and TSUNAMI (incl. implicit effects) except for 238U elastic scattering. The implicit effect is much larger for the SHARK-X calculations because of its coarser energy group structure between 10 eV and 10 keV compared to the applied SCALE libraries. It is concluded that the influence of the implicit effect strongly depends on the energy mesh of the nuclear data library of the neutron transport solver involved in the UQ calculations and may be magnified by the response considered.

An analysis of supersonic flows with low-Reynolds number compressible two-equation turbulence models using LU finite volume implicit numerical techniques

NASA Technical Reports Server (NTRS)

Lee, J.

1994-01-01

A generalized flow solver using an implicit Lower-upper (LU) diagonal decomposition based numerical technique has been coupled with three low-Reynolds number kappa-epsilon models for analysis of problems with engineering applications. The feasibility of using the LU technique to obtain efficient solutions to supersonic problems using the kappa-epsilon model has been demonstrated. The flow solver is then used to explore limitations and convergence characteristics of several popular two equation turbulence models. Several changes to the LU solver have been made to improve the efficiency of turbulent flow predictions. In general, the low-Reynolds number kappa-epsilon models are easier to implement than the models with wall-functions, but require much finer near-wall grid to accurately resolve the physics. The three kappa-epsilon models use different approaches to characterize the near wall regions of the flow. Therefore, the limitations imposed by the near wall characteristics have been carefully resolved. The convergence characteristics of a particular model using a given numerical technique are also an important, but most often overlooked, aspect of turbulence model predictions. It is found that some convergence characteristics could be sacrificed for more accurate near-wall prediction. However, even this gain in accuracy is not sufficient to model the effects of an external pressure gradient imposed by a shock-wave/ boundary-layer interaction. Additional work on turbulence models, especially for compressibility, is required since the solutions obtained with base line turbulence are in only reasonable agreement with the experimental data for the viscous interaction problems.

Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.

2017-11-01

This paper presents a discrete adjoint version of the recently developed non-intrusive least squares shadowing (NILSS) algorithm, which circumvents the instability that conventional adjoint methods encounter for chaotic systems. The NILSS approach involves solving a smaller minimization problem than other shadowing approaches and can be implemented with only minor modifications to preexisting tangent and adjoint solvers. Adjoint NILSS is demonstrated on a small chaotic ODE, a one-dimensional scalar PDE, and a direct numerical simulation (DNS) of the minimal flow unit, a turbulent channel flow on a small spatial domain. This is the first application of an adjoint shadowing-based algorithm to a three-dimensional turbulent flow.

A Fractional PDE Approach to Turbulent Mixing; Part II: Numerical Simulation

NASA Astrophysics Data System (ADS)

Samiee, Mehdi; Zayernouri, Mohsen

2016-11-01

We propose a generalizing fractional order transport model of advection-diffusion kind with fractional time- and space-derivatives, governing the evolution of passive scalar turbulence. This approach allows one to incorporate the nonlocal and memory effects in the underlying anomalous diffusion i.e., sub-to-standard diffusion to model the trapping of particles inside the eddied, and super-diffusion associated with the sudden jumps of particles from one coherent region to another. For this nonlocal model, we develop a high order numerical (spectral) method in addition to a fast solver, examined in the context of some canonical problems. PhD student, Department of Mechanical Engineering, & Department Computational Mathematics, Science, and Engineering.

Extension of a streamwise upwind algorithm to a moving grid system

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru; Goorjian, Peter M.; Guruswamy, Guru P.

1990-01-01

A new streamwise upwind algorithm was derived to compute unsteady flow fields with the use of a moving-grid system. The temporally nonconservative LU-ADI (lower-upper-factored, alternating-direction-implicit) method was applied for time marching computations. A comparison of the temporally nonconservative method with a time-conservative implicit upwind method indicates that the solutions are insensitive to the conservative properties of the implicit solvers when practical time steps are used. Using this new method, computations were made for an oscillating wing at a transonic Mach number. The computed results confirm that the present upwind scheme captures the shock motion better than the central-difference scheme based on the beam-warming algorithm. The new upwind option of the code allows larger time-steps and thus is more efficient, even though it requires slightly more computational time per time step than the central-difference option.

Multirate Particle-in-Cell Time Integration Techniques of Vlasov-Maxwell Equations for Collisionless Kinetic Plasma Simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Guangye; Chacon, Luis; Knoll, Dana Alan

2015-07-31

A multi-rate PIC formulation was developed that employs large timesteps for slow field evolution, and small (adaptive) timesteps for particle orbit integrations. Implementation is based on a JFNK solver with nonlinear elimination and moment preconditioning. The approach is free of numerical instabilities (ω peΔt >>1, and Δx >> λ D), and requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant gains (vs. conventional explicit PIC) may be possible for large scale simulations. The paper is organized as follows: Vlasov-Maxwell Particle-in-cell (PIC) methods for plasmas; Explicit, semi-implicit, and implicit time integrations; Implicit PIC formulation (Jacobian-Free Newton-Krylovmore » (JFNK) with nonlinear elimination allows different treatments of disparate scales, discrete conservation properties (energy, charge, canonical momentum, etc.)); Some numerical examples; and Summary.« less

Sierra/Solid Mechanics 4.48 User's Guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Merewether, Mark Thomas; Crane, Nathan K; de Frias, Gabriel Jose

Sierra/SolidMechanics (Sierra/SM) is a Lagrangian, three-dimensional code for finite element analysis of solids and structures. It provides capabilities for explicit dynamic, implicit quasistatic and dynamic analyses. The explicit dynamics capabilities allow for the efficient and robust solution of models with extensive contact subjected to large, suddenly applied loads. For implicit problems, Sierra/SM uses a multi-level iterative solver, which enables it to effectively solve problems with large deformations, nonlinear material behavior, and contact. Sierra/SM has a versatile library of continuum and structural elements, and a large library of material models. The code is written for parallel computing environments enabling scalable solutionsmore » of extremely large problems for both implicit and explicit analyses. It is built on the SIERRA Framework, which facilitates coupling with other SIERRA mechanics codes. This document describes the functionality and input syntax for Sierra/SM.« less

Fluid preconditioning for Newton–Krylov-based, fully implicit, electrostatic particle-in-cell simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, G., E-mail: gchen@lanl.gov; Chacón, L.; Leibs, C.A.

2014-02-01

A recent proof-of-principle study proposes an energy- and charge-conserving, nonlinearly implicit electrostatic particle-in-cell (PIC) algorithm in one dimension [9]. The algorithm in the reference employs an unpreconditioned Jacobian-free Newton–Krylov method, which ensures nonlinear convergence at every timestep (resolving the dynamical timescale of interest). Kinetic enslavement, which is one key component of the algorithm, not only enables fully implicit PIC as a practical approach, but also allows preconditioning the kinetic solver with a fluid approximation. This study proposes such a preconditioner, in which the linearized moment equations are closed with moments computed from particles. Effective acceleration of the linear GMRES solvemore » is demonstrated, on both uniform and non-uniform meshes. The algorithm performance is largely insensitive to the electron–ion mass ratio. Numerical experiments are performed on a 1D multi-scale ion acoustic wave test problem.« less

Calculation of the recirculating compressible flow downstream a sudden axisymmetric expansion

NASA Technical Reports Server (NTRS)

Vandromme, D.; Haminh, H.; Brunet, H.

1988-01-01

Significant progress has been made during the last five years to adapt conventional Navier-Stokes solver for handling nonconservative equations. A primary type of application is to use transport equation turbulence models, but the extension is also possible for describing the transport of nonpassive scalars, such as in reactive media. Among others, combustion and gas dissociation phenomena are topics needing a considerable research effort. An implicit two step scheme based on the well-known MacCormack scheme has been modified to treat compressible turbulent flows on complex geometries. Implicit treatment of nonconservative equations (in the present case a two-equation turbulence model) opens the way to the coupled solution of thermochemical transport equations.

Construction and comparison of parallel implicit kinetic solvers in three spatial dimensions

NASA Astrophysics Data System (ADS)

Titarev, Vladimir; Dumbser, Michael; Utyuzhnikov, Sergey

2014-01-01

The paper is devoted to the further development and systematic performance evaluation of a recent deterministic framework Nesvetay-3D for modelling three-dimensional rarefied gas flows. Firstly, a review of the existing discretization and parallelization strategies for solving numerically the Boltzmann kinetic equation with various model collision integrals is carried out. Secondly, a new parallelization strategy for the implicit time evolution method is implemented which improves scaling on large CPU clusters. Accuracy and scalability of the methods are demonstrated on a pressure-driven rarefied gas flow through a finite-length circular pipe as well as an external supersonic flow over a three-dimensional re-entry geometry of complicated aerodynamic shape.

Level set methods for detonation shock dynamics using high-order finite elements

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dobrev, V. A.; Grogan, F. C.; Kolev, T. V.

Level set methods are a popular approach to modeling evolving interfaces. We present a level set ad- vection solver in two and three dimensions using the discontinuous Galerkin method with high-order nite elements. During evolution, the level set function is reinitialized to a signed distance function to maintain ac- curacy. Our approach leads to stable front propagation and convergence on high-order, curved, unstructured meshes. The ability of the solver to implicitly track moving fronts lends itself to a number of applications; in particular, we highlight applications to high-explosive (HE) burn and detonation shock dynamics (DSD). We provide results for two-more » and three-dimensional benchmark problems as well as applications to DSD.« less

Use of a residual distribution Euler solver to study the occurrence of transonic flow in Wells turbine rotor blades

NASA Astrophysics Data System (ADS)

Henriques, J. C. C.; Gato, L. M. C.

The aim of the present study is to investigate the occurrence of transonic flow in several cascade geometries and blade sections that have been considered in the design of Wells turbine rotor blades. The calculations were performed using an implicit Euler solver for two-dimensional flow. The numerical method uses a multi-dimensional upwind matrix residual distribution scheme formulated on a new symmetrized form of the Euler equations, both in time and in space, that decouples the entropy and the enthalpy equations. Second-order accurate steady-state solutions where obtained using a compact three-point stencil. The results show that unwanted transonic flow may occur in the turbine rotor at relatively low mean-flow Mach numbers.

Detailed Aerodynamic Analysis of a Shrouded Tail Rotor Using an Unstructured Mesh Flow Solver

NASA Astrophysics Data System (ADS)

Lee, Hee Dong; Kwon, Oh Joon

The detailed aerodynamics of a shrouded tail rotor in hover has been numerically studied using a parallel inviscid flow solver on unstructured meshes. The numerical method is based on a cell-centered finite-volume discretization and an implicit Gauss-Seidel time integration. The calculation was made for a single blade by imposing a periodic boundary condition between adjacent rotor blades. The grid periodicity was also imposed at the periodic boundary planes to avoid numerical inaccuracy resulting from solution interpolation. The results were compared with available experimental data and those from a disk vortex theory for validation. It was found that realistic three-dimensional modeling is important for the prediction of detailed aerodynamics of shrouded rotors including the tip clearance gap flow.

BeamDyn: A High-Fidelity Wind Turbine Blade Solver in the FAST Modular Framework: Preprint

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Q.; Sprague, M.; Jonkman, J.

2015-01-01

BeamDyn, a Legendre-spectral-finite-element implementation of geometrically exact beam theory (GEBT), was developed to meet the design challenges associated with highly flexible composite wind turbine blades. In this paper, the governing equations of GEBT are reformulated into a nonlinear state-space form to support its coupling within the modular framework of the FAST wind turbine computer-aided engineering (CAE) tool. Different time integration schemes (implicit and explicit) were implemented and examined for wind turbine analysis. Numerical examples are presented to demonstrate the capability of this new beam solver. An example analysis of a realistic wind turbine blade, the CX-100, is also presented asmore » validation.« less

Numerical study of Reynolds stress in compressible flows

NASA Technical Reports Server (NTRS)

Vandromme, D.; Hamin, H.

1985-01-01

A second order closure has been implemented in an implicit Navier-Stokes solver to study the behavior of the Reynolds stresses under the influence of severe pressure gradients. In the boundary layer zone, the strongly sheared character of the mean flow dominates the turbulence generation mechanisms. However, the pressure gradients also play a very important role for these processes, but at different locations within the boundary layer.

Multigrid time-accurate integration of Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Arnone, Andrea; Liou, Meng-Sing; Povinelli, Louis A.

1993-01-01

Efficient acceleration techniques typical of explicit steady-state solvers are extended to time-accurate calculations. Stability restrictions are greatly reduced by means of a fully implicit time discretization. A four-stage Runge-Kutta scheme with local time stepping, residual smoothing, and multigridding is used instead of traditional time-expensive factorizations. Some applications to natural and forced unsteady viscous flows show the capability of the procedure.

Treatment of geometric singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Yu, Sining; Geng, Weihua; Wei, G. W.

2007-06-01

Geometric singularities, such as cusps and self-intersecting surfaces, are major obstacles to the accuracy, convergence, and stability of the numerical solution of the Poisson-Boltzmann (PB) equation. In earlier work, an interface technique based PB solver was developed using the matched interface and boundary (MIB) method, which explicitly enforces the flux jump condition at the solvent-solute interfaces and leads to highly accurate biomolecular electrostatics in continuum electric environments. However, such a PB solver, denoted as MIBPB-I, cannot maintain the designed second order convergence whenever there are geometric singularities, such as cusps and self-intersecting surfaces. Moreover, the matrix of the MIBPB-I is not optimally symmetrical, resulting in the convergence difficulty. The present work presents a new interface method based PB solver, denoted as MIBPB-II, to address the aforementioned problems. The present MIBPB-II solver is systematical and robust in treating geometric singularities and delivers second order convergence for arbitrarily complex molecular surfaces of proteins. A new procedure is introduced to make the MIBPB-II matrix optimally symmetrical and diagonally dominant. The MIBPB-II solver is extensively validated by the molecular surfaces of few-atom systems and a set of 24 proteins. Converged electrostatic potentials and solvation free energies are obtained at a coarse grid spacing of 0.5Å and are considerably more accurate than those obtained by the PBEQ and the APBS at finer grid spacings.

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Diskin, Boris; Thomas, James L.; Frink, Neal T.

2016-01-01

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

Block Preconditioning to Enable Physics-Compatible Implicit Multifluid Plasma Simulations

NASA Astrophysics Data System (ADS)

Phillips, Edward; Shadid, John; Cyr, Eric; Miller, Sean

2017-10-01

Multifluid plasma simulations involve large systems of partial differential equations in which many time-scales ranging over many orders of magnitude arise. Since the fastest of these time-scales may set a restrictively small time-step limit for explicit methods, the use of implicit or implicit-explicit time integrators can be more tractable for obtaining dynamics at time-scales of interest. Furthermore, to enforce properties such as charge conservation and divergence-free magnetic field, mixed discretizations using volume, nodal, edge-based, and face-based degrees of freedom are often employed in some form. Together with the presence of stiff modes due to integrating over fast time-scales, the mixed discretization makes the required linear solves for implicit methods particularly difficult for black box and monolithic solvers. This work presents a block preconditioning strategy for multifluid plasma systems that segregates the linear system based on discretization type and approximates off-diagonal coupling in block diagonal Schur complement operators. By employing multilevel methods for the block diagonal subsolves, this strategy yields algorithmic and parallel scalability which we demonstrate on a range of problems.

Implicit solution of Navier-Stokes equations on staggered curvilinear grids using a Newton-Krylov method with a novel analytical Jacobian.

NASA Astrophysics Data System (ADS)

Borazjani, Iman; Asgharzadeh, Hafez

2015-11-01

Flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates with explicit and semi-implicit schemes. Implicit schemes can be used to overcome these restrictions. However, implementing implicit solver for nonlinear equations including Navier-Stokes is not straightforward. Newton-Krylov subspace methods (NKMs) are one of the most advanced iterative methods to solve non-linear equations such as implicit descritization of the Navier-Stokes equation. The efficiency of NKMs massively depends on the Jacobian formation method, e.g., automatic differentiation is very expensive, and matrix-free methods slow down as the mesh is refined. Analytical Jacobian is inexpensive method, but derivation of analytical Jacobian for Navier-Stokes equation on staggered grid is challenging. The NKM with a novel analytical Jacobian was developed and validated against Taylor-Green vortex and pulsatile flow in a 90 degree bend. The developed method successfully handled the complex geometries such as an intracranial aneurysm with multiple overset grids, and immersed boundaries. It is shown that the NKM with an analytical Jacobian is 3 to 25 times faster than the fixed-point implicit Runge-Kutta method, and more than 100 times faster than automatic differentiation depending on the grid (size) and the flow problem. The developed methods are fully parallelized with parallel efficiency of 80-90% on the problems tested.

3D Gaussian Beam Modeling

DTIC Science & Technology

2011-09-01

optimized building blocks such as a parallelized tri-diagonal linear solver (used in the “implicit finite differences ” and split-step Pade PE models...and Ding Lee. “A finite - difference treatment of interface conditions for the parabolic wave equation: The horizontal interface.” The Journal of the...Acoustical Society of America, 71(4):855, 1982. 3. Ding Lee and Suzanne T. McDaniel. “A finite - difference treatment of interface conditions for

HPF Implementation of ARC3D

NASA Technical Reports Server (NTRS)

Frumkin, Michael; Yan, Jerry

1999-01-01

We present an HPF (High Performance Fortran) implementation of ARC3D code along with the profiling and performance data on SGI Origin 2000. Advantages and limitations of HPF as a parallel programming language for CFD applications are discussed. For achieving good performance results we used the data distributions optimized for implementation of implicit and explicit operators of the solver and boundary conditions. We compare the results with MPI and directive based implementations.

A three-dimensional application with the numerical grid generation code: EAGLE (utilizing an externally generated surface)

NASA Technical Reports Server (NTRS)

Houston, Johnny L.

1990-01-01

Program EAGLE (Eglin Arbitrary Geometry Implicit Euler) is a multiblock grid generation and steady-state flow solver system. This system combines a boundary conforming surface generation, a composite block structure grid generation scheme, and a multiblock implicit Euler flow solver algorithm. The three codes are intended to be used sequentially from the definition of the configuration under study to the flow solution about the configuration. EAGLE was specifically designed to aid in the analysis of both freestream and interference flow field configurations. These configurations can be comprised of single or multiple bodies ranging from simple axisymmetric airframes to complex aircraft shapes with external weapons. Each body can be arbitrarily shaped with or without multiple lifting surfaces. Program EAGLE is written to compile and execute efficiently on any CRAY machine with or without Solid State Disk (SSD) devices. Also, the code uses namelist inputs which are supported by all CRAY machines using the FORTRAN Compiler CF177. The use of namelist inputs makes it easier for the user to understand the inputs and to operate Program EAGLE. Recently, the Code was modified to operate on other computers, especially the Sun Spare4 Workstation. Several two-dimensional grid configurations were completely and successfully developed using EAGLE. Currently, EAGLE is being used for three-dimension grid applications.

Feedback and Control of Linear and Nonlinear Global MHD Modes in Rotating Plasmas

NASA Astrophysics Data System (ADS)

Finn, J. M.; Chacon, L.

2002-11-01

We present studies of feedback applied to resistive wall modes in the presence of plasma rotation. The main tool used is a Newton-Krylov nonlinear reduced resistive MHD code with completely implicit time stepping[1]. The effects of proportional and derivative gain and toroidal phase shift are investigated. In addition to studying the complete stabilization of the resistive wall mode, we present results on controlling the amplitude of nonlinear modes locked to the wall but propagating slowly; we also show results on reducing the hysteresis in the locking-unlocking bifurcation diagram. [1] L. Chacon, D. A. Knoll and J. M. Finn, "An implicit, nonlinear reduced resistive MHD solver", J. Comp. Phys. v. 178, pp 15-36 (2002).

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

Implicit methods were developed and tested for unstructured mesh computations. The approximate system which arises from the Newton linearization of the nonlinear evolution operator is solved by using the preconditioned GMRES (Generalized Minimum Residual) technique. Three different preconditioners were studied, namely, the incomplete LU factorization (ILU), block diagonal factorization, and the symmetric successive over relaxation (SSOR). The preconditioners were optimized to have good vectorization properties. SSOR and ILU were also studied as iterative schemes. The various methods are compared over a wide range of problems. Ordering of the unknowns, which affects the convergence of these sparse matrix iterative methods, is also studied. Results are presented for inviscid and turbulent viscous calculations on single and multielement airfoil configurations using globally and adaptively generated meshes.

Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry

NASA Technical Reports Server (NTRS)

Zheng, Xiaoqing; Liu, Chaoqun; Liao, Changming; Liu, Zhining; McCormick, Steve

1996-01-01

A highly accurate and efficient numerical method is developed for modeling 3-D reacting flows with detailed chemistry. A contravariant velocity-based governing system is developed for general curvilinear coordinates to maintain simplicity of the continuity equation and compactness of the discretization stencil. A fully-implicit backward Euler technique and a third-order monotone upwind-biased scheme on a staggered grid are used for the respective temporal and spatial terms. An efficient semi-coarsening multigrid method based on line-distributive relaxation is used as the flow solver. The species equations are solved in a fully coupled way and the chemical reaction source terms are treated implicitly. Example results are shown for a 3-D gas turbine combustor with strong swirling inflows.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner

NASA Astrophysics Data System (ADS)

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Wide-angle full-vector beam propagation method based on an alternating direction implicit preconditioner.

PubMed

Chui, Siu Lit; Lu, Ya Yan

2004-03-01

Wide-angle full-vector beam propagation methods (BPMs) for three-dimensional wave-guiding structures can be derived on the basis of rational approximants of a square root operator or its exponential (i.e., the one-way propagator). While the less accurate BPM based on the slowly varying envelope approximation can be efficiently solved by the alternating direction implicit (ADI) method, the wide-angle variants involve linear systems that are more difficult to handle. We present an efficient solver for these linear systems that is based on a Krylov subspace method with an ADI preconditioner. The resulting wide-angle full-vector BPM is used to simulate the propagation of wave fields in a Y branch and a taper.

Coupling MHD and PIC models in 2 dimensions

NASA Astrophysics Data System (ADS)

Daldorff, L.; Toth, G.; Sokolov, I.; Gombosi, T. I.; Lapenta, G.; Brackbill, J. U.; Markidis, S.; Amaya, J.

2013-12-01

Even for extended fluid plasma models, like Hall, anisotropic ion pressure and multi fluid MHD, there are still many plasma phenomena that are not well captured. For this reason, we have coupled the Implicit Particle-In-Cell (iPIC3D) code with the BATSRUS global MHD code. The PIC solver is applied in a part of the computational domain, for example, in the vicinity of reconnection sites, and overwrites the MHD solution. On the other hand, the fluid solver provides the boundary conditions for the PIC code. To demonstrate the use of the coupled codes for magnetospheric applications, we perform a 2D magnetosphere simulation, where BATSRUS solves for Hall MHD in the whole domain except for the tail reconnection region, which is handled by iPIC3D.

Overset grid applications on distributed memory MIMD computers

NASA Technical Reports Server (NTRS)

Chawla, Kalpana; Weeratunga, Sisira

1994-01-01

Analysis of modern aerospace vehicles requires the computation of flowfields about complex three dimensional geometries composed of regions with varying spatial resolution requirements. Overset grid methods allow the use of proven structured grid flow solvers to address the twin issues of geometrical complexity and the resolution variation by decomposing the complex physical domain into a collection of overlapping subdomains. This flexibility is accompanied by the need for irregular intergrid boundary communication among the overlapping component grids. This study investigates a strategy for implementing such a static overset grid implicit flow solver on distributed memory, MIMD computers; i.e., the 128 node Intel iPSC/860 and the 208 node Intel Paragon. Performance data for two composite grid configurations characteristic of those encountered in present day aerodynamic analysis are also presented.

Nektar++: An open-source spectral/ hp element framework

NASA Astrophysics Data System (ADS)

Cantwell, C. D.; Moxey, D.; Comerford, A.; Bolis, A.; Rocco, G.; Mengaldo, G.; De Grazia, D.; Yakovlev, S.; Lombard, J.-E.; Ekelschot, D.; Jordi, B.; Xu, H.; Mohamied, Y.; Eskilsson, C.; Nelson, B.; Vos, P.; Biotto, C.; Kirby, R. M.; Sherwin, S. J.

2015-07-01

Nektar++ is an open-source software framework designed to support the development of high-performance scalable solvers for partial differential equations using the spectral/ hp element method. High-order methods are gaining prominence in several engineering and biomedical applications due to their improved accuracy over low-order techniques at reduced computational cost for a given number of degrees of freedom. However, their proliferation is often limited by their complexity, which makes these methods challenging to implement and use. Nektar++ is an initiative to overcome this limitation by encapsulating the mathematical complexities of the underlying method within an efficient C++ framework, making the techniques more accessible to the broader scientific and industrial communities. The software supports a variety of discretisation techniques and implementation strategies, supporting methods research as well as application-focused computation, and the multi-layered structure of the framework allows the user to embrace as much or as little of the complexity as they need. The libraries capture the mathematical constructs of spectral/ hp element methods, while the associated collection of pre-written PDE solvers provides out-of-the-box application-level functionality and a template for users who wish to develop solutions for addressing questions in their own scientific domains.

A fast Chebyshev method for simulating flexible-wing propulsion

NASA Astrophysics Data System (ADS)

Moore, M. Nicholas J.

2017-09-01

We develop a highly efficient numerical method to simulate small-amplitude flapping propulsion by a flexible wing in a nearly inviscid fluid. We allow the wing's elastic modulus and mass density to vary arbitrarily, with an eye towards optimizing these distributions for propulsive performance. The method to determine the wing kinematics is based on Chebyshev collocation of the 1D beam equation as coupled to the surrounding 2D fluid flow. Through small-amplitude analysis of the Euler equations (with trailing-edge vortex shedding), the complete hydrodynamics can be represented by a nonlocal operator that acts on the 1D wing kinematics. A class of semi-analytical solutions permits fast evaluation of this operator with O (Nlog ⁡ N) operations, where N is the number of collocation points on the wing. This is in contrast to the minimum O (N2) cost of a direct 2D fluid solver. The coupled wing-fluid problem is thus recast as a PDE with nonlocal operator, which we solve using a preconditioned iterative method. These techniques yield a solver of near-optimal complexity, O (Nlog ⁡ N) , allowing one to rapidly search the infinite-dimensional parameter space of all possible material distributions and even perform optimization over this space.

Examination of Wave Speed in Rotating Detonation Engines Using Simplified Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Paxson, Daniel E.

2018-01-01

A simplified, two-dimensional, computational fluid dynamic (CFD) simulation, with a reactive Euler solver is used to examine possible causes for the low detonation wave propagation speeds that are consistently observed in air breathing rotating detonation engine (RDE) experiments. Intense, small-scale turbulence is proposed as the primary mechanism. While the solver cannot model this turbulence, it can be used to examine the most likely, and profound effect of turbulence. That is a substantial enlargement of the reaction zone, or equivalently, an effective reduction in the chemical reaction rate. It is demonstrated that in the unique flowfield of the RDE, a reduction in reaction rate leads to a reduction in the detonation speed. A subsequent test of reduced reaction rate in a purely one-dimensional pulsed detonation engine (PDE) flowfield yields no reduction in wave speed. The reasons for this are explained. The impact of reduced wave speed on RDE performance is then examined, and found to be minimal. Two other potential mechanisms are briefly examined. These are heat transfer, and reactive mixture non-uniformity. In the context of the simulation used for this study, both mechanisms are shown to have negligible effect on either wave speed or performance.

Program Code Generator for Cardiac Electrophysiology Simulation with Automatic PDE Boundary Condition Handling

PubMed Central

Punzalan, Florencio Rusty; Kunieda, Yoshitoshi; Amano, Akira

2015-01-01

Clinical and experimental studies involving human hearts can have certain limitations. Methods such as computer simulations can be an important alternative or supplemental tool. Physiological simulation at the tissue or organ level typically involves the handling of partial differential equations (PDEs). Boundary conditions and distributed parameters, such as those used in pharmacokinetics simulation, add to the complexity of the PDE solution. These factors can tailor PDE solutions and their corresponding program code to specific problems. Boundary condition and parameter changes in the customized code are usually prone to errors and time-consuming. We propose a general approach for handling PDEs and boundary conditions in computational models using a replacement scheme for discretization. This study is an extension of a program generator that we introduced in a previous publication. The program generator can generate code for multi-cell simulations of cardiac electrophysiology. Improvements to the system allow it to handle simultaneous equations in the biological function model as well as implicit PDE numerical schemes. The replacement scheme involves substituting all partial differential terms with numerical solution equations. Once the model and boundary equations are discretized with the numerical solution scheme, instances of the equations are generated to undergo dependency analysis. The result of the dependency analysis is then used to generate the program code. The resulting program code are in Java or C programming language. To validate the automatic handling of boundary conditions in the program code generator, we generated simulation code using the FHN, Luo-Rudy 1, and Hund-Rudy cell models and run cell-to-cell coupling and action potential propagation simulations. One of the simulations is based on a published experiment and simulation results are compared with the experimental data. We conclude that the proposed program code generator can be used to generate code for physiological simulations and provides a tool for studying cardiac electrophysiology. PMID:26356082

A GPU-based incompressible Navier-Stokes solver on moving overset grids

NASA Astrophysics Data System (ADS)

Chandar, Dominic D. J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.

2013-07-01

In pursuit of obtaining high fidelity solutions to the fluid flow equations in a short span of time, graphics processing units (GPUs) which were originally intended for gaming applications are currently being used to accelerate computational fluid dynamics (CFD) codes. With a high peak throughput of about 1 TFLOPS on a PC, GPUs seem to be favourable for many high-resolution computations. One such computation that involves a lot of number crunching is computing time accurate flow solutions past moving bodies. The aim of the present paper is thus to discuss the development of a flow solver on unstructured and overset grids and its implementation on GPUs. In its present form, the flow solver solves the incompressible fluid flow equations on unstructured/hybrid/overset grids using a fully implicit projection method. The resulting discretised equations are solved using a matrix-free Krylov solver using several GPU kernels such as gradient, Laplacian and reduction. Some of the simple arithmetic vector calculations are implemented using the CU++: An Object Oriented Framework for Computational Fluid Dynamics Applications using Graphics Processing Units, Journal of Supercomputing, 2013, doi:10.1007/s11227-013-0985-9 approach where GPU kernels are automatically generated at compile time. Results are presented for two- and three-dimensional computations on static and moving grids.

A Numerical Study of Scalable Cardiac Electro-Mechanical Solvers on HPC Architectures

PubMed Central

Colli Franzone, Piero; Pavarino, Luca F.; Scacchi, Simone

2018-01-01

We introduce and study some scalable domain decomposition preconditioners for cardiac electro-mechanical 3D simulations on parallel HPC (High Performance Computing) architectures. The electro-mechanical model of the cardiac tissue is composed of four coupled sub-models: (1) the static finite elasticity equations for the transversely isotropic deformation of the cardiac tissue; (2) the active tension model describing the dynamics of the intracellular calcium, cross-bridge binding and myofilament tension; (3) the anisotropic Bidomain model describing the evolution of the intra- and extra-cellular potentials in the deforming cardiac tissue; and (4) the ionic membrane model describing the dynamics of ionic currents, gating variables, ionic concentrations and stretch-activated channels. This strongly coupled electro-mechanical model is discretized in time with a splitting semi-implicit technique and in space with isoparametric finite elements. The resulting scalable parallel solver is based on Multilevel Additive Schwarz preconditioners for the solution of the Bidomain system and on BDDC preconditioned Newton-Krylov solvers for the non-linear finite elasticity system. The results of several 3D parallel simulations show the scalability of both linear and non-linear solvers and their application to the study of both physiological excitation-contraction cardiac dynamics and re-entrant waves in the presence of different mechano-electrical feedbacks. PMID:29674971

HEAT.PRO - THERMAL IMBALANCE FORCE SIMULATION AND ANALYSIS USING PDE2D

NASA Technical Reports Server (NTRS)

Vigue, Y.

1994-01-01

HEAT.PRO calculates the thermal imbalance force resulting from satellite surface heating. The heated body of a satellite re-radiates energy at a rate that is proportional to its temperature, losing the energy in the form of photons. By conservation of momentum, this momentum flux out of the body creates a reaction force against the radiation surface, and the net thermal force can be observed as a small perturbation that affects long term orbital behavior of the satellite. HEAT.PRO calculates this thermal imbalance force and then determines its effects on satellite orbits, especially where the Earth's shadowing of an orbiting satellite causes periodic changes in the spacecraft's thermal environment. HEAT.PRO implements a finite element method routine called PDE2D which incorporates material properties to determine the solar panel surface temperatures. The nodal temperatures are computed at specified time steps and are used to determine the magnitude and direction of the thermal force on the spacecraft. These calculations are based on the solar panel orientation and satellite's position with respect to the earth and sun. It is necessary to have accurate, current knowledge of surface emissivity, thermal conductivity, heat capacity, and material density. These parameters, which may change due to degradation of materials in the environment of space, influence the nodal temperatures that are computed and thus the thermal force calculations. HEAT.PRO was written in FORTRAN 77 for Cray series computers running UNICOS. The source code contains directives for and is used as input to the required partial differential equation solver, PDE2D. HEAT.PRO is available on a 9-track 1600 BPI magnetic tape in UNIX tar format (standard distribution medium) or a .25 inch streaming magnetic tape cartridge in UNIX tar format. An electronic copy of the documentation in Macintosh Microsoft Word format is included on the distribution tape. HEAT.PRO was developed in 1991. Cray and UNICOS are registered trademarks of Cray Research, Inc. UNIX is a trademark of AT&T Bell Laboratories. PDE2D is available from Granville Sewell, Mathematics Dept., University of Texas at El Paso, El Paso, Texas 79968.

A high-order semi-explicit discontinuous Galerkin solver for 3D incompressible flow with application to DNS and LES of turbulent channel flow

NASA Astrophysics Data System (ADS)

Krank, Benjamin; Fehn, Niklas; Wall, Wolfgang A.; Kronbichler, Martin

2017-11-01

We present an efficient discontinuous Galerkin scheme for simulation of the incompressible Navier-Stokes equations including laminar and turbulent flow. We consider a semi-explicit high-order velocity-correction method for time integration as well as nodal equal-order discretizations for velocity and pressure. The non-linear convective term is treated explicitly while a linear system is solved for the pressure Poisson equation and the viscous term. The key feature of our solver is a consistent penalty term reducing the local divergence error in order to overcome recently reported instabilities in spatially under-resolved high-Reynolds-number flows as well as small time steps. This penalty method is similar to the grad-div stabilization widely used in continuous finite elements. We further review and compare our method to several other techniques recently proposed in literature to stabilize the method for such flow configurations. The solver is specifically designed for large-scale computations through matrix-free linear solvers including efficient preconditioning strategies and tensor-product elements, which have allowed us to scale this code up to 34.4 billion degrees of freedom and 147,456 CPU cores. We validate our code and demonstrate optimal convergence rates with laminar flows present in a vortex problem and flow past a cylinder and show applicability of our solver to direct numerical simulation as well as implicit large-eddy simulation of turbulent channel flow at Reτ = 180 as well as 590.

Towards development of enhanced fully-Lagrangian mesh-free computational methods for fluid-structure interaction

NASA Astrophysics Data System (ADS)

Khayyer, Abbas; Gotoh, Hitoshi; Falahaty, Hosein; Shimizu, Yuma

2018-02-01

Simulation of incompressible fluid flow-elastic structure interactions is targeted by using fully-Lagrangian mesh-free computational methods. A projection-based fluid model (moving particle semi-implicit (MPS)) is coupled with either a Newtonian or a Hamiltonian Lagrangian structure model (MPS or HMPS) in a mathematically-physically consistent manner. The fluid model is founded on the solution of Navier-Stokes and continuity equations. The structure models are configured either in the framework of Newtonian mechanics on the basis of conservation of linear and angular momenta, or Hamiltonian mechanics on the basis of variational principle for incompressible elastodynamics. A set of enhanced schemes are incorporated for projection-based fluid model (Enhanced MPS), thus, the developed coupled solvers for fluid structure interaction (FSI) are referred to as Enhanced MPS-MPS and Enhanced MPS-HMPS. Besides, two smoothed particle hydrodynamics (SPH)-based FSI solvers, being developed by the authors, are considered and their potential applicability and comparable performance are briefly discussed in comparison with MPS-based FSI solvers. The SPH-based FSI solvers are established through coupling of projection-based incompressible SPH (ISPH) fluid model and SPH-based Newtonian/Hamiltonian structure models, leading to Enhanced ISPH-SPH and Enhanced ISPH-HSPH. A comparative study is carried out on the performances of the FSI solvers through a set of benchmark tests, including hydrostatic water column on an elastic plate, high speed impact of an elastic aluminum beam, hydroelastic slamming of a marine panel and dam break with elastic gate.

A set of parallel, implicit methods for a reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids

DOE PAGES

Xia, Yidong; Luo, Hong; Frisbey, Megan; ...

2014-07-01

A set of implicit methods are proposed for a third-order hierarchical WENO reconstructed discontinuous Galerkin method for compressible flows on 3D hybrid grids. An attractive feature in these methods are the application of the Jacobian matrix based on the P1 element approximation, resulting in a huge reduction of memory requirement compared with DG (P2). Also, three approaches -- analytical derivation, divided differencing, and automatic differentiation (AD) are presented to construct the Jacobian matrix respectively, where the AD approach shows the best robustness. A variety of compressible flow problems are computed to demonstrate the fast convergence property of the implemented flowmore » solver. Furthermore, an SPMD (single program, multiple data) programming paradigm based on MPI is proposed to achieve parallelism. The numerical results on complex geometries indicate that this low-storage implicit method can provide a viable and attractive DG solution for complicated flows of practical importance.« less

Fully implicit adaptive mesh refinement solver for 2D MHD

NASA Astrophysics Data System (ADS)

Philip, B.; Chacon, L.; Pernice, M.

2008-11-01

Application of implicit adaptive mesh refinement (AMR) to simulate resistive magnetohydrodynamics is described. Solving this challenging multi-scale, multi-physics problem can improve understanding of reconnection in magnetically-confined plasmas. AMR is employed to resolve extremely thin current sheets, essential for an accurate macroscopic description. Implicit time stepping allows us to accurately follow the dynamical time scale of the developing magnetic field, without being restricted by fast Alfven time scales. At each time step, the large-scale system of nonlinear equations is solved by a Jacobian-free Newton-Krylov method together with a physics-based preconditioner. Each block within the preconditioner is solved optimally using the Fast Adaptive Composite grid method, which can be considered as a multiplicative Schwarz method on AMR grids. We will demonstrate the excellent accuracy and efficiency properties of the method with several challenging reduced MHD applications, including tearing, island coalescence, and tilt instabilities. B. Philip, L. Chac'on, M. Pernice, J. Comput. Phys., in press (2008)

A Spectral Element Discretisation on Unstructured Triangle / Tetrahedral Meshes for Elastodynamics

NASA Astrophysics Data System (ADS)

May, Dave A.; Gabriel, Alice-A.

2017-04-01

The spectral element method (SEM) defined over quadrilateral and hexahedral element geometries has proven to be a fast, accurate and scalable approach to study wave propagation phenomena. In the context of regional scale seismology and or simulations incorporating finite earthquake sources, the geometric restrictions associated with hexahedral elements can limit the applicability of the classical quad./hex. SEM. Here we describe a continuous Galerkin spectral element discretisation defined over unstructured meshes composed of triangles (2D), or tetrahedra (3D). The method uses a stable, nodal basis constructed from PKD polynomials and thus retains the spectral accuracy and low dispersive properties of the classical SEM, in addition to the geometric versatility provided by unstructured simplex meshes. For the particular basis and quadrature rule we have adopted, the discretisation results in a mass matrix which is not diagonal, thereby mandating linear solvers be utilised. To that end, we have developed efficient solvers and preconditioners which are robust with respect to the polynomial order (p), and possess high arithmetic intensity. Furthermore, we also consider using implicit time integrators, together with a p-multigrid preconditioner to circumvent the CFL condition. Implicit time integrators become particularly relevant when considering solving problems on poor quality meshes, or meshes containing elements with a widely varying range of length scales - both of which frequently arise when meshing non-trivial geometries. We demonstrate the applicability of the new method by examining a number of two- and three-dimensional wave propagation scenarios. These scenarios serve to characterise the accuracy and cost of the new method. Lastly, we will assess the potential benefits of using implicit time integrators for regional scale wave propagation simulations.

Second derivative time integration methods for discontinuous Galerkin solutions of unsteady compressible flows

NASA Astrophysics Data System (ADS)

Nigro, A.; De Bartolo, C.; Crivellini, A.; Bassi, F.

2017-12-01

In this paper we investigate the possibility of using the high-order accurate A (α) -stable Second Derivative (SD) schemes proposed by Enright for the implicit time integration of the Discontinuous Galerkin (DG) space-discretized Navier-Stokes equations. These multistep schemes are A-stable up to fourth-order, but their use results in a system matrix difficult to compute. Furthermore, the evaluation of the nonlinear function is computationally very demanding. We propose here a Matrix-Free (MF) implementation of Enright schemes that allows to obtain a method without the costs of forming, storing and factorizing the system matrix, which is much less computationally expensive than its matrix-explicit counterpart, and which performs competitively with other implicit schemes, such as the Modified Extended Backward Differentiation Formulae (MEBDF). The algorithm makes use of the preconditioned GMRES algorithm for solving the linear system of equations. The preconditioner is based on the ILU(0) factorization of an approximated but computationally cheaper form of the system matrix, and it has been reused for several time steps to improve the efficiency of the MF Newton-Krylov solver. We additionally employ a polynomial extrapolation technique to compute an accurate initial guess to the implicit nonlinear system. The stability properties of SD schemes have been analyzed by solving a linear model problem. For the analysis on the Navier-Stokes equations, two-dimensional inviscid and viscous test cases, both with a known analytical solution, are solved to assess the accuracy properties of the proposed time integration method for nonlinear autonomous and non-autonomous systems, respectively. The performance of the SD algorithm is compared with the ones obtained by using an MF-MEBDF solver, in order to evaluate its effectiveness, identifying its limitations and suggesting possible further improvements.

Agglomeration Multigrid for an Unstructured-Grid Flow Solver

NASA Technical Reports Server (NTRS)

Frink, Neal; Pandya, Mohagna J.

2004-01-01

An agglomeration multigrid scheme has been implemented into the sequential version of the NASA code USM3Dns, tetrahedral cell-centered finite volume Euler/Navier-Stokes flow solver. Efficiency and robustness of the multigrid-enhanced flow solver have been assessed for three configurations assuming an inviscid flow and one configuration assuming a viscous fully turbulent flow. The inviscid studies include a transonic flow over the ONERA M6 wing and a generic business jet with flow-through nacelles and a low subsonic flow over a high-lift trapezoidal wing. The viscous case includes a fully turbulent flow over the RAE 2822 rectangular wing. The multigrid solutions converged with 12%-33% of the Central Processing Unit (CPU) time required by the solutions obtained without multigrid. For all of the inviscid cases, multigrid in conjunction with an explicit time-stepping scheme performed the best with regard to the run time memory and CPU time requirements. However, for the viscous case multigrid had to be used with an implicit backward Euler time-stepping scheme that increased the run time memory requirement by 22% as compared to the run made without multigrid.

On the eddy-resolving capability of high-order discontinuous Galerkin approaches to implicit LES / under-resolved DNS of Euler turbulence

NASA Astrophysics Data System (ADS)

Moura, R. C.; Mengaldo, G.; Peiró, J.; Sherwin, S. J.

2017-02-01

We present estimates of spectral resolution power for under-resolved turbulent Euler flows obtained with high-order discontinuous Galerkin (DG) methods. The '1% rule' based on linear dispersion-diffusion analysis introduced by Moura et al. (2015) [10] is here adapted for 3D energy spectra and validated through the inviscid Taylor-Green vortex problem. The 1% rule estimates the wavenumber beyond which numerical diffusion induces an artificial dissipation range on measured energy spectra. As the original rule relies on standard upwinding, different Riemann solvers are tested. Very good agreement is found for solvers which treat the different physical waves in a consistent manner. Relatively good agreement is still found for simpler solvers. The latter however displayed spurious features attributed to the inconsistent treatment of different physical waves. It is argued that, in the limit of vanishing viscosity, such features might have a significant impact on robustness and solution quality. The estimates proposed are regarded as useful guidelines for no-model DG-based simulations of free turbulence at very high Reynolds numbers.

Technical report series on global modeling and data assimilation. Volume 2: Direct solution of the implicit formulation of fourth order horizontal diffusion for gridpoint models on the sphere

NASA Technical Reports Server (NTRS)

Li, Yong; Moorthi, S.; Bates, J. Ray; Suarez, Max J.

1994-01-01

High order horizontal diffusion of the form K Delta(exp 2m) is widely used in spectral models as a means of preventing energy accumulation at the shortest resolved scales. In the spectral context, an implicit formation of such diffusion is trivial to implement. The present note describes an efficient method of implementing implicit high order diffusion in global finite difference models. The method expresses the high order diffusion equation as a sequence of equations involving Delta(exp 2). The solution is obtained by combining fast Fourier transforms in longitude with a finite difference solver for the second order ordinary differential equation in latitude. The implicit diffusion routine is suitable for use in any finite difference global model that uses a regular latitude/longitude grid. The absence of a restriction on the timestep makes it particularly suitable for use in semi-Lagrangian models. The scale selectivity of the high order diffusion gives it an advantage over the uncentering method that has been used to control computational noise in two-time-level semi-Lagrangian models.

Development of a fully implicit particle-in-cell scheme for gyrokinetic electromagnetic turbulence simulation in XGC1

NASA Astrophysics Data System (ADS)

Ku, Seung-Hoe; Hager, R.; Chang, C. S.; Chacon, L.; Chen, G.; EPSI Team

2016-10-01

The cancelation problem has been a long-standing issue for long wavelengths modes in electromagnetic gyrokinetic PIC simulations in toroidal geometry. As an attempt of resolving this issue, we implemented a fully implicit time integration scheme in the full-f, gyrokinetic PIC code XGC1. The new scheme - based on the implicit Vlasov-Darwin PIC algorithm by G. Chen and L. Chacon - can potentially resolve cancelation problem. The time advance for the field and the particle equations is space-time-centered, with particle sub-cycling. The resulting system of equations is solved by a Picard iteration solver with fixed-point accelerator. The algorithm is implemented in the parallel velocity formalism instead of the canonical parallel momentum formalism. XGC1 specializes in simulating the tokamak edge plasma with magnetic separatrix geometry. A fully implicit scheme could be a way to accurate and efficient gyrokinetic simulations. We will test if this numerical scheme overcomes the cancelation problem, and reproduces the dispersion relation of Alfven waves and tearing modes in cylindrical geometry. Funded by US DOE FES and ASCR, and computing resources provided by OLCF through ALCC.

GroPBS: Fast Solver for Implicit Electrostatics of Biomolecules

PubMed Central

Bertelshofer, Franziska; Sun, Liping; Greiner, Günther; Böckmann, Rainer A.

2015-01-01

Knowledge about the electrostatic potential on the surface of biomolecules or biomembranes under physiological conditions is an important step in the attempt to characterize the physico-chemical properties of these molecules and, in particular, also their interactions with each other. Additionally, knowledge about solution electrostatics may also guide the design of molecules with specified properties. However, explicit water models come at a high computational cost, rendering them unsuitable for large design studies or for docking purposes. Implicit models with the water phase treated as a continuum require the numerical solution of the Poisson–Boltzmann equation (PBE). Here, we present a new flexible program for the numerical solution of the PBE, allowing for different geometries, and the explicit and implicit inclusion of membranes. It involves a discretization of space and the computation of the molecular surface. The PBE is solved using finite differences, the resulting set of equations is solved using a Gauss–Seidel method. It is shown for the example of the sucrose transporter ScrY that the implicit inclusion of a surrounding membrane has a strong effect also on the electrostatics within the pore region and, thus, needs to be carefully considered, e.g., in design studies on membrane proteins. PMID:26636074

An Inviscid Decoupled Method for the Roe FDS Scheme in the Reacting Gas Path of FUN3D

NASA Technical Reports Server (NTRS)

Thompson, Kyle B.; Gnoffo, Peter A.

2016-01-01

An approach is described to decouple the species continuity equations from the mixture continuity, momentum, and total energy equations for the Roe flux difference splitting scheme. This decoupling simplifies the implicit system, so that the flow solver can be made significantly more efficient, with very little penalty on overall scheme robustness. Most importantly, the computational cost of the point implicit relaxation is shown to scale linearly with the number of species for the decoupled system, whereas the fully coupled approach scales quadratically. Also, the decoupled method significantly reduces the cost in wall time and memory in comparison to the fully coupled approach. This work lays the foundation for development of an efficient adjoint solution procedure for high speed reacting flow.

Directional Agglomeration Multigrid Techniques for High-Reynolds Number Viscous Flows

NASA Technical Reports Server (NTRS)

Mavriplis, Dimitri J.

1998-01-01

A preconditioned directional-implicit agglomeration algorithm is developed for solving two- and three-dimensional viscous flows on highly anisotropic unstructured meshes of mixed-element types. The multigrid smoother consists of a pre-conditioned point- or line-implicit solver which operates on lines constructed in the unstructured mesh using a weighted graph algorithm. Directional coarsening or agglomeration is achieved using a similar weighted graph algorithm. A tight coupling of the line construction and directional agglomeration algorithms enables the use of aggressive coarsening ratios in the multigrid algorithm, which in turn reduces the cost of a multigrid cycle. Convergence rates which are independent of the degree of grid stretching are demonstrated in both two and three dimensions. Further improvement of the three-dimensional convergence rates through a GMRES technique is also demonstrated.

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1992-01-01

The development of efficient iterative solution methods for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations is discussed. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. In this work, another approach based on the classical conjugate gradient method, known as the Generalized Minimum Residual (GMRES) algorithm is investigated. The GMRES algorithm has been used in the past by a number of researchers for solving steady viscous and inviscid flow problems. Here, we investigate the suitability of this algorithm for solving the system of non-linear equations that arise in unsteady Navier-Stokes solvers at each time step.

Evaluation of a Multigrid Scheme for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, R. C.

2004-01-01

A fast multigrid solver for the steady, incompressible Navier-Stokes equations is presented. The multigrid solver is based upon a factorizable discrete scheme for the velocity-pressure form of the Navier-Stokes equations. This scheme correctly distinguishes between the advection-diffusion and elliptic parts of the operator, allowing efficient smoothers to be constructed. To evaluate the multigrid algorithm, solutions are computed for flow over a flat plate, parabola, and a Karman-Trefftz airfoil. Both nonlifting and lifting airfoil flows are considered, with a Reynolds number range of 200 to 800. Convergence and accuracy of the algorithm are discussed. Using Gauss-Seidel line relaxation in alternating directions, multigrid convergence behavior approaching that of O(N) methods is achieved. The computational efficiency of the numerical scheme is compared with that of Runge-Kutta and implicit upwind based multigrid methods.

Solution of elliptic PDEs by fast Poisson solvers using a local relaxation factor

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1986-01-01

A large class of two- and three-dimensional, nonseparable elliptic partial differential equations (PDEs) is presently solved by means of novel one-step (D'Yakanov-Gunn) and two-step (accelerated one-step) iterative procedures, using a local, discrete Fourier analysis. In addition to being easily implemented and applicable to a variety of boundary conditions, these procedures are found to be computationally efficient on the basis of the results of numerical comparison with other established methods, which lack the present one's: (1) insensitivity to grid cell size and aspect ratio, and (2) ease of convergence rate estimation by means of the coefficient of the PDE being solved. The two-step procedure is numerically demonstrated to outperform the one-step procedure in the case of PDEs with variable coefficients.

Analysis of Aluminum-Nitride SOI for High-Temperature Electronics

NASA Technical Reports Server (NTRS)

Biegel, Bryan A.; Osman, Mohamed A.; Yu, Zhiping

2000-01-01

We use numerical simulation to investigate the high-temperature (up to 500K) operation of SOI MOSFETs with Aluminum-Nitride (AIN) buried insulators, rather than the conventional silicon-dioxide (SiO2). Because the thermal conductivity of AIN is about 100 times that of SiO2, AIN SOI should greatly reduce the often severe self-heating problem of conventional SOI, making SOI potentially suitable for high-temperature applications. A detailed electrothermal transport model is used in the simulations, and solved with a PDE solver called PROPHET In this work, we compare the performance of AIN-based SOI with that of SiO2-based SOI and conventional MOSFETs. We find that AIN SOI does indeed remove the self-heating penalty of SOL However, several device design trade-offs remain, which our simulations highlight.

Solution algorithms for the two-dimensional Euler equations on unstructured meshes

NASA Technical Reports Server (NTRS)

Whitaker, D. L.; Slack, David C.; Walters, Robert W.

1990-01-01

The objective of the study was to analyze implicit techniques employed in structured grid algorithms for solving two-dimensional Euler equations and extend them to unstructured solvers in order to accelerate convergence rates. A comparison is made between nine different algorithms for both first-order and second-order accurate solutions. Higher-order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The discussion is illustrated by results for flow over a transonic circular arc.

Aerothermodynamic Design Sensitivities for a Reacting Gas Flow Solver on an Unstructured Mesh Using a Discrete Adjoint Formulation

NASA Astrophysics Data System (ADS)

Thompson, Kyle Bonner

An algorithm is described to efficiently compute aerothermodynamic design sensitivities using a decoupled variable set. In a conventional approach to computing design sensitivities for reacting flows, the species continuity equations are fully coupled to the conservation laws for momentum and energy. In this algorithm, the species continuity equations are solved separately from the mixture continuity, momentum, and total energy equations. This decoupling simplifies the implicit system, so that the flow solver can be made significantly more efficient, with very little penalty on overall scheme robustness. Most importantly, the computational cost of the point implicit relaxation is shown to scale linearly with the number of species for the decoupled system, whereas the fully coupled approach scales quadratically. Also, the decoupled method significantly reduces the cost in wall time and memory in comparison to the fully coupled approach. This decoupled approach for computing design sensitivities with the adjoint system is demonstrated for inviscid flow in chemical non-equilibrium around a re-entry vehicle with a retro-firing annular nozzle. The sensitivities of the surface temperature and mass flow rate through the nozzle plenum are computed with respect to plenum conditions and verified against sensitivities computed using a complex-variable finite-difference approach. The decoupled scheme significantly reduces the computational time and memory required to complete the optimization, making this an attractive method for high-fidelity design of hypersonic vehicles.

Matlab Geochemistry: An open source geochemistry solver based on MRST

NASA Astrophysics Data System (ADS)

McNeece, C. J.; Raynaud, X.; Nilsen, H.; Hesse, M. A.

2017-12-01

The study of geological systems often requires the solution of complex geochemical relations. To address this need we present an open source geochemical solver based on the Matlab Reservoir Simulation Toolbox (MRST) developed by SINTEF. The implementation supports non-isothermal multicomponent aqueous complexation, surface complexation, ion exchange, and dissolution/precipitation reactions. The suite of tools available in MRST allows for rapid model development, in particular the incorporation of geochemical calculations into transport simulations of multiple phases, complex domain geometry and geomechanics. Different numerical schemes and additional physics can be easily incorporated into the existing tools through the object-oriented framework employed by MRST. The solver leverages the automatic differentiation tools available in MRST to solve arbitrarily complex geochemical systems with any choice of species or element concentration as input. Four mathematical approaches enable the solver to be quite robust: 1) the choice of chemical elements as the basis components makes all entries in the composition matrix positive thus preserving convexity, 2) a log variable transformation is used which transfers the nonlinearity to the convex composition matrix, 3) a priori bounds on variables are calculated from the structure of the problem, constraining Netwon's path and 4) an initial guess is calculated implicitly by sequentially adding model complexity. As a benchmark we compare the model to experimental and semi-analytic solutions of the coupled salinity-acidity transport system. Together with the reservoir simulation capabilities of MRST the solver offers a promising tool for geochemical simulations in reservoir domains for applications in a diversity of fields from enhanced oil recovery to radionuclide storage.

Scalable smoothing strategies for a geometric multigrid method for the immersed boundary equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bhalla, Amneet Pal Singh; Knepley, Matthew G.; Adams, Mark F.

2016-12-20

The immersed boundary (IB) method is a widely used approach to simulating fluid-structure interaction (FSI). Although explicit versions of the IB method can suffer from severe time step size restrictions, these methods remain popular because of their simplicity and generality. In prior work (Guy et al., Adv Comput Math, 2015), some of us developed a geometric multigrid preconditioner for a stable semi-implicit IB method under Stokes flow conditions; however, this solver methodology used a Vanka-type smoother that presented limited opportunities for parallelization. This work extends this Stokes-IB solver methodology by developing smoothing techniques that are suitable for parallel implementation. Specifically,more » we demonstrate that an additive version of the Vanka smoother can yield an effective multigrid preconditioner for the Stokes-IB equations, and we introduce an efficient Schur complement-based smoother that is also shown to be effective for the Stokes-IB equations. We investigate the performance of these solvers for a broad range of material stiffnesses, both for Stokes flows and flows at nonzero Reynolds numbers, and for thick and thin structural models. We show here that linear solver performance degrades with increasing Reynolds number and material stiffness, especially for thin interface cases. Nonetheless, the proposed approaches promise to yield effective solution algorithms, especially at lower Reynolds numbers and at modest-to-high elastic stiffnesses.« less

Comparing Split and Unsplit Numerical Methods for Simulating Low and High Mach Number Turbulent Flows in Xrage

NASA Astrophysics Data System (ADS)

Saenz, Juan; Grinstein, Fernando; Dolence, Joshua; Rauenzahn, Rick; Masser, Thomas; Francois, Marianne; LANL Team

2017-11-01

We report progress in evaluating an unsplit hydrodynamic solver being implemented in the radiation adaptive grid Eulerian (xRAGE) code, and compare to a split scheme. xRage is a Eulerian hydrodynamics code used for implicit large eddy simulations (ILES) of multi-material, multi-physics flows where low and high Mach number (Ma) processes and instabilities interact and co-exist. The hydrodynamic solver in xRAGE uses a directionally split, second order Godunov, finite volume (FV) scheme. However, a standard, unsplit, Godunov-type FV scheme with 2nd and 3rd order reconstruction options, low Ma correction and a variety of Riemann solvers has recently become available. To evaluate the hydrodynamic solvers for turbulent low Ma flows, we use simulations of the Taylor Green Vortex (TGV), where there is a transition to turbulence via vortex stretching and production of small-scale eddies. We also simulate a high-low Ma shock-tube flow, where a shock passing over a perturbed surface generates a baroclinic Richtmyer-Meshkov instability (RMI); after the shock has passed, the turbulence in the accelerated interface region resembles Rayleigh Taylor (RT) instability. We compare turbulence spectra and decay in simulated TGV flows, and we present progress in simulating the high-low Ma RMI-RT flow. LANL is operated by LANS LLC for the U.S. DOE NNSA under Contract No. DE-AC52-06NA25396.

ML 3.0 smoothed aggregation user's guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-05-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Az = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the AZTEC 2.1 and AZTECOO iterative package [15]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and non-symmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

ML 3.1 smoothed aggregation user's guide.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sala, Marzio; Hu, Jonathan Joseph; Tuminaro, Raymond Stephen

2004-10-01

ML is a multigrid preconditioning package intended to solve linear systems of equations Ax = b where A is a user supplied n x n sparse matrix, b is a user supplied vector of length n and x is a vector of length n to be computed. ML should be used on large sparse linear systems arising from partial differential equation (PDE) discretizations. While technically any linear system can be considered, ML should be used on linear systems that correspond to things that work well with multigrid methods (e.g. elliptic PDEs). ML can be used as a stand-alone package ormore » to generate preconditioners for a traditional iterative solver package (e.g. Krylov methods). We have supplied support for working with the Aztec 2.1 and AztecOO iterative package [16]. However, other solvers can be used by supplying a few functions. This document describes one specific algebraic multigrid approach: smoothed aggregation. This approach is used within several specialized multigrid methods: one for the eddy current formulation for Maxwell's equations, and a multilevel and domain decomposition method for symmetric and nonsymmetric systems of equations (like elliptic equations, or compressible and incompressible fluid dynamics problems). Other methods exist within ML but are not described in this document. Examples are given illustrating the problem definition and exercising multigrid options.« less

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES

PubMed Central

Wan, Xiaohai; Li, Zhilin

2012-01-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size. PMID:22701346

SOME NEW FINITE DIFFERENCE METHODS FOR HELMHOLTZ EQUATIONS ON IRREGULAR DOMAINS OR WITH INTERFACES.

PubMed

Wan, Xiaohai; Li, Zhilin

2012-06-01

Solving a Helmholtz equation Δu + λu = f efficiently is a challenge for many applications. For example, the core part of many efficient solvers for the incompressible Navier-Stokes equations is to solve one or several Helmholtz equations. In this paper, two new finite difference methods are proposed for solving Helmholtz equations on irregular domains, or with interfaces. For Helmholtz equations on irregular domains, the accuracy of the numerical solution obtained using the existing augmented immersed interface method (AIIM) may deteriorate when the magnitude of λ is large. In our new method, we use a level set function to extend the source term and the PDE to a larger domain before we apply the AIIM. For Helmholtz equations with interfaces, a new maximum principle preserving finite difference method is developed. The new method still uses the standard five-point stencil with modifications of the finite difference scheme at irregular grid points. The resulting coefficient matrix of the linear system of finite difference equations satisfies the sign property of the discrete maximum principle and can be solved efficiently using a multigrid solver. The finite difference method is also extended to handle temporal discretized equations where the solution coefficient λ is inversely proportional to the mesh size.

Far-Field Turbulent Vortex-Wake/Exhaust Plume Interaction for Subsonic and HSCT Airplanes

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; Adam, Ihab; Wong, Tin-Chee

1996-01-01

Computational study of the far-field turbulent vortex-wake/exhaust plume interaction for subsonic and high speed civil transport (HSCT) airplanes is carried out. The Reynolds-averaged Navier-Stokes (NS) equations are solved using the implicit, upwind, Roe-flux-differencing, finite-volume scheme. The two-equation shear stress transport model of Menter is implemented with the NS solver for turbulent-flow calculation. For the far-field study, the computations of vortex-wake interaction with the exhaust plume of a single engine of a Boeing 727 wing in a holding condition and two engines of an HSCT in a cruise condition are carried out using overlapping zonal method for several miles downstream. These results are obtained using the computer code FTNS3D. The results of the subsonic flow of this code are compared with those of a parabolized NS solver known as the UNIWAKE code.

Upwind MacCormack Euler solver with non-equilibrium chemistry

NASA Technical Reports Server (NTRS)

Sherer, Scott E.; Scott, James N.

1993-01-01

A computer code, designated UMPIRE, is currently under development to solve the Euler equations in two dimensions with non-equilibrium chemistry. UMPIRE employs an explicit MacCormack algorithm with dissipation introduced via Roe's flux-difference split upwind method. The code also has the capability to employ a point-implicit methodology for flows where stiffness is introduced through the chemical source term. A technique consisting of diagonal sweeps across the computational domain from each corner is presented, which is used to reduce storage and execution requirements. Results depicting one dimensional shock tube flow for both calorically perfect gas and thermally perfect, dissociating nitrogen are presented to verify current capabilities of the program. Also, computational results from a chemical reactor vessel with no fluid dynamic effects are presented to check the chemistry capability and to verify the point implicit strategy.

High-speed extended-term time-domain simulation for online cascading analysis of power system

NASA Astrophysics Data System (ADS)

Fu, Chuan

A high-speed extended-term (HSET) time domain simulator (TDS), intended to become a part of an energy management system (EMS), has been newly developed for use in online extended-term dynamic cascading analysis of power systems. HSET-TDS includes the following attributes for providing situational awareness of high-consequence events: (i) online analysis, including n-1 and n-k events, (ii) ability to simulate both fast and slow dynamics for 1-3 hours in advance, (iii) inclusion of rigorous protection-system modeling, (iv) intelligence for corrective action ID, storage, and fast retrieval, and (v) high-speed execution. Very fast on-line computational capability is the most desired attribute of this simulator. Based on the process of solving algebraic differential equations describing the dynamics of power system, HSET-TDS seeks to develop computational efficiency at each of the following hierarchical levels, (i) hardware, (ii) strategies, (iii) integration methods, (iv) nonlinear solvers, and (v) linear solver libraries. This thesis first describes the Hammer-Hollingsworth 4 (HH4) implicit integration method. Like the trapezoidal rule, HH4 is symmetrically A-Stable but it possesses greater high-order precision (h4 ) than the trapezoidal rule. Such precision enables larger integration steps and therefore improves simulation efficiency for variable step size implementations. This thesis provides the underlying theory on which we advocate use of HH4 over other numerical integration methods for power system time-domain simulation. Second, motivated by the need to perform high speed extended-term time domain simulation (HSET-TDS) for on-line purposes, this thesis presents principles for designing numerical solvers of differential algebraic systems associated with power system time-domain simulation, including DAE construction strategies (Direct Solution Method), integration methods(HH4), nonlinear solvers(Very Dishonest Newton), and linear solvers(SuperLU). We have implemented a design appropriate for HSET-TDS, and we compare it to various solvers, including the commercial grade PSSE program, with respect to computational efficiency and accuracy, using as examples the New England 39 bus system, the expanded 8775 bus system, and PJM 13029 buses system. Third, we have explored a stiffness-decoupling method, intended to be part of parallel design of time domain simulation software for super computers. The stiffness-decoupling method is able to combine the advantages of implicit methods (A-stability) and explicit method(less computation). With the new stiffness detection method proposed herein, the stiffness can be captured. The expanded 975 buses system is used to test simulation efficiency. Finally, several parallel strategies for super computer deployment to simulate power system dynamics are proposed and compared. Design A partitions the task via scale with the stiffness decoupling method, waveform relaxation, and parallel linear solver. Design B partitions the task via the time axis using a highly precise integration method, the Kuntzmann-Butcher Method - order 8 (KB8). The strategy of partitioning events is designed to partition the whole simulation via the time axis through a simulated sequence of cascading events. For all strategies proposed, a strategy of partitioning cascading events is recommended, since the sub-tasks for each processor are totally independent, and therefore minimum communication time is needed.

A weakly-compressible Cartesian grid approach for hydrodynamic flows

NASA Astrophysics Data System (ADS)

Bigay, P.; Oger, G.; Guilcher, P.-M.; Le Touzé, D.

2017-11-01

The present article aims at proposing an original strategy to solve hydrodynamic flows. In introduction, the motivations for this strategy are developed. It aims at modeling viscous and turbulent flows including complex moving geometries, while avoiding meshing constraints. The proposed approach relies on a weakly-compressible formulation of the Navier-Stokes equations. Unlike most hydrodynamic CFD (Computational Fluid Dynamics) solvers usually based on implicit incompressible formulations, a fully-explicit temporal scheme is used. A purely Cartesian grid is adopted for numerical accuracy and algorithmic simplicity purposes. This characteristic allows an easy use of Adaptive Mesh Refinement (AMR) methods embedded within a massively parallel framework. Geometries are automatically immersed within the Cartesian grid with an AMR compatible treatment. The method proposed uses an Immersed Boundary Method (IBM) adapted to the weakly-compressible formalism and imposed smoothly through a regularization function, which stands as another originality of this work. All these features have been implemented within an in-house solver based on this WCCH (Weakly-Compressible Cartesian Hydrodynamic) method which meets the above requirements whilst allowing the use of high-order (> 3) spatial schemes rarely used in existing hydrodynamic solvers. The details of this WCCH method are presented and validated in this article.

Implicit Space-Time Conservation Element and Solution Element Schemes

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung; Himansu, Ananda; Wang, Xiao-Yen

1999-01-01

Artificial numerical dissipation is in important issue in large Reynolds number computations. In such computations, the artificial dissipation inherent in traditional numerical schemes can overwhelm the physical dissipation and yield inaccurate results on meshes of practical size. In the present work, the space-time conservation element and solution element method is used to construct new and accurate implicit numerical schemes such that artificial numerical dissipation will not overwhelm physical dissipation. Specifically, these schemes have the property that numerical dissipation vanishes when the physical viscosity goes to zero. These new schemes therefore accurately model the physical dissipation even when it is extremely small. The new schemes presented are two highly accurate implicit solvers for a convection-diffusion equation. The two schemes become identical in the pure convection case, and in the pure diffusion case. The implicit schemes are applicable over the whole Reynolds number range, from purely diffusive equations to convection-dominated equations with very small viscosity. The stability and consistency of the schemes are analysed, and some numerical results are presented. It is shown that, in the inviscid case, the new schemes become explicit and their amplification factors are identical to those of the Leapfrog scheme. On the other hand, in the pure diffusion case, their principal amplification factor becomes the amplification factor of the Crank-Nicolson scheme.

Multigrid treatment of implicit continuum diffusion

NASA Astrophysics Data System (ADS)

Francisquez, Manaure; Zhu, Ben; Rogers, Barrett

2017-10-01

Implicit treatment of diffusive terms of various differential orders common in continuum mechanics modeling, such as computational fluid dynamics, is investigated with spectral and multigrid algorithms in non-periodic 2D domains. In doubly periodic time dependent problems these terms can be efficiently and implicitly handled by spectral methods, but in non-periodic systems solved with distributed memory parallel computing and 2D domain decomposition, this efficiency is lost for large numbers of processors. We built and present here a multigrid algorithm for these types of problems which outperforms a spectral solution that employs the highly optimized FFTW library. This multigrid algorithm is not only suitable for high performance computing but may also be able to efficiently treat implicit diffusion of arbitrary order by introducing auxiliary equations of lower order. We test these solvers for fourth and sixth order diffusion with idealized harmonic test functions as well as a turbulent 2D magnetohydrodynamic simulation. It is also shown that an anisotropic operator without cross-terms can improve model accuracy and speed, and we examine the impact that the various diffusion operators have on the energy, the enstrophy, and the qualitative aspect of a simulation. This work was supported by DOE-SC-0010508. This research used resources of the National Energy Research Scientific Computing Center (NERSC).

The behaviour of turbulence anisotropy through shock waves and expansions

NASA Technical Reports Server (NTRS)

Minh, H. H.; Kollmann, W.; Vandromme, D.

1985-01-01

A second order closure has been implemented in an implicit Navier-Stokes solver to study the behavior of the Reynolds stresses under the influence of severe pressure gradients. In the boundary layer zone, the strongly sheared character of the mean flow dominates the turbulence generation mechanisms. However, the pressure gradients play also a very important role for these processes, but at different locations within the boundary layer. This aspect may be emphasized by the analysis of turbulence anisotropy through shock waves and expansions.

Numerical solution of the two-dimensional time-dependent incompressible Euler equations

NASA Technical Reports Server (NTRS)

Whitfield, David L.; Taylor, Lafayette K.

1994-01-01

A numerical method is presented for solving the artificial compressibility form of the 2D time-dependent incompressible Euler equations. The approach is based on using an approximate Riemann solver for the cell face numerical flux of a finite volume discretization. Characteristic variable boundary conditions are developed and presented for all boundaries and in-flow out-flow situations. The system of algebraic equations is solved using the discretized Newton-relaxation (DNR) implicit method. Numerical results are presented for both steady and unsteady flow.

A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map

PubMed Central

Callegari, S.; Lake, G. R.; Tkachenko, N.; Weissmann, J. D.; Zollikofer, Ch. P. E.

2017-01-01

We describe a general Godunov-type splitting for numerical simulations of the Fisher–Kolmogorov–Petrovski–Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas. PMID:28085882

Method of Lines Transpose an Implicit Vlasov Maxwell Solver for Plasmas

DTIC Science & Technology

2015-04-17

boundary crossings should be rare. Numerical results for the Bennett pinch are given in Figure 9. In order to resolve large gradients near the center of the...contributing to the large error at the center of the beam due to large gradients there) and with the finite beam cut-off radius and the outflow boundary...usable time step size can be limited by the numerical accuracy of the method when there are large gradients (high-frequency content) in the solution. We

Computation of the unsteady facilitated transport of oxygen in hemoglobin

NASA Technical Reports Server (NTRS)

Davis, Sanford

1990-01-01

The transport of a reacting permeant diffusing through a thin membrane is extended to more realistic dissociation models. A new nonlinear analysis of the reaction-diffusion equations, using implicit finite-difference methods and direct block solvers, is used to study the limits of linearized and equilibrium theories. Computed curves of molecular oxygen permeating through hemoglobin solution are used to illustrate higher-order reaction models, the effect of concentration boundary layers at the membrane interfaces, and the transient buildup of oxygen flux.

Development of a Two-Dimensional/Axisymmetric Implicit Navier-Stokes Solver Using Flux-Difference Splitting Concepts and Fully General Geometry

DTIC Science & Technology

1985-09-01

Q+ + Q-)(A~tO~+ A~xei~+ A,fyfi~) + (R+ + R - ) (A~/tO ~ + A~/xein + AT/yfin ) - [A~x ev~ + A~ yfv ~ + a’lx ev~ q- A~y fv~] -t- O(A 2) 24 AEDC...8217 ~ - BAr Q+ + Q - A~t~ ~ + A/~xei~ (23) + A/~yfi~)+ ( R + + R-)(A~lt¢.~ + A~/xei.~ + A~yf.~)] + ~Ar(A~xev~ + A~ yfv ~ + A%ev, 1 + A~ yfv ~ + 0(A2

An Analysis of Elliptic Grid Generation Techniques Using an Implicit Euler Solver.

DTIC Science & Technology

1986-06-09

automatic determination of the control fu.nction, . elements of covariant metric tensor in the elliptic grid generation system , from the Cm = 1,2,3...computational fluid d’nan1-cs code. Tne code Inclues a tnree-dimensional current research is aimed primaril: at algebraic generation system based on transfinite...start the iterative solution of the f. ow, nea, transfer, and combustion proble:s. elliptic generation system . Tn13 feature also .:ven-.ts :.t be made

A numerical study of the contrarotating vortex pair associated with a jet in a crossflow

NASA Technical Reports Server (NTRS)

Roth, Karlin R.; Fearn, Richard L.; Thakur, Siddharth S.

1989-01-01

An implicit two-factor partially flux split solver for the thin-layer Navier-Stokes equations is used to solve the aerodynamic/propulsive interaction between a subsonic jet exhausting perpendicularly through a flat plat plate into a crossflow. The algorithm is applied to flows with a range of jet to crossflow velocity ratios between 4 and 8. The computed velocity field is analyzed and comparisons are made with experimentally determined properties of the contrarotating vortex pair.

A Stable Finite-Difference Scheme for Population Growth and Diffusion on a Map.

PubMed

Petersen, W P; Callegari, S; Lake, G R; Tkachenko, N; Weissmann, J D; Zollikofer, Ch P E

2017-01-01

We describe a general Godunov-type splitting for numerical simulations of the Fisher-Kolmogorov-Petrovski-Piskunov growth and diffusion equation on a world map with Neumann boundary conditions. The procedure is semi-implicit, hence quite stable. Our principal application for this solver is modeling human population dispersal over geographical maps with changing paleovegetation and paleoclimate in the late Pleistocene. As a proxy for carrying capacity we use Net Primary Productivity (NPP) to predict times for human arrival in the Americas.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Weston, Brian T.

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations ofmore » the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.« less

A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers.

PubMed

Cooper, Christopher D; Bardhan, Jaydeep P; Barba, L A

2014-03-01

The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known apbs finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the apbs solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is in the order of 1-2% error, when running on one gpu card (nvidia Tesla C2075), compared with apbs running on six Intel Xeon cpu cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using gpus via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.

A biomolecular electrostatics solver using Python, GPUs and boundary elements that can handle solvent-filled cavities and Stern layers

NASA Astrophysics Data System (ADS)

Cooper, Christopher D.; Bardhan, Jaydeep P.; Barba, L. A.

2014-03-01

The continuum theory applied to biomolecular electrostatics leads to an implicit-solvent model governed by the Poisson-Boltzmann equation. Solvers relying on a boundary integral representation typically do not consider features like solvent-filled cavities or ion-exclusion (Stern) layers, due to the added difficulty of treating multiple boundary surfaces. This has hindered meaningful comparisons with volume-based methods, and the effects on accuracy of including these features has remained unknown. This work presents a solver called PyGBe that uses a boundary-element formulation and can handle multiple interacting surfaces. It was used to study the effects of solvent-filled cavities and Stern layers on the accuracy of calculating solvation energy and binding energy of proteins, using the well-known APBS finite-difference code for comparison. The results suggest that if required accuracy for an application allows errors larger than about 2% in solvation energy, then the simpler, single-surface model can be used. When calculating binding energies, the need for a multi-surface model is problem-dependent, becoming more critical when ligand and receptor are of comparable size. Comparing with the APBS solver, the boundary-element solver is faster when the accuracy requirements are higher. The cross-over point for the PyGBe code is on the order of 1-2% error, when running on one GPU card (NVIDIA Tesla C2075), compared with APBS running on six Intel Xeon CPU cores. PyGBe achieves algorithmic acceleration of the boundary element method using a treecode, and hardware acceleration using GPUs via PyCuda from a user-visible code that is all Python. The code is open-source under MIT license.

libmpdata++ 1.0: a library of parallel MPDATA solvers for systems of generalised transport equations

NASA Astrophysics Data System (ADS)

Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

2015-04-01

This paper accompanies the first release of libmpdata++, a C++ library implementing the multi-dimensional positive-definite advection transport algorithm (MPDATA) on regular structured grid. The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; a shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

libmpdata++ 0.1: a library of parallel MPDATA solvers for systems of generalised transport equations

NASA Astrophysics Data System (ADS)

Jaruga, A.; Arabas, S.; Jarecka, D.; Pawlowska, H.; Smolarkiewicz, P. K.; Waruszewski, M.

2014-11-01

This paper accompanies first release of libmpdata++, a C++ library implementing the Multidimensional Positive-Definite Advection Transport Algorithm (MPDATA). The library offers basic numerical solvers for systems of generalised transport equations. The solvers are forward-in-time, conservative and non-linearly stable. The libmpdata++ library covers the basic second-order-accurate formulation of MPDATA, its third-order variant, the infinite-gauge option for variable-sign fields and a flux-corrected transport extension to guarantee non-oscillatory solutions. The library is equipped with a non-symmetric variational elliptic solver for implicit evaluation of pressure gradient terms. All solvers offer parallelisation through domain decomposition using shared-memory parallelisation. The paper describes the library programming interface, and serves as a user guide. Supported options are illustrated with benchmarks discussed in the MPDATA literature. Benchmark descriptions include code snippets as well as quantitative representations of simulation results. Examples of applications include: homogeneous transport in one, two and three dimensions in Cartesian and spherical domains; shallow-water system compared with analytical solution (originally derived for a 2-D case); and a buoyant convection problem in an incompressible Boussinesq fluid with interfacial instability. All the examples are implemented out of the library tree. Regardless of the differences in the problem dimensionality, right-hand-side terms, boundary conditions and parallelisation approach, all the examples use the same unmodified library, which is a key goal of libmpdata++ design. The design, based on the principle of separation of concerns, prioritises the user and developer productivity. The libmpdata++ library is implemented in C++, making use of the Blitz++ multi-dimensional array containers, and is released as free/libre and open-source software.

Numerical simulation of the solitary wave interacting with an elastic structure using MPS-FEM coupled method

NASA Astrophysics Data System (ADS)

Rao, Chengping; Zhang, Youlin; Wan, Decheng

2017-12-01

Fluid-Structure Interaction (FSI) caused by fluid impacting onto a flexible structure commonly occurs in naval architecture and ocean engineering. Research on the problem of wave-structure interaction is important to ensure the safety of offshore structures. This paper presents the Moving Particle Semi-implicit and Finite Element Coupled Method (MPS-FEM) to simulate FSI problems. The Moving Particle Semi-implicit (MPS) method is used to calculate the fluid domain, while the Finite Element Method (FEM) is used to address the structure domain. The scheme for the coupling of MPS and FEM is introduced first. Then, numerical validation and convergent study are performed to verify the accuracy of the solver for solitary wave generation and FSI problems. The interaction between the solitary wave and an elastic structure is investigated by using the MPS-FEM coupled method.

The ePLAS code for Ignition Studies

NASA Astrophysics Data System (ADS)

Faehl, R. J.; Mason, R. J.; Kirkpatrick, R. C.

2012-10-01

The ePLAS code is a multi-fluid/PIC hybrid developing self-consistent E & B-fields by the Implicit Moment Method for stable calculations of high density plasma problems with voids on the electron Courant time scale. See: http://www.researchapplicationscorp.com. Here, we outline typical applications to: 1) short pulse driven electron transport along void (or high Z) insulated wires, and 2) the 2D development of shock ignition pressure peaks with B-fields. We outline the code's recent inclusion of SESAME EOS data, a DT/DD burn capability, a new option for K-alpha imaging of modeling output, and demonstrate a foil expansion tracked with either fluid or particle ions. Also, we describe a new super-hybrid extension of our implicit solver that permits full target dynamics studies on the ion Courant scale. Finally, we will touch on the very recent application of ePLAS to possible non-local/kinetic hydro effects NIF capsules.

Accelerating Time Integration for the Shallow Water Equations on the Sphere Using GPUs

DOE PAGES

Archibald, R.; Evans, K. J.; Salinger, A.

2015-06-01

The push towards larger and larger computational platforms has made it possible for climate simulations to resolve climate dynamics across multiple spatial and temporal scales. This direction in climate simulation has created a strong need to develop scalable timestepping methods capable of accelerating throughput on high performance computing. This study details the recent advances in the implementation of implicit time stepping of the spectral element dynamical core within the United States Department of Energy (DOE) Accelerated Climate Model for Energy (ACME) on graphical processing units (GPU) based machines. We demonstrate how solvers in the Trilinos project are interfaced with ACMEmore » and GPU kernels to increase computational speed of the residual calculations in the implicit time stepping method for the atmosphere dynamics. We demonstrate the optimization gains and data structure reorganization that facilitates the performance improvements.« less

Parallel Implicit Runge-Kutta Methods Applied to Coupled Orbit/Attitude Propagation

NASA Astrophysics Data System (ADS)

Hatten, Noble; Russell, Ryan P.

2017-12-01

A variable-step Gauss-Legendre implicit Runge-Kutta (GLIRK) propagator is applied to coupled orbit/attitude propagation. Concepts previously shown to improve efficiency in 3DOF propagation are modified and extended to the 6DOF problem, including the use of variable-fidelity dynamics models. The impact of computing the stage dynamics of a single step in parallel is examined using up to 23 threads and 22 associated GLIRK stages; one thread is reserved for an extra dynamics function evaluation used in the estimation of the local truncation error. Efficiency is found to peak for typical examples when using approximately 8 to 12 stages for both serial and parallel implementations. Accuracy and efficiency compare favorably to explicit Runge-Kutta and linear-multistep solvers for representative scenarios. However, linear-multistep methods are found to be more efficient for some applications, particularly in a serial computing environment, or when parallelism can be applied across multiple trajectories.

Toward high-speed 3D nonlinear soft tissue deformation simulations using Abaqus software.

PubMed

Idkaidek, Ashraf; Jasiuk, Iwona

2015-12-01

We aim to achieve a fast and accurate three-dimensional (3D) simulation of a porcine liver deformation under a surgical tool pressure using the commercial finite element software Abaqus. The liver geometry is obtained using magnetic resonance imaging, and a nonlinear constitutive law is employed to capture large deformations of the tissue. Effects of implicit versus explicit analysis schemes, element type, and mesh density on computation time are studied. We find that Abaqus explicit and implicit solvers are capable of simulating nonlinear soft tissue deformations accurately using first-order tetrahedral elements in a relatively short time by optimizing the element size. This study provides new insights and guidance on accurate and relatively fast nonlinear soft tissue simulations. Such simulations can provide force feedback during robotic surgery and allow visualization of tissue deformations for surgery planning and training of surgical residents.

Identification of the gamma subunit-interacting residues on photoreceptor cGMP phosphodiesterase, PDE6alpha '.

PubMed

Granovsky, A E; Artemyev, N O

2000-12-29

Photoreceptor cGMP phosphodiesterase (PDE6) is the effector enzyme in the G protein-mediated visual transduction cascade. In the dark, the activity of PDE6 is shut off by the inhibitory gamma subunit (Pgamma). Chimeric proteins between cone PDE6alpha' and cGMP-binding and cGMP-specific PDE (PDE5) have been constructed and expressed in Sf9 cells to study the mechanism of inhibition of PDE6 catalytic activity by Pgamma. Substitution of the segment PDE5-(773-820) by the corresponding PDE6alpha'-(737-784) sequence in the wild-type PDE5 or in a PDE5/PDE6alpha' chimera containing the catalytic domain of PDE5 results in chimeric enzymes capable of inhibitory interaction with Pgamma. The catalytic properties of the chimeric PDEs remained similar to those of PDE5. Ala-scanning mutational analysis of the Pgamma-binding region, PDE6alpha'-(750-760), revealed PDE6alpha' residues essential for the interaction. The M758A mutation markedly impaired and the Q752A mutation moderately impaired the inhibition of chimeric PDE by Pgamma. The analysis of the catalytic properties of mutant PDEs and a model of the PDE6 catalytic domain suggest that residues Met(758) and Gln(752) directly bind Pgamma. A model of the PDE6 catalytic site shows that PDE6alpha'-(750-760) forms a loop at the entrance to the cGMP-binding pocket. Binding of Pgamma to Met(758) would effectively block access of cGMP to the catalytic cavity, providing a structural basis for the mechanism of PDE6 inhibition.

Cyclic AMP-specific phosphodiesterase-4 as a target for the development of antidepressant drugs.

PubMed

Zhang, Han-Ting

2009-01-01

Phosphodiesterase-4 (PDE4), one of eleven PDE enzyme families, specifically catalyzes hydrolysis of cyclic AMP (cAMP); it has four subtypes (PDE4A-D) with at least 25 splice variants. PDE4 plays a critical role in the control of intracellular cAMP concentrations. PDE4 inhibitors produce antidepressant actions in both animals and humans via enhancement of cAMP signaling in the brain. However, their clinical utility has been hampered by side effects, in particular nausea and emesis. While there is still a long way to go before PDE4 inhibitors with high therapeutic indices are available for treatment of depressive disorders, important advances have been made in the development of PDE4 inhibitors as antidepressants. First, limited, but significant studies point to PDE4D as the major PDE4 subtype responsible for antidepressant-like effects of PDE4 inhibitors, although the role of PDE4A cannot be excluded. Second, PDE4D may contribute to emesis, the major side effect of PDE4 inhibitors. For this reason, identification of roles of PDE4D splice variants in mediating antidepressant activity is particularly important. Recent studies using small interfering RNAs (siRNAs) have demonstrated the feasibility to identify cellular functions of individual PDE4 variants. Third, mixed inhibitors of PDE4 and PDE7 or PDE4 and serotonin reuptake have been developed and may be potential antidepressants with minimized side effects. Finally, relatively selective inhibitors of one or two PDE4 subtypes have been synthesized using structure- and scaffold-based design. This review also discusses the relationship between PDE4 and antidepressant activity based on structures, brain distributions, and pharmacological properties of PDE4 and its isoforms.

Nitric oxide-induced changes in endothelial expression of phosphodiesterases 2, 3, and 5.

PubMed

Schankin, Christoph J; Kruse, Lars S; Reinisch, Veronika M; Jungmann, Steffen; Kristensen, Julie C; Grau, Stefan; Ferrari, Uta; Sinicina, Inga; Goldbrunner, Roland; Straube, Andreas; Kruuse, Christina

2010-03-01

To investigate nitric oxide (NO)-mediated changes in expression of cyclic nucleotide degrading phosphodiesterases 2A (PDE2A), PDE3B, and PDE5A in human endothelial cells. Nitric oxide induces production of cyclic guanosine monophosphate (cGMP), which along with cyclic adenosine monophosphate (cAMP) is degraded by PDEs. NO donors and selective inhibitors of PDE3 and PDE5 induce migraine-like headache and play a role in endothelial dysfunction during stroke. The current study investigates possible NO modulation of cGMP-related PDEs relevant to headache induction in a cell line containing such PDEs. Real time polymerase chain reaction and Western blots were used to show expression of PDE2A, PDE3B, and PDE5A in a stable cell line of human brain microvascular endothelial cells. Effects of NO on PDE expression were analyzed at specific time intervals after continued DETA NONOate administration. This study shows the expression of PDE2A, PDE3B, and PDE5A mRNA and PDE3B and PDE5A protein in human cerebral endothelial cells. Long-term DETA NONOate administration induced an immediate mRNA up-regulation of PDE5A (1.9-fold, 0.5 hour), an early peak of PDE2A (1.4-fold, 1 and 2 hours) and later up-regulation of both PDE3B (1.6-fold, 4 hours) and PDE2A (1.7-fold, 8 hours and 1.2-fold after 24 hours). Such changes were, however, not translated into significant changes in protein expression indicating few, if any, functional effects. Long-term NO stimulation modulated PDE3 and PDE5 mRNA expression in endothelial cells. However, PDE3 and PDE5 protein levels were unaffected by NO. The presence of PDE3 or PDE5 in endothelial cells indicates that selective inhibitors may have functional effects in such cells. A complex interaction of cGMP and cAMP in response to NO administration may take place if the mRNA translates into active protein. Whether or not this plays a role in the headache mechanisms remains to be investigated.

Implicit time accurate simulation of unsteady flow

NASA Astrophysics Data System (ADS)

van Buuren, René; Kuerten, Hans; Geurts, Bernard J.

2001-03-01

Implicit time integration was studied in the context of unsteady shock-boundary layer interaction flow. With an explicit second-order Runge-Kutta scheme, a reference solution to compare with the implicit second-order Crank-Nicolson scheme was determined. The time step in the explicit scheme is restricted by both temporal accuracy as well as stability requirements, whereas in the A-stable implicit scheme, the time step has to obey temporal resolution requirements and numerical convergence conditions. The non-linear discrete equations for each time step are solved iteratively by adding a pseudo-time derivative. The quasi-Newton approach is adopted and the linear systems that arise are approximately solved with a symmetric block Gauss-Seidel solver. As a guiding principle for properly setting numerical time integration parameters that yield an efficient time accurate capturing of the solution, the global error caused by the temporal integration is compared with the error resulting from the spatial discretization. Focus is on the sensitivity of properties of the solution in relation to the time step. Numerical simulations show that the time step needed for acceptable accuracy can be considerably larger than the explicit stability time step; typical ratios range from 20 to 80. At large time steps, convergence problems that are closely related to a highly complex structure of the basins of attraction of the iterative method may occur. Copyright

Studies of numerical algorithms for gyrokinetics and the effects of shaping on plasma turbulence

NASA Astrophysics Data System (ADS)

Belli, Emily Ann

Advanced numerical algorithms for gyrokinetic simulations are explored for more effective studies of plasma turbulent transport. The gyrokinetic equations describe the dynamics of particles in 5-dimensional phase space, averaging over the fast gyromotion, and provide a foundation for studying plasma microturbulence in fusion devices and in astrophysical plasmas. Several algorithms for Eulerian/continuum gyrokinetic solvers are compared. An iterative implicit scheme based on numerical approximations of the plasma response is developed. This method reduces the long time needed to set-up implicit arrays, yet still has larger time step advantages similar to a fully implicit method. Various model preconditioners and iteration schemes, including Krylov-based solvers, are explored. An Alternating Direction Implicit algorithm is also studied and is surprisingly found to yield a severe stability restriction on the time step. Overall, an iterative Krylov algorithm might be the best approach for extensions of core tokamak gyrokinetic simulations to edge kinetic formulations and may be particularly useful for studies of large-scale ExB shear effects. The effects of flux surface shape on the gyrokinetic stability and transport of tokamak plasmas are studied using the nonlinear GS2 gyrokinetic code with analytic equilibria based on interpolations of representative JET-like shapes. High shaping is found to be a stabilizing influence on both the linear ITG instability and nonlinear ITG turbulence. A scaling of the heat flux with elongation of chi ˜ kappa-1.5 or kappa-2 (depending on the triangularity) is observed, which is consistent with previous gyrofluid simulations. Thus, the GS2 turbulence simulations are explaining a significant fraction, but not all, of the empirical elongation scaling. The remainder of the scaling may come from (1) the edge boundary conditions for core turbulence, and (2) the larger Dimits nonlinear critical temperature gradient shift due to the enhancement of zonal flows with shaping, which is observed with the GS2 simulations. Finally, a local linear trial function-based gyrokinetic code is developed to aid in fast scoping studies of gyrokinetic linear stability. This code is successfully benchmarked with the full GS2 code in the collisionless, electrostatic limit, as well as in the more general electromagnetic description with higher-order Hermite basis functions.

A consistent spatial differencing scheme for the transonic full-potential equation in three dimensions

NASA Technical Reports Server (NTRS)

Thomas, S. D.; Holst, T. L.

1985-01-01

A full-potential steady transonic wing flow solver has been modified so that freestream density and residual are captured in regions of constant velocity. This numerically precise freestream consistency is obtained by slightly altering the differencing scheme without affecting the implicit solution algorithm. The changes chiefly affect the fifteen metrics per grid point, which are computed once and stored. With this new method, the outer boundary condition is captured accurately, and the smoothness of the solution is especially improved near regions of grid discontinuity.

Adaptive Mesh Refinement in Curvilinear Body-Fitted Grid Systems

NASA Technical Reports Server (NTRS)

Steinthorsson, Erlendur; Modiano, David; Colella, Phillip

1995-01-01

To be truly compatible with structured grids, an AMR algorithm should employ a block structure for the refined grids to allow flow solvers to take advantage of the strengths of unstructured grid systems, such as efficient solution algorithms for implicit discretizations and multigrid schemes. One such algorithm, the AMR algorithm of Berger and Colella, has been applied to and adapted for use with body-fitted structured grid systems. Results are presented for a transonic flow over a NACA0012 airfoil (AGARD-03 test case) and a reflection of a shock over a double wedge.

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

NASA Technical Reports Server (NTRS)

Woodard, Paul R.; Batina, John T.; Yang, Henry T. Y.

1992-01-01

Quality assessment procedures are described for two-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate accuracy of an implicit upwind Euler solution algorithm.

Multitasking the INS3D-LU code on the Cray Y-MP

NASA Technical Reports Server (NTRS)

Fatoohi, Rod; Yoon, Seokkwan

1991-01-01

This paper presents the results of multitasking the INS3D-LU code on eight processors. The code is a full Navier-Stokes solver for incompressible fluid in three dimensional generalized coordinates using a lower-upper symmetric-Gauss-Seidel implicit scheme. This code has been fully vectorized on oblique planes of sweep and parallelized using autotasking with some directives and minor modifications. The timing results for five grid sizes are presented and analyzed. The code has achieved a processing rate of over one Gflops.

Characteristics of the Shuttle Orbiter Leeside Flow During A Reentry Condition

NASA Technical Reports Server (NTRS)

Kleb, William L.; Weilmuenster, K. James

1992-01-01

A study of the leeside flow characteristics of the Shuttle Orbiter is presented for a reentry flight condition. The flow is computed using a point-implicit, finite-volume scheme known as the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA). LAURA is a second-order accurate, laminar Navier-Stokes solver, incorporating finite-rate chemistry with a radiative equilibrium wall temperature distribution and finite-rate wall catalysis. The resulting computational solution is analyzed in terms of salient flow features and the surface quantities are compared with flight data.

Exactly energy conserving semi-implicit particle in cell formulation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lapenta, Giovanni, E-mail: giovanni.lapenta@kuleuven.be

We report a new particle in cell (PIC) method based on the semi-implicit approach. The novelty of the new method is that unlike any of its semi-implicit predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. Recent research has presented fully implicit methods where energy conservation is obtained as part of a non-linear iteration procedure. The new method (referred to as Energy Conserving Semi-Implicit Method, ECSIM), instead, does not require any non-linear iteration and its computational cycle is similar to that of explicit PIC. The properties of the new method are: i) it conservesmore » energy exactly to round-off for any time step or grid spacing; ii) it is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency and allowing the user to select any desired time step; iii) it eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length; iv) the particle mover has a computational complexity identical to that of the explicit PIC, only the field solver has an increased computational cost. The new ECSIM is tested in a number of benchmarks where accuracy and computational performance are tested. - Highlights: • We present a new fully energy conserving semi-implicit particle in cell (PIC) method based on the implicit moment method (IMM). The new method is called Energy Conserving Implicit Moment Method (ECIMM). • The novelty of the new method is that unlike any of its predecessors at the same time it retains the explicit computational cycle and conserves energy exactly. • The new method is unconditionally stable in time, freeing the user from the need to resolve the electron plasma frequency. • The new method eliminates the constraint of the finite grid instability, allowing the user to select any desired resolution without being forced to resolve the Debye length. • These features are achieved at a reduced cost compared with either previous IMM or fully implicit implementation of PIC.« less

Multiphase three-dimensional direct numerical simulation of a rotating impeller with code Blue

NASA Astrophysics Data System (ADS)

Kahouadji, Lyes; Shin, Seungwon; Chergui, Jalel; Juric, Damir; Craster, Richard V.; Matar, Omar K.

2017-11-01

The flow driven by a rotating impeller inside an open fixed cylindrical cavity is simulated using code Blue, a solver for massively-parallel simulations of fully three-dimensional multiphase flows. The impeller is composed of four blades at a 45° inclination all attached to a central hub and tube stem. In Blue, solid forms are constructed through the definition of immersed objects via a distance function that accounts for the object's interaction with the flow for both single and two-phase flows. We use a moving frame technique for imposing translation and/or rotation. The variation of the Reynolds number, the clearance, and the tank aspect ratio are considered, and we highlight the importance of the confinement ratio (blade radius versus the tank radius) in the mixing process. Blue uses a domain decomposition strategy for parallelization with MPI. The fluid interface solver is based on a parallel implementation of a hybrid front-tracking/level-set method designed complex interfacial topological changes. Parallel GMRES and multigrid iterative solvers are applied to the linear systems arising from the implicit solution for the fluid velocities and pressure in the presence of strong density and viscosity discontinuities across fluid phases. EPSRC, UK, MEMPHIS program Grant (EP/K003976/1), RAEng Research Chair (OKM).

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

NASA Technical Reports Server (NTRS)

Carton De Wiart, Corentin; Diosady, Laslo T.; Garai, Anirban; Burgess, Nicholas; Blonigan, Patrick; Ekelschot, Dirk; Murman, Scott M.

2018-01-01

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

The high-affinity phosphodiesterase PdeH regulates development and aflatoxin biosynthesis in Aspergillus flavus.

PubMed

Yang, Kunlong; Liu, Yinghang; Liang, Linlin; Li, Zhenguo; Qin, Qiuping; Nie, Xinyi; Wang, Shihua

2017-04-01

Cyclic AMP signaling controls a range of physiological processes in response to extracellular stimuli in organisms. Among the signaling cascades, cAMP, as a second messenger, is orchestrated by adenylate cyclase (biosynthesis) and cAMP phosphodiesterases (PDEs) (hydrolysis). In this study, we investigated the function of the high-affinity (PdeH) and low-affinity (PdeL) cAMP phosphodiesterase from the carcinogenic aflatoxin producing fungus Aspergillus flavus, and found that instead of PdeL, inactivation of PdeH exhibited a reduction in conidiation and sclerotia formation. However, the ΔpdeL/ΔpdeH mutant exhibited an enhanced phenotype defects, a similar phenotype defects to wild-type strain treated with exogenous cAMP. The activation of PKA activity was inhibited in the ΔpdeH or ΔpdeL/ΔpdeH mutant, both of whom exhibited increasing AF production. Further analysis by qRT-PCR revealed that pdeH had a high transcriptional level compared to pdeL in wild-type strain, and affected pdeL transcription. Green fluorescent protein tagging at the C-terminus of PDEs showed that PdeH-GFP is broadly compartmentalized in the cytosol, while PdeL-GFP localized mainly to the nucleus. Overall, our results indicated that PdeH plays a major role, but has overlapping function with PdeL, in vegetative growth, development and AF biosynthesis in A. flavus. Copyright © 2017 The Author(s). Published by Elsevier Inc. All rights reserved.

Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes

NASA Technical Reports Server (NTRS)

Movriplis, Dimitri J.

1998-01-01

Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach is developed which employs directional implicit smoothing with regular fully coarsened multigrid levels. The directional implicit smoothing is obtained by constructing implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergence rates over the traditional explicit full-coarsening multigrid algorithm. However, maximum benefits are achieved by combining the two approaches in a coupled manner into a single algorithm. An order of magnitude increase in convergence rate over the traditional explicit full-coarsening algorithm is demonstrated, and convergence rates for high-Reynolds number viscous flows which are independent of the grid aspect ratio are obtained. Further acceleration is provided by incorporating low-Mach-number preconditioning techniques, and a Newton-GMRES strategy which employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is documented through several example test cases.

A scalable, fully implicit algorithm for the reduced two-field low-β extended MHD model

DOE PAGES

Chacon, Luis; Stanier, Adam John

2016-12-01

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

An Energy- and Charge-conserving, Implicit, Electrostatic Particle-in-Cell Algorithm in curvilinear geometry

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.; Barnes, D. C.

2012-03-01

A recent proof-of-principle study proposes an energy- and charge-conserving, fully implicit particle-in-cell algorithm in one dimension [1], which is able to use timesteps comparable to the dynamical timescale of interest. Here, we generalize the method to employ non-uniform meshes via a curvilinear map. The key enabling technology is a hybrid particle pusher [2], with particle positions updated in logical space and particle velocities updated in physical space. The self-adaptive, charge-conserving particle mover of Ref. [1] is extended to the non-uniform mesh case. The fully implicit implementation, using a Jacobian-free Newton-Krylov iterative solver, remains exactly charge- and energy-conserving. The extension of the formulation to multiple dimensions will be discussed. We present numerical experiments of 1D electrostatic, long-timescale ion-acoustic wave and ion-acoustic shock wave simulations, demonstrating that charge and energy are conserved to round-off for arbitrary mesh non-uniformity, and that the total momentum remains well conserved.[4pt] [1] Chen, Chac'on, Barnes, J. Comput. Phys. 230 (2011). [0pt] [2] Camporeale and Delzanno, Bull. Am. Phys. Soc. 56(6) (2011); Wang, et al., J. Plasma Physics, 61 (1999).

Human PDE4D isoform composition is deregulated in primary prostate cancer and indicative for disease progression and development of distant metastases

PubMed Central

Böttcher, René; Dulla, Kalyan; van Strijp, Dianne; Dits, Natasja; Verhoef, Esther I.; Baillie, George S.; van Leenders, Geert J.L.H.; Houslay, Miles D.; Jenster, Guido; Hoffmann, Ralf

2016-01-01

Phosphodiesterase 4D7 was recently shown to be specifically over-expressed in localized prostate cancer, raising the question as to which regulatory mechanisms are involved and whether other isoforms of this gene family (PDE4D) are affected under the same conditions. We investigated PDE4D isoform composition in prostatic tissues using a total of seven independent expression datasets and also included data on DNA methylation, copy number and AR and ERG binding in PDE4D promoters to gain insight into their effect on PDE4D transcription. We show that expression of PDE4D isoforms is consistently altered in primary human prostate cancer compared to benign tissue, with PDE4D7 being up-regulated while PDE4D5 and PDE4D9 are down-regulated. Disease progression is marked by an overall down-regulation of long PDE4D isoforms, while short isoforms (PDE4D1/2) appear to be relatively unaffected. While these alterations seem to be independent of copy number alterations in the PDE4D locus and driven by AR and ERG binding, we also observed increased DNA methylation in the promoter region of PDE4D5, indicating a long lasting alteration of the isoform composition in prostate cancer tissues. We propose two independent metrics that may serve as diagnostic and prognostic markers for prostate disease: (PDE4D7 - PDE4D5) provides an effective means for distinguishing PCa from normal adjacent prostate, whereas PDE4D1/2 - (PDE4D5 + PDE4D7 + PDE4D9) offers strong prognostic potential to detect aggressive forms of PCa and is associated with metastasis free survival. Overall, our findings highlight the relevance of PDE4D as prostate cancer biomarker and potential drug target. PMID:27683107

Online learning in optical tomography: a stochastic approach

NASA Astrophysics Data System (ADS)

Chen, Ke; Li, Qin; Liu, Jian-Guo

2018-07-01

We study the inverse problem of radiative transfer equation (RTE) using stochastic gradient descent method (SGD) in this paper. Mathematically, optical tomography amounts to recovering the optical parameters in RTE using the incoming–outgoing pair of light intensity. We formulate it as a PDE-constraint optimization problem, where the mismatch of computed and measured outgoing data is minimized with same initial data and RTE constraint. The memory and computation cost it requires, however, is typically prohibitive, especially in high dimensional space. Smart iterative solvers that only use partial information in each step is called for thereafter. Stochastic gradient descent method is an online learning algorithm that randomly selects data for minimizing the mismatch. It requires minimum memory and computation, and advances fast, therefore perfectly serves the purpose. In this paper we formulate the problem, in both nonlinear and its linearized setting, apply SGD algorithm and analyze the convergence performance.

Implicit methods for efficient musculoskeletal simulation and optimal control

PubMed Central

van den Bogert, Antonie J.; Blana, Dimitra; Heinrich, Dieter

2011-01-01

The ordinary differential equations for musculoskeletal dynamics are often numerically stiff and highly nonlinear. Consequently, simulations require small time steps, and optimal control problems are slow to solve and have poor convergence. In this paper, we present an implicit formulation of musculoskeletal dynamics, which leads to new numerical methods for simulation and optimal control, with the expectation that we can mitigate some of these problems. A first order Rosenbrock method was developed for solving forward dynamic problems using the implicit formulation. It was used to perform real-time dynamic simulation of a complex shoulder arm system with extreme dynamic stiffness. Simulations had an RMS error of only 0.11 degrees in joint angles when running at real-time speed. For optimal control of musculoskeletal systems, a direct collocation method was developed for implicitly formulated models. The method was applied to predict gait with a prosthetic foot and ankle. Solutions were obtained in well under one hour of computation time and demonstrated how patients may adapt their gait to compensate for limitations of a specific prosthetic limb design. The optimal control method was also applied to a state estimation problem in sports biomechanics, where forces during skiing were estimated from noisy and incomplete kinematic data. Using a full musculoskeletal dynamics model for state estimation had the additional advantage that forward dynamic simulations, could be done with the same implicitly formulated model to simulate injuries and perturbation responses. While these methods are powerful and allow solution of previously intractable problems, there are still considerable numerical challenges, especially related to the convergence of gradient-based solvers. PMID:22102983

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dumbser, Michael, E-mail: michael.dumbser@unitn.it; Balsara, Dinshaw S., E-mail: dbalsara@nd.edu

In this paper a new, simple and universal formulation of the HLLEM Riemann solver (RS) is proposed that works for general conservative and non-conservative systems of hyperbolic equations. For non-conservative PDE, a path-conservative formulation of the HLLEM RS is presented for the first time in this paper. The HLLEM Riemann solver is built on top of a novel and very robust path-conservative HLL method. It thus naturally inherits the positivity properties and the entropy enforcement of the underlying HLL scheme. However, with just the slight additional cost of evaluating eigenvectors and eigenvalues of intermediate characteristic fields, we can represent linearlymore » degenerate intermediate waves with a minimum of smearing. For conservative systems, our paper provides the easiest and most seamless path for taking a pre-existing HLL RS and quickly and effortlessly converting it to a RS that provides improved results, comparable with those of an HLLC, HLLD, Osher or Roe-type RS. This is done with minimal additional computational complexity, making our variant of the HLLEM RS also a very fast RS that can accurately represent linearly degenerate discontinuities. Our present HLLEM RS also transparently extends these advantages to non-conservative systems. For shallow water-type systems, the resulting method is proven to be well-balanced. Several test problems are presented for shallow water-type equations and two-phase flow models, as well as for gas dynamics with real equation of state, magnetohydrodynamics (MHD & RMHD), and nonlinear elasticity. Since our new formulation accommodates multiple intermediate waves and has a broader applicability than the original HLLEM method, it could alternatively be called the HLLI Riemann solver, where the “I” stands for the intermediate characteristic fields that can be accounted for. -- Highlights: •New simple and general path-conservative formulation of the HLLEM Riemann solver. •Application to general conservative and non-conservative hyperbolic systems. •Inclusion of sub-structure and resolution of intermediate characteristic fields. •Well-balanced for single- and two-layer shallow water equations and multi-phase flows. •Euler equations with real equation of state, MHD equations, nonlinear elasticity.« less

Extending fields in a level set method by solving a biharmonic equation

NASA Astrophysics Data System (ADS)

Moroney, Timothy J.; Lusmore, Dylan R.; McCue, Scott W.; McElwain, D. L. Sean

2017-08-01

We present an approach for computing extensions of velocities or other fields in level set methods by solving a biharmonic equation. The approach differs from other commonly used approaches to velocity extension because it deals with the interface fully implicitly through the level set function. No explicit properties of the interface, such as its location or the velocity on the interface, are required in computing the extension. These features lead to a particularly simple implementation using either a sparse direct solver or a matrix-free conjugate gradient solver. Furthermore, we propose a fast Poisson preconditioner that can be used to accelerate the convergence of the latter. We demonstrate the biharmonic extension on a number of test problems that serve to illustrate its effectiveness at producing smooth and accurate extensions near interfaces. A further feature of the method is the natural way in which it deals with symmetry and periodicity, ensuring through its construction that the extension field also respects these symmetries.

Flexible Inhibitor Fluid-Structure Interaction Simulation in RSRM.

NASA Astrophysics Data System (ADS)

Wasistho, Bono

2005-11-01

We employ our tightly coupled fluid/structure/combustion simulation code 'Rocstar-3' for solid propellant rocket motors to study 3D flows past rigid and flexible inhibitors in the Reusable Solid Rocket Motor (RSRM). We perform high resolution simulations of a section of the rocket near the center joint slot at 100 seconds after ignition, using inflow conditions based on less detailed 3D simulations of the full RSRM. Our simulations include both inviscid and turbulent flows (using LES dynamic subgrid-scale model), and explore the interaction between the inhibitor and the resulting fluid flow. The response of the solid components is computed by an implicit finite element solver. The internal mesh motion scheme in our block-structured fluid solver enables our code to handle significant changes in geometry. We compute turbulent statistics and determine the compound instabilities originated from the natural hydrodynamic instabilities and the inhibitor motion. The ultimate goal is to studdy the effect of inhibitor flexing on the turbulent field.

Function-Space-Based Solution Scheme for the Size-Modified Poisson-Boltzmann Equation in Full-Potential DFT.

PubMed

Ringe, Stefan; Oberhofer, Harald; Hille, Christoph; Matera, Sebastian; Reuter, Karsten

2016-08-09

The size-modified Poisson-Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green's function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

Higher Order Time Integration Schemes for the Unsteady Navier-Stokes Equations on Unstructured Meshes

NASA Technical Reports Server (NTRS)

Jothiprasad, Giridhar; Mavriplis, Dimitri J.; Caughey, David A.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The efficiency gains obtained using higher-order implicit Runge-Kutta schemes as compared with the second-order accurate backward difference schemes for the unsteady Navier-Stokes equations are investigated. Three different algorithms for solving the nonlinear system of equations arising at each timestep are presented. The first algorithm (NMG) is a pseudo-time-stepping scheme which employs a non-linear full approximation storage (FAS) agglomeration multigrid method to accelerate convergence. The other two algorithms are based on Inexact Newton's methods. The linear system arising at each Newton step is solved using iterative/Krylov techniques and left preconditioning is used to accelerate convergence of the linear solvers. One of the methods (LMG) uses Richardson's iterative scheme for solving the linear system at each Newton step while the other (PGMRES) uses the Generalized Minimal Residual method. Results demonstrating the relative superiority of these Newton's methods based schemes are presented. Efficiency gains as high as 10 are obtained by combining the higher-order time integration schemes with the more efficient nonlinear solvers.

Cloning and characterization of a cAMP-specific phosphodiesterase (TbPDE2B) from Trypanosoma brucei

PubMed Central

Rascón, Ana; Soderling, Scott H.; Schaefer, Jonathan B.; Beavo, Joseph A.

2002-01-01

Here we report the cloning, expression, and characterization of a cAMP-specific phosphodiesterase (PDE) from Trypanosoma brucei (TbPDE2B). Using a bioinformatic approach, two different expressed sequence tag clones were identified and used to isolate the complete sequence of two identical PDE genes arranged in tandem. Each gene consists of 2,793 bases that predict a protein of 930 aa with a molecular mass of 103.2 kDa. Two GAF (for cGMP binding and stimulated PDEs, Anabaena adenylyl cyclases, and Escherichia coli FhlA) domains, similar to those contained in many signaling molecules including mammalian PDE2, PDE5, PDE6, PDE10, and PDE11, were located N-terminal to a consensus PDE catalytic domain. The catalytic domain is homologous to the catalytic domain of all 11 mammalian PDEs, the Dictyostelium discoideum RegA, and a probable PDE from Caenorhabditis elegans. It is most similar to the T. brucei PDE2A (89% identity). TbPDE2B has substrate specificity for cAMP with a Km of 2.4 μM. cGMP is not hydrolyzed by TbPDE2B nor does this cyclic nucleotide modulate cAMP PDE activity. The nonselective PDE inhibitors 3-isobutyl-1-methylxanthine, papaverine and pentoxifyline are poor inhibitors of TbPDE2B. Similarly, PDE inhibitors selective for the mammalian PDE families 2, 3, 5, and 6 (erythro-9-[3-(2-hydroxynonyl)]-adenine, enoximone, zaprinast, and sildenafil) were also unable to inhibit this enzyme. However, dipyridamole was a reasonably good inhibitor of this enzyme with an IC50 of 27 μM. cAMP plays key roles in cell growth and differentiation in this parasite, and PDEs are responsible for the hydrolysis of this important second messenger. Therefore, parasite PDEs, including this one, have the potential to be attractive targets for selective drug design. PMID:11930017

Treatment of charge singularities in implicit solvent models.

PubMed

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-21

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2 A for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

Treatment of charge singularities in implicit solvent models

NASA Astrophysics Data System (ADS)

Geng, Weihua; Yu, Sining; Wei, Guowei

2007-09-01

This paper presents a novel method for solving the Poisson-Boltzmann (PB) equation based on a rigorous treatment of geometric singularities of the dielectric interface and a Green's function formulation of charge singularities. Geometric singularities, such as cusps and self-intersecting surfaces, in the dielectric interfaces are bottleneck in developing highly accurate PB solvers. Based on an advanced mathematical technique, the matched interface and boundary (MIB) method, we have recently developed a PB solver by rigorously enforcing the flux continuity conditions at the solvent-molecule interface where geometric singularities may occur. The resulting PB solver, denoted as MIBPB-II, is able to deliver second order accuracy for the molecular surfaces of proteins. However, when the mesh size approaches half of the van der Waals radius, the MIBPB-II cannot maintain its accuracy because the grid points that carry the interface information overlap with those that carry distributed singular charges. In the present Green's function formalism, the charge singularities are transformed into interface flux jump conditions, which are treated on an equal footing as the geometric singularities in our MIB framework. The resulting method, denoted as MIBPB-III, is able to provide highly accurate electrostatic potentials at a mesh as coarse as 1.2Å for proteins. Consequently, at a given level of accuracy, the MIBPB-III is about three times faster than the APBS, a recent multigrid PB solver. The MIBPB-III has been extensively validated by using analytically solvable problems, molecular surfaces of polyatomic systems, and 24 proteins. It provides reliable benchmark numerical solutions for the PB equation.

Analytic Approximations to the Free Boundary and Multi-dimensional Problems in Financial Derivatives Pricing

NASA Astrophysics Data System (ADS)

Lau, Chun Sing

This thesis studies two types of problems in financial derivatives pricing. The first type is the free boundary problem, which can be formulated as a partial differential equation (PDE) subject to a set of free boundary condition. Although the functional form of the free boundary condition is given explicitly, the location of the free boundary is unknown and can only be determined implicitly by imposing continuity conditions on the solution. Two specific problems are studied in details, namely the valuation of fixed-rate mortgages and CEV American options. The second type is the multi-dimensional problem, which involves multiple correlated stochastic variables and their governing PDE. One typical problem we focus on is the valuation of basket-spread options, whose underlying asset prices are driven by correlated geometric Brownian motions (GBMs). Analytic approximate solutions are derived for each of these three problems. For each of the two free boundary problems, we propose a parametric moving boundary to approximate the unknown free boundary, so that the original problem transforms into a moving boundary problem which can be solved analytically. The governing parameter of the moving boundary is determined by imposing the first derivative continuity condition on the solution. The analytic form of the solution allows the price and the hedging parameters to be computed very efficiently. When compared against the benchmark finite-difference method, the computational time is significantly reduced without compromising the accuracy. The multi-stage scheme further allows the approximate results to systematically converge to the benchmark results as one recasts the moving boundary into a piecewise smooth continuous function. For the multi-dimensional problem, we generalize the Kirk (1995) approximate two-asset spread option formula to the case of multi-asset basket-spread option. Since the final formula is in closed form, all the hedging parameters can also be derived in closed form. Numerical examples demonstrate that the pricing and hedging errors are in general less than 1% relative to the benchmark prices obtained by numerical integration or Monte Carlo simulation. By exploiting an explicit relationship between the option price and the underlying probability distribution, we further derive an approximate distribution function for the general basket-spread variable. It can be used to approximate the transition probability distribution of any linear combination of correlated GBMs. Finally, an implicit perturbation is applied to reduce the pricing errors by factors of up to 100. When compared against the existing methods, the basket-spread option formula coupled with the implicit perturbation turns out to be one of the most robust and accurate approximation methods.

A hybrid incremental projection method for thermal-hydraulics applications

NASA Astrophysics Data System (ADS)

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.; Berndt, Markus; Francois, Marianne M.; Stagg, Alan K.; Xia, Yidong; Luo, Hong

2016-07-01

A new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya-Babuška-Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie-Chow interpolation or by using a Petrov-Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes, and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.

A hybrid incremental projection method for thermal-hydraulics applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes,more » and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.« less

A hybrid incremental projection method for thermal-hydraulics applications

DOE PAGES

Christon, Mark A.; Bakosi, Jozsef; Nadiga, Balasubramanya T.; ...

2016-07-01

In this paper, a new second-order accurate, hybrid, incremental projection method for time-dependent incompressible viscous flow is introduced in this paper. The hybrid finite-element/finite-volume discretization circumvents the well-known Ladyzhenskaya–Babuška–Brezzi conditions for stability, and does not require special treatment to filter pressure modes by either Rhie–Chow interpolation or by using a Petrov–Galerkin finite element formulation. The use of a co-velocity with a high-resolution advection method and a linearly consistent edge-based treatment of viscous/diffusive terms yields a robust algorithm for a broad spectrum of incompressible flows. The high-resolution advection method is shown to deliver second-order spatial convergence on mixed element topology meshes,more » and the implicit advective treatment significantly increases the stable time-step size. The algorithm is robust and extensible, permitting the incorporation of features such as porous media flow, RANS and LES turbulence models, and semi-/fully-implicit time stepping. A series of verification and validation problems are used to illustrate the convergence properties of the algorithm. The temporal stability properties are demonstrated on a range of problems with 2 ≤ CFL ≤ 100. The new flow solver is built using the Hydra multiphysics toolkit. The Hydra toolkit is written in C++ and provides a rich suite of extensible and fully-parallel components that permit rapid application development, supports multiple discretization techniques, provides I/O interfaces, dynamic run-time load balancing and data migration, and interfaces to scalable popular linear solvers, e.g., in open-source packages such as HYPRE, PETSc, and Trilinos.« less

Pharmacophore Based Virtual Screening Approach to Identify Selective PDE4B Inhibitors

PubMed Central

Gaurav, Anand; Gautam, Vertika

2017-01-01

Phosphodiesterase 4 (PDE4) has been established as a promising target in asthma and chronic obstructive pulmonary disease. PDE4B subtype selective inhibitors are known to reduce the dose limiting adverse effect associated with non-selective PDE4B inhibitors. This makes the development of PDE4B subtype selective inhibitors a desirable research goal. To achieve this goal, ligand based pharmacophore modeling approach is employed. Separate pharmacophore hypotheses for PDE4B and PDE4D inhibitors were generated using HypoGen algorithm and 106 PDE4 inhibitors from literature having thiopyrano [3,2-d] Pyrimidines, 2-arylpyrimidines, and triazines skeleton. Suitable training and test sets were created using the molecules as per the guidelines available for HypoGen program. Training set was used for hypothesis development while test set was used for validation purpose. Fisher validation was also used to test the significance of the developed hypothesis. The validated pharmacophore hypotheses for PDE4B and PDE4D inhibitors were used in sequential virtual screening of zinc database of drug like molecules to identify selective PDE4B inhibitors. The hits were screened for their estimated activity and fit value. The top hit was subjected to docking into the active sites of PDE4B and PDE4D to confirm its selectivity for PDE4B. The hits are proposed to be evaluated further using in-vitro assays. PMID:29201082

Partial reconstitution of photoreceptor cGMP phosphodiesterase characteristics in cGMP phosphodiesterase-5.

PubMed

Granovsky, A E; Artemyev, N O

2001-06-15

Photoreceptor cGMP phosphodiesterases (PDE6) are uniquely qualified to serve as effector enzymes in the vertebrate visual transduction cascade. In the dark-adapted photoreceptors, the activity of PDE6 is blocked via tight association with the inhibitory gamma-subunits (Pgamma). The Pgamma block is removed in the light-activated PDE6 by the visual G protein, transducin. Transducin-activated PDE6 exhibits an exceptionally high catalytic rate of cGMP hydrolysis ensuring high signal amplification. To identify the structural determinants for the inhibitory interaction with Pgamma and the remarkable cGMP hydrolytic ability, we sought to reproduce the PDE6 characteristics by mutagenesis of PDE5, a related cyclic GMP-specific, cGMP-binding PDE. PDE5 is insensitive to Pgamma and has a more than 100-fold lower k(cat) for cGMP hydrolysis. Our mutational analysis of chimeric PDE5/PDE6alpha' enzymes revealed that the inhibitory interaction of cone PDE6 catalytic subunits (PDE6alpha') with Pgamma is mediated primarily by three hydrophobic residues at the entry to the catalytic pocket, Met(758), Phe(777), and Phe(781). The maximal catalytic rate of PDE5 was enhanced by at least 10-fold with substitutions of PDE6alpha'-specific glycine residues for the corresponding PDE5 alanine residues, Ala(608) and Ala(612). The Gly residues are adjacent to the highly conserved metal binding motif His-Asn-X-X-His, which is essential for cGMP hydrolysis. Our results suggest that the unique Gly residues allow the PDE6 metal binding site to adopt a more favorable conformation for cGMP hydrolysis.

Phosphodiesterase 4 regulates the migration of B16-F10 melanoma cells.

PubMed

Watanabe, Yoshihiro; Murata, Taku; Shimizu, Kasumi; Morita, Hiroshi; Inui, Madoka; Tagawa, Toshiro

2012-08-01

Phosphodiesterases (PDEs) are important regulators of signal transduction processes. Eleven PDE gene families (PDE1-11) have been identified and several PDE isoforms are selectively expressed in various cell types. PDE4 family members specifically hydrolyze cyclic AMP (cAMP). Four genes (PDE4A-D) are known to encode PDE4 enzymes, with additional diversity generated by the use of alternative mRNA splicing and the use of different promoters. While PDE4 selective inhibitors show therapeutic potential for treating major diseases such as asthma and chronic obstructive pulmonary disease, little is known concerning the role of PDE4 in malignant melanoma. In this study, we examined the role of PDE4 in mouse B16-F10 melanoma cells. In these cells, PDE4 activity was found to be ∼60% of total PDE activity. RT-PCR detected only PDE4B and PDE4D mRNA. Cell growth was inhibited by the cAMP analog, 8-bromo-cAMP, but not by the specific PDE4 inhibitors, rolipram and denbufylline, which increased intracellular cAMP concentrations. Finally, migration of the B16-F10 cells was inhibited by the PDE4 inhibitors and 8-bromo-cAMP, while migration was increased by a protein kinase A (PKA) inhibitor, PKI(14-22), and was not affected by 8-pCPT-2'-O-Me-cAMP, which is an analog of exchange protein activated by cAMP (Epac). The inhibitory effect of rolipram on migration was reversed by PKI(14-22). Based on these results, PDE4 appears to play an important role in the migration of B16-F10 cells, and therefore may be a novel target for the treatment of malignant melanoma.

Direct interaction of the inhibitory gamma-subunit of Rod cGMP phosphodiesterase (PDE6) with the PDE6 GAFa domains.

PubMed

Muradov, Khakim G; Granovsky, Alexey E; Schey, Kevin L; Artemyev, Nikolai O

2002-03-26

Retinal rod and cone cGMP phosphodiesterases (PDE6 family) function as the effector enzyme in the vertebrate visual transduction cascade. The activity of PDE6 catalytic subunits is controlled by the Pgamma-subunits. In addition to the inhibition of cGMP hydrolysis at the catalytic sites, Pgamma is known to stimulate a noncatalytic binding of cGMP to the regulatory GAFa-GAFb domains of PDE6. The latter role of Pgamma has been attributed to its polycationic region. To elucidate the structural basis for the regulation of cGMP binding to the GAF domains of PDE6, a photoexcitable peptide probe corresponding to the polycationic region of Pgamma, Pgamma-21-45, was specifically cross-linked to rod PDE6alphabeta. The site of Pgamma-21-45 cross-linking was localized to Met138Gly139 within the PDE6alpha GAFa domain using mass spectrometric analysis. Chimeras between PDE5 and cone PDE6alpha', containing GAFa and/or GAFb domains of PDE6alpha' have been generated to probe a potential role of the GAFb domains in binding to Pgamma. Analysis of the inhibition of the PDE5/PDE6alpha' chimeras by Pgamma supported the role of PDE6 GAFa but not GAFb domains in the interaction with Pgamma. Our results suggest that a direct binding of the polycationic region of Pgamma to the GAFa domains of PDE6 may lead to a stabilization of the noncatalytic cGMP-binding sites.

Targeted Ablation of the Pde6h Gene in Mice Reveals Cross-species Differences in Cone and Rod Phototransduction Protein Isoform Inventory*

PubMed Central

Brennenstuhl, Christina; Tanimoto, Naoyuki; Burkard, Markus; Wagner, Rebecca; Bolz, Sylvia; Trifunovic, Dragana; Kabagema-Bilan, Clement; Paquet-Durand, Francois; Beck, Susanne C.; Huber, Gesine; Seeliger, Mathias W.; Ruth, Peter; Wissinger, Bernd; Lukowski, Robert

2015-01-01

Phosphodiesterase-6 (PDE6) is a multisubunit enzyme that plays a key role in the visual transduction cascade in rod and cone photoreceptors. Each type of photoreceptor utilizes discrete catalytic and inhibitory PDE6 subunits to fulfill its physiological tasks, i.e. the degradation of cyclic guanosine-3′,5′-monophosphate at specifically tuned rates and kinetics. Recently, the human PDE6H gene was identified as a novel locus for autosomal recessive (incomplete) color blindness. However, the three different classes of cones were not affected to the same extent. Short wave cone function was more preserved than middle and long wave cone function indicating that some basic regulation of the PDE6 multisubunit enzyme was maintained albeit by a unknown mechanism. To study normal and disease-related functions of cone Pde6h in vivo, we generated Pde6h knock-out (Pde6h−/−) mice. Expression of PDE6H in murine eyes was restricted to both outer segments and synaptic terminals of short and long/middle cone photoreceptors, whereas Pde6h−/− retinae remained PDE6H-negative. Combined in vivo assessment of retinal morphology with histomorphological analyses revealed a normal overall integrity of the retinal organization and an unaltered distribution of the different cone photoreceptor subtypes upon Pde6h ablation. In contrast to human patients, our electroretinographic examinations of Pde6h−/− mice suggest no defects in cone/rod-driven retinal signaling and therefore preserved visual functions. To this end, we were able to demonstrate the presence of rod PDE6G in cones indicating functional substitution of PDE6. The disparities between human and murine phenotypes caused by mutant Pde6h/PDE6H suggest species-to-species differences in the vulnerability of biochemical and neurosensory pathways of the visual signal transduction system. PMID:25739440

Effects of PDE4 Pathway Inhibition in Rat Experimental Stroke

PubMed Central

Yang, Fan; Sumbria, Rachita K.; Xue, Dong; Yu, Chuanhui; He, Dan; Liu, Shuo; Paganini-Hill, Annlia; Fisher, Mark J.

2015-01-01

PURPOSE The first genomewide association study indicated that variations in the phosphodiesterase 4D (PDE4D) gene confer risk for ischemic stroke. However, inconsistencies among the studies designed to replicate the findings indicated the need for further investigation to elucidate the role of the PDE4 pathway in stroke pathogenesis. Hence, we studied the effect of global inhibition of the PDE4 pathway in two rat experimental stroke models, using the PDE4 inhibitor rolipram. Further, the specific role of the PDE4D isoform in ischemic stroke pathogenesis was studied using PDE4D knockout rats in experimental stroke. METHODS Rats were subjected to either the ligation or embolic stroke model and treated with rolipram (3mg/kg; i.p.) prior to the ischemic insult. Similarly, the PDE4D knockout rats were subjected to experimental stroke using the embolic model. RESULTS Global inhibition of the PDE4 pathway using rolipram produced infarcts that were 225% (p<0.01) and 138% (p<0.05) of control in the ligation and embolic models, respectively. PDE4D knockout rats subjected to embolic stroke showed no change in infarct size compared to wild-type control. CONCLUSIONS Despite increase in infarct size after global inhibition of the PDE4 pathway with rolipram, specific inhibition of the PDE4D isoform had no effect on experimental stroke. These findings support a role for the PDE4 pathway, independent of the PDE4D isoform, in ischemic stroke pathogenesis. PMID:25224348

Fully Coupled Aero-Thermochemical-Elastic Simulations of an Eroding Graphite Nozzle

NASA Technical Reports Server (NTRS)

Blades, E. L.; Reveles, N. D.; Nucci, M.; Maclean, M.

2017-01-01

A multiphysics simulation capability has been developed that incorporates mutual interactions between aerodynamics, structural response from aero/thermal loading, ablation/pyrolysis, heating, and surface-to-surface radiation to perform high-fidelity, fully coupled aerothermoelastic ablation simulations, which to date had been unattainable. The multiphysics framework couples CHAR (a 3-D implicit charring ablator solver), Loci/CHEM (a computational fluid dynamics solver for high-speed chemically reacting flows), and Abaqus (a nonlinear structural dynamics solver) to create a fully coupled aerothermoelastic charring ablative solver. The solvers are tightly coupled in a fully integrated fashion to resolve the effects of the ablation pyrolysis and charring process and chemistry products upon the flow field, the changes in surface geometry due to recession upon the flow field, and thermal-structural analysis of the body from the induced aerodynamic heating from the flow field. The multiphysics framework was successfully demonstrated on a solid rocket motor graphite nozzle erosion application. Comparisons were made with available experimental data that measured the throat erosion during the motor firing. The erosion data is well characterized, as the test rig was equipped with a windowed nozzle section for real-time X-ray radiography diagnostics of the instantaneous throat variations for deducing the instantaneous erosion rates. The nozzle initially undergoes a nozzle contraction due to thermal expansion before ablation effects are able to widen the throat. A series of parameters studies were conducted using the coupled simulation capability to determine the sensitivity of the nozzle erosion to different parameters. The parameter studies included the shape of the nozzle throat (flat versus rounded), the material properties, the effect of the choice of turbulence model, and the inclusion or exclusion of the mechanical thermal expansion. Overall, the predicted results match the experiment very well, and the predictions were able to bound the data within acceptable limits.

Extending substructure based iterative solvers to multiple load and repeated analyses

NASA Technical Reports Server (NTRS)

Farhat, Charbel

1993-01-01

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

Mutation in rod PDE6 linked to congenital stationary night blindness impairs the enzyme inhibition by its gamma-subunit.

PubMed

Muradov, Khakim G; Granovsky, Alexey E; Artemyev, Nikolai O

2003-03-25

Photoreceptor cGMP phosphodiesterase (PDE6) is the effector enzyme in the vertebrate visual transduction cascade. The activity of rod PDE6 catalytic alpha- and beta-subunits is blocked in the dark by two inhibitory Pgamma-subunits. The inhibition is released upon light-stimulation of photoreceptor cells. Mutation H258N in PDE6beta has been linked to congenital stationary night blindness (CSNB) in a large Danish family (Rambusch pedigree) (Gal, A., Orth, U., Baehr, W., Schwinger, E., and Rosenberg, T. (1994) Nat. Genet. 7, 64-67.) We have analyzed the consequences of this mutation for PDE6 function using a Pgamma-sensitive PDE6alpha'/PDE5 chimera, Chi16. Biochemical analysis of the H257N mutant, an equivalent of PDE6betaH258N, demonstrates that this substitution does not alter the ability of chimeric PDE to dimerize or the enzyme's catalytic properties. The sensitivity of H257N to a competitive inhibitor zaprinast was also unaffected. However, the mutant displayed a significant impairment in the inhibitory interaction with Pgamma, which was apparent from a approximately 20-fold increase in the K(i) value (46 nM) and incomplete maximal inhibition. The inhibitory defect of H257N is not due to perturbation of noncatalytic cGMP binding to the PDE6alpha' GAF domains. The noncatalytic cGMP-binding characteristics of the H257N mutant were similar to those of the parent PDE6alpha'/PDE5 chimera. Since rod PDE6 in the Rambusch CSNB is a catalytic heterodimer of the wild-type PDE6alpha and mutant PDE6beta, Chi16 and H257N were coexpressed, and a heterodimeric PDE, Chi16/H257N, was isolated. It displayed two Pgamma inhibitory sites with the K(i) values of 5 and 57 nM. Our results support the hypothesis that mutation H258N in PDE6beta causes CSNB through incomplete inhibition of PDE6 activity by Pgamma, which leads to desensitization of rod photoreceptors.

An energy- and charge-conserving, nonlinearly implicit, electromagnetic 1D-3V Vlasov-Darwin particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2014-10-01

A recent proof-of-principle study proposes a nonlinear electrostatic implicit particle-in-cell (PIC) algorithm in one dimension (Chen et al., 2011). The algorithm employs a kinetically enslaved Jacobian-free Newton-Krylov (JFNK) method, and conserves energy and charge to numerical round-off. In this study, we generalize the method to electromagnetic simulations in 1D using the Darwin approximation to Maxwell's equations, which avoids radiative noise issues by ordering out the light wave. An implicit, orbit-averaged, time-space-centered finite difference scheme is employed in both the 1D Darwin field equations (in potential form) and the 1D-3V particle orbit equations to produce a discrete system that remains exactly charge- and energy-conserving. Furthermore, enabled by the implicit Darwin equations, exact conservation of the canonical momentum per particle in any ignorable direction is enforced via a suitable scattering rule for the magnetic field. We have developed a simple preconditioner that targets electrostatic waves and skin currents, and allows us to employ time steps O(√{mi /me } c /veT) larger than the explicit CFL. Several 1D numerical experiments demonstrate the accuracy, performance, and conservation properties of the algorithm. In particular, the scheme is shown to be second-order accurate, and CPU speedups of more than three orders of magnitude vs. an explicit Vlasov-Maxwell solver are demonstrated in the "cold" plasma regime (where kλD ≪ 1).

Benchmarking the Multidimensional Stellar Implicit Code MUSIC

NASA Astrophysics Data System (ADS)

Goffrey, T.; Pratt, J.; Viallet, M.; Baraffe, I.; Popov, M. V.; Walder, R.; Folini, D.; Geroux, C.; Constantino, T.

2017-04-01

We present the results of a numerical benchmark study for the MUltidimensional Stellar Implicit Code (MUSIC) based on widely applicable two- and three-dimensional compressible hydrodynamics problems relevant to stellar interiors. MUSIC is an implicit large eddy simulation code that uses implicit time integration, implemented as a Jacobian-free Newton Krylov method. A physics based preconditioning technique which can be adjusted to target varying physics is used to improve the performance of the solver. The problems used for this benchmark study include the Rayleigh-Taylor and Kelvin-Helmholtz instabilities, and the decay of the Taylor-Green vortex. Additionally we show a test of hydrostatic equilibrium, in a stellar environment which is dominated by radiative effects. In this setting the flexibility of the preconditioning technique is demonstrated. This work aims to bridge the gap between the hydrodynamic test problems typically used during development of numerical methods and the complex flows of stellar interiors. A series of multidimensional tests were performed and analysed. Each of these test cases was analysed with a simple, scalar diagnostic, with the aim of enabling direct code comparisons. As the tests performed do not have analytic solutions, we verify MUSIC by comparing it to established codes including ATHENA and the PENCIL code. MUSIC is able to both reproduce behaviour from established and widely-used codes as well as results expected from theoretical predictions. This benchmarking study concludes a series of papers describing the development of the MUSIC code and provides confidence in future applications.

AKAP3 Selectively Binds PDE4A Isoforms in Bovine Spermatozoa1

PubMed Central

Bajpai, Malini; Fiedler, Sarah E.; Huang, Zaohua; Vijayaraghavan, Srinivasan; Olson, Gary E.; Livera, Gabriel; Conti, Marco; Carr, Daniel W.

2006-01-01

Cyclic AMP plays an important role in regulating sperm motility and acrosome reaction through activation of cAMP-dependent protein kinase A (PKA). Phosphodiesterases (PDEs) modulate the levels of cyclic nucleotides by catalyzing their degradation. Although PDE inhibitors specific to PDE1 and PDE4 are known to alter sperm motility and capacitation in humans, little is known about the role or subcellular distribution of PDEs in spermatozoa. The localization of PKA is regulated by A-kinase anchoring proteins (AKAPs), which may also control the intracellular distribution of PDE. The present study was undertaken to investigate the role and localization of PDE4 during sperm capacitation. Addition of Rolipram or RS25344, PDE4-specific inhibitors significantly increased the progressive motility of bovine spermatozoa. Immunolocalization techniques detected both PDE4A and AKAP3 (formerly known as AKAP110) in the principal piece of bovine spermatozoa. The PDE4A5 isoform was detected primarily in the Triton X-100-soluble fraction of caudal epididymal spermatozoa. However, in ejaculated spermatozoa it was seen primarily in the SDS-soluble fraction, indicating a shift in PDE4A5 localization into insoluble organelles during sperm capacitation. AKAP3 was detected only in the SDS-soluble fraction of both caudal and ejaculated sperm. Immunoprecipitation experiments using COS cells cotransfected with AKAP3 and either Pde4a5 or Pde4d provide evidence that PDE4A5 but not PDE4D interacts with AKAP3. Pulldown assays using sperm cell lysates confirm this interaction in vitro. These data suggest that AKAP3 binds both PKA and PDE4A and functions as a scaffolding protein in spermatozoa to regulate local cAMP concentrations and modulate sperm functions. PMID:16177223

Estimating the magnitude of near-membrane PDE4 activity in living cells.

PubMed

Xin, Wenkuan; Feinstein, Wei P; Britain, Andrea L; Ochoa, Cristhiaan D; Zhu, Bing; Richter, Wito; Leavesley, Silas J; Rich, Thomas C

2015-09-15

Recent studies have demonstrated that functionally discrete pools of phosphodiesterase (PDE) activity regulate distinct cellular functions. While the importance of localized pools of enzyme activity has become apparent, few studies have estimated enzyme activity within discrete subcellular compartments. Here we present an approach to estimate near-membrane PDE activity. First, total PDE activity is measured using traditional PDE activity assays. Second, known cAMP concentrations are dialyzed into single cells and the spatial spread of cAMP is monitored using cyclic nucleotide-gated channels. Third, mathematical models are used to estimate the spatial distribution of PDE activity within cells. Using this three-tiered approach, we observed two pharmacologically distinct pools of PDE activity, a rolipram-sensitive pool and an 8-methoxymethyl IBMX (8MM-IBMX)-sensitive pool. We observed that the rolipram-sensitive PDE (PDE4) was primarily responsible for cAMP hydrolysis near the plasma membrane. Finally, we observed that PDE4 was capable of blunting cAMP levels near the plasma membrane even when 100 μM cAMP were introduced into the cell via a patch pipette. Two compartment models predict that PDE activity near the plasma membrane, near cyclic nucleotide-gated channels, was significantly lower than total cellular PDE activity and that a slow spatial spread of cAMP allowed PDE activity to effectively hydrolyze near-membrane cAMP. These results imply that cAMP levels near the plasma membrane are distinct from those in other subcellular compartments; PDE activity is not uniform within cells; and localized pools of AC and PDE activities are responsible for controlling cAMP levels within distinct subcellular compartments. Copyright © 2015 the American Physiological Society.

Kaempferia parviflora, a plant used in traditional medicine to enhance sexual performance contains large amounts of low affinity PDE5 inhibitors

PubMed Central

Temkitthawon, Prapapan; Hinds, Thomas R.; Beavo, Joseph A.; Viyoch, Jarupa; Suwanborirux, Khanit; Pongamornkul, Wittaya; Sawasdee, Pattara; Ingkaninan, Kornkanok

2014-01-01

Aim of the study A number of medicinal plants are used in traditional medicine to treat erectile dysfunction. Since cyclic nucleotide PDEs inhibitors underlie several current treatments for this condition, we sought to show whether these plants might contain substantial amounts of PDE5 inhibitors. Materials and methods Forty one plant extracts and eight 7-methoxyflavones from Kaempferia parviflora Wall. ex Baker were screened for PDE5 and PDE6 inhibitory activities using the two-step radioactive assay. The PDE5 and PDE6 were prepared from mice lung and chicken retinas, respectively. All plant extracts were tested at 50 μg/ml whereas the pure compounds were tested at 10 μM. Results From forty one plant extracts tested, four showed the PDE5 inhibitory effect. The chemical constituents isolated from rhizomes of Kaempferia parviflora were further investigated on inhibitory activity against PDE5 and PDE6. The results showed that 7-methoxyflavones from this plant showed inhibition toward both enzymes. The most potent PDE5 inhibitor was 5,7-dimethoxyflavone (IC50 = 10.64 ± 2.09 μM, selectivity on PDE5 over PDE6 = 3.71). Structure activity relationship showed that the methoxyl group at C-5 position of 7-methoxyflavones was necessary for PDE5 inhibition. Conclusions Kaempferia parviflora rhizome extract and its 7-methoxyflavone constituents had moderate inhibitory activity against PDE5. This finding provides an explanation for enhancing sexual performance in the traditional use of Kaempferia parviflora. Moreover, 5,7-dimethoxyflavones should make a useful lead compound to further develop clinically efficacious PDE5 inhibitors. PMID:21884777

Mice deficient in phosphodiesterase-4A display anxiogenic-like behavior.

PubMed

Hansen, Rolf T; Conti, Marco; Zhang, Han-Ting

2014-08-01

Phosphodiesterases (PDEs) are a super family of enzymes responsible for the halting of intracellular cyclic nucleotide signaling and may represent novel therapeutic targets for treatment of cognitive disorders. PDE4 is of considerable interest to cognitive research because it is highly expressed in the brain, particularly in the cognition-related brain regions. Recently, the functional role of PDE4B and PDE4D, two of the four PDE4 subtypes (PDE4A, B, C, and D), in behavior has begun to be identified; however, the role of PDE4A in the regulation of behavior is still unknown. The purpose of this study was to characterize the functional role of PDE4A in behavior. The role of PDE4A in behavior was evaluated through a battery of behavioral tests using PDE4A knockout (KO) mice; urine corticosterone levels were also measured. PDE4A KO mice exhibited improved memory in the step-through-passive-avoidance test. They also displayed anxiogenic-like behavior in elevated-plus maze, holeboard, light-dark transition, and novelty suppressed feeding tests. Consistent with the anxiety profile, PDE4A KO mice had elevated corticosterone levels compared with wild-type controls post-stress. Interestingly, PDE4A KO mice displayed no change in object recognition, Morris water maze, forced swim, tail suspension, and duration of anesthesia induced by co-administration of xylazine and ketamine (suggesting that PDE4A KO may not be emetic). These results suggest that PDE4A may be important in the regulation of emotional memory and anxiety-like behavior, but not emesis. PDE4A could possibly represent a novel therapeutic target in the future for anxiety or disorders affecting memory.

A conformational switch in the inhibitory gamma-subunit of PDE6 upon enzyme activation by transducin.

PubMed

Granovsky, A E; Artemyev, N O

2001-11-06

In response to light, a photoreceptor G protein, transducin, activates cGMP-phosphodiesterase (PDE6) by displacing the inhibitory gamma-subunits (Pgamma) from the enzyme's catalytic sites. Evidence suggests that the activation of PDE6 involves a conformational change of the key inhibitory C-terminal domain of Pgamma. In this study, the C-terminal region of Pgamma, Pgamma-73-85, has been targeted for Ala-scanning mutagenesis to identify the point-to-point interactions between Pgamma and the PDE6 catalytic subunits and to probe the nature of the conformational change. Pgamma mutants were tested for their ability to inhibit PDE6 and a chimeric PDE5-conePDE6 enzyme containing the Pgamma C-terminus-binding site of cone PDE. This analysis has revealed that in addition to previously characterized Ile86 and Ile87, important inhibitory contact residues of Pgamma include Asn74, His75, and Leu78. The patterns of mutant PDE5-conePDE6 enzyme inhibition suggest the interaction between the PgammaAsn74/His75 sequence and Met758 of the cone PDE6alpha' catalytic subunit. This interaction, and the interaction between the PgammaIle86/Ile87 and PDE6alpha'Phe777/Phe781 residues, is most consistent with an alpha-helical structure of the Pgamma C-terminus. The analysis of activation of PDE6 enzymes containing Pgamma mutants with Ala-substituted transducin-contact residues demonstrated the critical role of PgammaLeu76. Accordingly, we hypothesize that the initial step in PDE6 activation involves an interaction of transducin-alpha with PgammaLeu76. This interaction introduces a bend into the alpha-helical structure of the Pgamma C-terminus, allowing transducin-alpha to further twist the C-terminus thereby uncovering the catalytic pocket of PDE6.

Estimating the magnitude of near-membrane PDE4 activity in living cells

PubMed Central

Xin, Wenkuan; Feinstein, Wei P.; Britain, Andrea L.; Ochoa, Cristhiaan D.; Zhu, Bing; Richter, Wito; Leavesley, Silas J.

2015-01-01

Recent studies have demonstrated that functionally discrete pools of phosphodiesterase (PDE) activity regulate distinct cellular functions. While the importance of localized pools of enzyme activity has become apparent, few studies have estimated enzyme activity within discrete subcellular compartments. Here we present an approach to estimate near-membrane PDE activity. First, total PDE activity is measured using traditional PDE activity assays. Second, known cAMP concentrations are dialyzed into single cells and the spatial spread of cAMP is monitored using cyclic nucleotide-gated channels. Third, mathematical models are used to estimate the spatial distribution of PDE activity within cells. Using this three-tiered approach, we observed two pharmacologically distinct pools of PDE activity, a rolipram-sensitive pool and an 8-methoxymethyl IBMX (8MM-IBMX)-sensitive pool. We observed that the rolipram-sensitive PDE (PDE4) was primarily responsible for cAMP hydrolysis near the plasma membrane. Finally, we observed that PDE4 was capable of blunting cAMP levels near the plasma membrane even when 100 μM cAMP were introduced into the cell via a patch pipette. Two compartment models predict that PDE activity near the plasma membrane, near cyclic nucleotide-gated channels, was significantly lower than total cellular PDE activity and that a slow spatial spread of cAMP allowed PDE activity to effectively hydrolyze near-membrane cAMP. These results imply that cAMP levels near the plasma membrane are distinct from those in other subcellular compartments; PDE activity is not uniform within cells; and localized pools of AC and PDE activities are responsible for controlling cAMP levels within distinct subcellular compartments. PMID:26201952

cAMP-specific PDE4 Phosphodiesterases and AIP in the Pathogenesis of Pituitary Tumors

PubMed Central

Bolger, Graeme B.; Bizzi, Mariana Ferreira; Brant Pinheiro, Sergio Veloso; Trivellin, Giampaolo; Smoot, Lisa; Accavitti, Mary-Ann; Korbonits, Márta; Ribeiro-Oliveira, Antonio

2016-01-01

PDE4 cyclic nucleotide phosphodiesterases regulate cAMP abundance in cells and thereby regulate numerous processes, including cell growth and differentiation. The rat PDE4A5 isoform (human homologue PDE4A4) interacts with the AIP protein (also called XAP2 or ARA-9). Germline mutations in AIP occur in approximately 20% of patients with Familial Isolated Pituitary Adenoma (FIPA) and 20% of childhood-onset simplex somatotroph adenomas. We therefore examined the protein expression of PDE4A4 and the closely-related isoform PDE4A8 in normal human pituitary tissue and in pituitary adenomas. PDE4A4 had low expression in normal pituitary, but was significantly over-expressed in somatotroph, lactotroph, corticotroph and clinically non-functioning gonadotroph adenomas (P<0.0001 for all subtypes). Likewise, PDE4A8 was expressed in normal pituitary and was also significantly over-expressed in the adenoma subtypes (P<0.0001 for all). Among the different adenoma subtypes, corticotroph and lactotroph adenomas were the highest and lowest expressed for PDE4A4, respectively, whereas the opposite was observed for PDE4A8. Naturally occurring oncogenic variants in AIP were shown by a two-hybrid assay to disrupt the ability of AIP to interact with PDE4A5. A reverse-two-hybrid screen identified numerous additional variants in the TPR region of AIP that also disrupted its ability to interact with PDE4A5. The expression of PDE4A4 and PDE4A8 in normal pituitary, their increased expression in adenomatous pituitary cells where AIP is meant to participate, and the disruption of the PDE4A4-AIP interaction by AIP mutants may play a role in pituitary tumorigenesis. PMID:27267386

Three-dimensional calculations of rotor-airframe interaction in forward flight

NASA Technical Reports Server (NTRS)

Zori, Laith A. J.; Mathur, Sanjay R.; Rajagopalan, R. G.

1992-01-01

A method for analyzing the mutual aerodynamic interaction between a rotor and an airframe model has been developed. This technique models the rotor implicitly through the source terms of the momentum equations. A three-dimensional, incompressible, laminar, Navier-Stokes solver in cylindrical coordinates was developed for analyzing the rotor/airframe problem. The calculations are performed on a simplified model at an advance ratio of 0.1. The airframe surface pressure predictions are found to be in good agreement with wind tunnel test data. Results are presented for velocity and pressure field distributions in the wake of the rotor.

The block adaptive multigrid method applied to the solution of the Euler equations

NASA Technical Reports Server (NTRS)

Pantelelis, Nikos

1993-01-01

In the present study, a scheme capable of solving very fast and robust complex nonlinear systems of equations is presented. The Block Adaptive Multigrid (BAM) solution method offers multigrid acceleration and adaptive grid refinement based on the prediction of the solution error. The proposed solution method was used with an implicit upwind Euler solver for the solution of complex transonic flows around airfoils. Very fast results were obtained (18-fold acceleration of the solution) using one fourth of the volumes of a global grid with the same solution accuracy for two test cases.

Quality assessment of two- and three-dimensional unstructured meshes and validation of an upwind Euler flow solver

NASA Technical Reports Server (NTRS)

Woodard, Paul R.; Yang, Henry T. Y.; Batina, John T.

1992-01-01

Quality assessment procedures are described for two-dimensional and three-dimensional unstructured meshes. The procedures include measurement of minimum angles, element aspect ratios, stretching, and element skewness. Meshes about the ONERA M6 wing and the Boeing 747 transport configuration are generated using an advancing front method grid generation package of programs. Solutions of Euler's equations for these meshes are obtained at low angle-of-attack, transonic conditions. Results for these cases, obtained as part of a validation study demonstrate the accuracy of an implicit upwind Euler solution algorithm.

An assessment of computational fluid dynamic techniques in the analysis and design of turbomachinery - The 1990 Freeman Scholar Lecture

NASA Technical Reports Server (NTRS)

Lakshminarayana, B.

1991-01-01

Various computational fluid dynamic techniques are reviewed focusing on the Euler and Navier-Stokes solvers with a brief assessment of boundary layer solutions, and quasi-3D and quasi-viscous techniques. Particular attention is given to a pressure-based method, explicit and implicit time marching techniques, a pseudocompressibility technique for incompressible flow, and zonal techniques. Recommendations are presented with regard to the most appropriate technique for various flow regimes and types of turbomachinery, incompressible and compressible flows, cascades, rotors, stators, liquid-handling, and gas-handling turbomachinery.

Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

NASA Astrophysics Data System (ADS)

Philip, B.; Wang, Z.; Berrill, M. A.; Birke, M.; Pernice, M.

2014-04-01

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton-Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

Development of advanced Navier-Stokes solver

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan

1994-01-01

The objective of research was to develop and validate new computational algorithms for solving the steady and unsteady Euler and Navier-Stokes equations. The end-products are new three-dimensional Euler and Navier-Stokes codes that are faster, more reliable, more accurate, and easier to use. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible/incompressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. Convergence rates and the robustness of the codes are enhanced by the use of an implicit full approximation storage multigrid method.

Effect of analysis parameters on non-linear implicit finite element analysis of marine corroded steel plate

NASA Astrophysics Data System (ADS)

Islam, Muhammad Rabiul; Sakib-Ul-Alam, Md.; Nazat, Kazi Kaarima; Hassan, M. Munir

2017-12-01

FEA results greatly depend on analysis parameters. MSC NASTRAN nonlinear implicit analysis code has been used in large deformation finite element analysis of pitted marine SM490A steel rectangular plate. The effect of two types actual pit shape on parameters of integrity of structure has been analyzed. For 3-D modeling, a proposed method for simulation of pitted surface by probabilistic corrosion model has been used. The result has been verified with the empirical formula proposed by finite element analysis of steel surface generated with different pitted data where analyses have been carried out by the code of LS-DYNA 971. In the both solver, an elasto-plastic material has been used where an arbitrary stress versus strain curve can be defined. In the later one, the material model is based on the J2 flow theory with isotropic hardening where a radial return algorithm is used. The comparison shows good agreement between the two results which ensures successful simulation with comparatively less energy and time.

An adaptive, implicit, conservative, 1D-2V multi-species Vlasov-Fokker-Planck multi-scale solver in planar geometry

NASA Astrophysics Data System (ADS)

Taitano, W. T.; Chacón, L.; Simakov, A. N.

2018-07-01

We consider a 1D-2V Vlasov-Fokker-Planck multi-species ionic description coupled to fluid electrons. We address temporal stiffness with implicit time stepping, suitably preconditioned. To address temperature disparity in time and space, we extend the conservative adaptive velocity-space discretization scheme proposed in [Taitano et al., J. Comput. Phys., 318, 391-420, (2016)] to a spatially inhomogeneous system. In this approach, we normalize the velocity-space coordinate to a temporally and spatially varying local characteristic speed per species. We explicitly consider the resulting inertial terms in the Vlasov equation, and derive a discrete formulation that conserves mass, momentum, and energy up to a prescribed nonlinear tolerance upon convergence. Our conservation strategy employs nonlinear constraints to enforce these properties discretely for both the Vlasov operator and the Fokker-Planck collision operator. Numerical examples of varying degrees of complexity, including shock-wave propagation, demonstrate the favorable efficiency and accuracy properties of the scheme.

Compressible, multiphase semi-implicit method with moment of fluid interface representation

DOE PAGES

Jemison, Matthew; Sussman, Mark; Arienti, Marco

2014-09-16

A unified method for simulating multiphase flows using an exactly mass, momentum, and energy conserving Cell-Integrated Semi-Lagrangian advection algorithm is presented. The deforming material boundaries are represented using the moment-of-fluid method. Our new algorithm uses a semi-implicit pressure update scheme that asymptotically preserves the standard incompressible pressure projection method in the limit of infinite sound speed. The asymptotically preserving attribute makes the new method applicable to compressible and incompressible flows including stiff materials; enabling large time steps characteristic of incompressible flow algorithms rather than the small time steps required by explicit methods. Moreover, shocks are captured and material discontinuities aremore » tracked, without the aid of any approximate or exact Riemann solvers. As a result, wimulations of underwater explosions and fluid jetting in one, two, and three dimensions are presented which illustrate the effectiveness of the new algorithm at efficiently computing multiphase flows containing shock waves and material discontinuities with large “impedance mismatch.”« less

Explicit methods in extended phase space for inseparable Hamiltonian problems

NASA Astrophysics Data System (ADS)

Pihajoki, Pauli

2015-03-01

We present a method for explicit leapfrog integration of inseparable Hamiltonian systems by means of an extended phase space. A suitably defined new Hamiltonian on the extended phase space leads to equations of motion that can be numerically integrated by standard symplectic leapfrog (splitting) methods. When the leapfrog is combined with coordinate mixing transformations, the resulting algorithm shows good long term stability and error behaviour. We extend the method to non-Hamiltonian problems as well, and investigate optimal methods of projecting the extended phase space back to original dimension. Finally, we apply the methods to a Hamiltonian problem of geodesics in a curved space, and a non-Hamiltonian problem of a forced non-linear oscillator. We compare the performance of the methods to a general purpose differential equation solver LSODE, and the implicit midpoint method, a symplectic one-step method. We find the extended phase space methods to compare favorably to both for the Hamiltonian problem, and to the implicit midpoint method in the case of the non-linear oscillator.

A third-order implicit discontinuous Galerkin method based on a Hermite WENO reconstruction for time-accurate solution of the compressible Navier-Stokes equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Xia, Yidong; Liu, Xiaodong; Luo, Hong

2015-06-01

Here, a space and time third-order discontinuous Galerkin method based on a Hermite weighted essentially non-oscillatory reconstruction is presented for the unsteady compressible Euler and Navier–Stokes equations. At each time step, a lower-upper symmetric Gauss–Seidel preconditioned generalized minimal residual solver is used to solve the systems of linear equations arising from an explicit first stage, single diagonal coefficient, diagonally implicit Runge–Kutta time integration scheme. The performance of the developed method is assessed through a variety of unsteady flow problems. Numerical results indicate that this method is able to deliver the designed third-order accuracy of convergence in both space and time,more » while requiring remarkably less storage than the standard third-order discontinous Galerkin methods, and less computing time than the lower-order discontinous Galerkin methods to achieve the same level of temporal accuracy for computing unsteady flow problems.« less

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems

PubMed Central

Lo, Wing-Cheong; Chen, Long; Wang, Ming; Nie, Qing

2012-01-01

An inhomogeneous steady state pattern of nonlinear reaction-diffusion equations with no-flux boundary conditions is usually computed by solving the corresponding time-dependent reaction-diffusion equations using temporal schemes. Nonlinear solvers (e.g., Newton’s method) take less CPU time in direct computation for the steady state; however, their convergence is sensitive to the initial guess, often leading to divergence or convergence to spatially homogeneous solution. Systematically numerical exploration of spatial patterns of reaction-diffusion equations under different parameter regimes requires that the numerical method be efficient and robust to initial condition or initial guess, with better likelihood of convergence to an inhomogeneous pattern. Here, a new approach that combines the advantages of temporal schemes in robustness and Newton’s method in fast convergence in solving steady states of reaction-diffusion equations is proposed. In particular, an adaptive implicit Euler with inexact solver (AIIE) method is found to be much more efficient than temporal schemes and more robust in convergence than typical nonlinear solvers (e.g., Newton’s method) in finding the inhomogeneous pattern. Application of this new approach to two reaction-diffusion equations in one, two, and three spatial dimensions, along with direct comparisons to several other existing methods, demonstrates that AIIE is a more desirable method for searching inhomogeneous spatial patterns of reaction-diffusion equations in a large parameter space. PMID:22773849

A Role for Phosphodiesterase 11A (PDE11A) in the Formation of Social Memories and the Stabilization of Mood

PubMed Central

Kelly, Michy P.

2017-01-01

The most recently discovered 3′,5′-cyclic nucleotide phosphodiesterase family is the Phosphodiesterase 11 (PDE11) family, which is encoded by a single gene PDE11A. PDE11A is a dual-specific PDE, breaking down both cAMP and cGMP. There are four PDE11A splice variants (PDE11A1–4) with distinct tissue expression profiles and unique N-terminal regulatory regions, suggesting that each isoform could be individually targeted with a small molecule or biologic. PDE11A4 is the PDE11A isoform expressed in brain and is found in the hippocampal formation of humans and rodents. Studies in rodents show that PDE11A4 mRNA expression in brain is, in fact, restricted to the hippocampal formation (CA1, possibly CA2, subiculum, and the adjacently connected amygdalohippocampal area). Within the hippocampal formation of rodents, PDE11A4 protein is expressed in neurons but not astrocytes, with a distribution across nuclear, cytoplasmic, and membrane compartments. This subcellular localization of PDE11A4 is altered in response to social experience in mouse, and in vitro studies show the compartmentalization of PDE11A4 is controlled, at least in part, by homodimerization and N-terminal phosphorylation. PDE11A4 expression dramatically increases in the hippocampus with age in the rodent hippocampus, from early postnatal life to late aging, suggesting PDE11A4 function may evolve across the lifespan. Interestingly, PDE11A4 protein shows a 3–10-fold enrichment in the rodent ventral hippocampal formation (VHIPP; a.k.a. anterior in primates) versus dorsal hippocampal formation (DHIPP). Consistent with this enrichment in VHIPP, studies in knockout mice show that PDE11A regulates the formation of social memories and the stabilization of mood and is a critical mechanism by which social experience feeds back to modify the brain and subsequent social behaviors. PDE11A4 likely controls behavior by regulating hippocampal glutamatergic, oxytocin, and cytokine signaling, as well as protein translation. Given its unique tissue distribution and relatively selective effects on behavior, PDE11A may represent a novel therapeutic target for neuropsychiatric, neurodevelopmental, or age-related disorders. Therapeutically targeting PDE11A4 may be a way to selectively restore aberrant cyclic nucleotide signaling in the hippocampal formation while leaving the rest of the brain and periphery untouched, thus, relieving deficits while avoiding unwanted side effects. PMID:28956334

Numerical simulation of steady three-dimensional flows in axial turbomachinery bladerows

NASA Astrophysics Data System (ADS)

Basson, Anton Herman

The formulation for and application of a numerical model for low Mach number steady three-dimensional flows in axial turbomachinery blade rows is presented. The formulation considered here includes an efficient grid generation scheme (particularly suited to computational grids for the analysis of turbulent turbomachinery flows) and a semi-implicit, pressure-based computational fluid dynamics scheme that directly includes artificial dissipation, applicable to viscous and inviscid flows. The grid generation technique uses a combination of algebraic and elliptic methods, in conjunction with the Minimal Residual Method, to economically generate smooth structured grids. For typical H-grids in turbomachinery bladerows, when compared to a purely elliptic grid generation scheme, the presented grid generation scheme produces grids with much improved smoothness near the leading and trailing edges, allows the use of small near wall grid spacing required by low Reynolds number turbulence models, and maintains orthogonality of the grid near the solid boundaries even for high flow angle cascades. A specialized embedded H-grid for application particularly to tip clearance flows is presented. This topology smoothly discretizes the domain without modifying the tip shape, while requiring only minor modifications to H-grid flow solvers. Better quantitative modeling of the tip clearance vortex structure than that obtained with a pinched tip approximation is demonstrated. The formulation of artificial dissipation terms for a semi-implicit, pressure-based (SIMPLE type) flow solver, is presented. It is applied to both the Euler and the Navier-Stokes equations, expressed in generalized coordinates using a non-staggered grid. This formulation is compared to some SIMPLE and time marching formulations, revealing the artificial dissipation inherent in some commonly used semi-implicit formulations. The effect of the amount of dissipation on the accuracy of the solution and the convergence rate is quantitatively demonstrated for a number of flow cases. The ability of the formulation to model complex steady turbomachinery flows is demonstrated, e.g. for pressure driven secondary flows, turbine nozzle wakes, turbulent boundary layers. The formulation's modeling of blade surface heat transfer is assessed. The numerical model is used to investigate the structure of phenomena associated with tip clearance flows in a turbine nozzle.

Catecholic amides as potential selective phosphodiesterase 4D inhibitors: Design, synthesis, pharmacological evaluation and structure-activity relationships.

PubMed

Zhou, Zhong-Zhen; Ge, Bing-Chen; Chen, Yu-Fang; Shi, Xiu-Dong; Yang, Xue-Mei; Xu, Jiang-Ping

2015-11-15

In this study, a series of catechol-based amides (8a-n) with different amide linkers linking the catecholic moiety to the terminal phenyl ring was designed and synthesized as potent phosphodiesterase (PDE) 4D inhibitors. The inhibitory activities of these compounds were evaluated against the core catalytic domains of human PDE4 (PDE4CAT), full-length PDE4B1 and PDE4D7 enzymes, and other PDE family members. The results indicated the majority of compounds 8a-n displayed moderate to good inhibitory activities against PDE4CAT. Among these compounds, compound 8 j with a short amide linker (-CONHCH2-) displayed comparable PDE4CAT inhibitory activity (IC50=410 nM) with rolipram. More interestingly, compound 8 g, a potent and selective PDE4D inhibitor (IC50=94 nM), exhibited a 10-fold selectivity over the PDE4B subtypes and an over 1000-fold selectivity against other PDE family members. Docking simulations suggested that 8 g forms three extra H-bonds with the N-H of residue Asn487 and two water molecules. Copyright © 2015 Elsevier Ltd. All rights reserved.

Myocardial Response to Milrinone in Single Right Ventricle Heart Disease.

PubMed

Nakano, Stephanie J; Nelson, Penny; Sucharov, Carmen C; Miyamoto, Shelley D

2016-07-01

Empiric treatment with milrinone, a phosphodiesterase (PDE) 3 inhibitor, has become increasingly common in patients with single ventricle heart disease of right ventricular (RV) morphology (SRV); our objective was to characterize the myocardial response to PDE3 inhibition (PDE3i) in the pediatric population with SRV. Cyclic adenosine monophosphate levels, PDE activity, and phosphorylated phospholamban (PLN) were determined in explanted human ventricular myocardium from nonfailing pediatric donors (n = 10) and pediatric patients transplanted secondary to SRV. Subjects with SRV were further classified by PDE3i treatment (n = 13 with PDE3i and n = 12 without PDE3i). In comparison with nonfailing RV myocardium (n = 8), cyclic adenosine monophosphate levels are lower in patients with SRV treated with PDE3i (n = 12, P = .021). Chronic PDE3i does not alter total PDE or PDE3 activity in SRV myocardium. Compared with nonfailing RV myocardium, SRV myocardium (both with and without PDE3i) demonstrates equivalent phosphorylated PLN at the protein kinase A phosphorylation site. As evidenced by preserved phosphorylated PLN, the molecular adaptation associated with SRV differs significantly from that demonstrated in pediatric heart failure because of dilated cardiomyopathy. These alterations support a pathophysiologically distinct mechanism of heart failure in pediatric patients with SRV, which has direct implications regarding the presumed response to PDE3i treatment in this population. Copyright © 2016 Elsevier Inc. All rights reserved.

An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.; Barnes, D. C.

2011-08-01

This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov-Poisson formulation), ours is based on a nonlinearly converged Vlasov-Ampére (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant-Friedrichs-Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicit time steps (unlike the earlier "energy-conserving" explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton-Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.

A spectral radius scaling semi-implicit iterative time stepping method for reactive flow simulations with detailed chemistry

NASA Astrophysics Data System (ADS)

Xie, Qing; Xiao, Zhixiang; Ren, Zhuyin

2018-09-01

A spectral radius scaling semi-implicit time stepping scheme has been developed for simulating unsteady compressible reactive flows with detailed chemistry, in which the spectral radius in the LUSGS scheme has been augmented to account for viscous/diffusive and reactive terms and a scalar matrix is proposed to approximate the chemical Jacobian using the minimum species destruction timescale. The performance of the semi-implicit scheme, together with a third-order explicit Runge-Kutta scheme and a Strang splitting scheme, have been investigated in auto-ignition and laminar premixed and nonpremixed flames of three representative fuels, e.g., hydrogen, methane, and n-heptane. Results show that the minimum species destruction time scale can well represent the smallest chemical time scale in reactive flows and the proposed scheme can significantly increase the allowable time steps in simulations. The scheme is stable when the time step is as large as 10 μs, which is about three to five orders of magnitude larger than the smallest time scales in various tests considered. For the test flames considered, the semi-implicit scheme achieves second order of accuracy in time. Moreover, the errors in quantities of interest are smaller than those from the Strang splitting scheme indicating the accuracy gain when the reaction and transport terms are solved coupled. Results also show that the relative efficiency of different schemes depends on fuel mechanisms and test flames. When the minimum time scale in reactive flows is governed by transport processes instead of chemical reactions, the proposed semi-implicit scheme is more efficient than the splitting scheme. Otherwise, the relative efficiency depends on the cost in sub-iterations for convergence within each time step and in the integration for chemistry substep. Then, the capability of the compressible reacting flow solver and the proposed semi-implicit scheme is demonstrated for capturing the hydrogen detonation waves. Finally, the performance of the proposed method is demonstrated in a two-dimensional hydrogen/air diffusion flame.

Role of Ca2+/calmodulin-stimulated cyclic nucleotide phosphodiesterase 1 in mediating cardiomyocyte hypertrophy

PubMed Central

Miller, Clint L.; Oikawa, Masayoshi; Cai, Yujun; Wojtovich, Andrew P.; Nagel, David J.; Xu, Xiangbin; Xu, Haodong; Florio, Vince; Rybalkin, Sergei D.; Beavo, Joseph A.; Chen, Yiu-Fai; Li, Jian-Dong; Blaxall, Burns C.; Abe, Jun-ichi; Yan, Chen

2009-01-01

Rationale Cyclic nucleotide phosphodiesterases (PDE) through the degradation of second messenger cyclic guanosine monophosphate (cGMP) play critical roles in maintaining cardiomyocyte homeostasis. Ca2+/CaM-activated cGMP-hydrolyzing PDE1 family may play a pivotal role in balancing intracellular Ca2+/CaM and cGMP signaling, however its function in cardiomyocytes is unknown. Objective Herein we investigate the role of Ca2+/CaM-stimulated PDE1 in regulating pathological cardiomyocyte hypertrophy in neonatal and adult rat ventricular myocytes (NRVM and ARVM) and in the heart in vivo. Methods and Results Inhibition of PDE1 activity using a PDE1 selective inhibitor IC86340 or downregulation of PDE1A using siRNA prevented phenylephrine (PE) induced pathological myocyte hypertrophy and hypertrophic marker expression in neonatal (NRVM) and adult (ARVM) rat ventricular myocytes. Importantly, administration of the PDE1 inhibitor IC86340 attenuated cardiac hypertrophy induced by chronic ISO infusion in vivo. Both PDE1A and PDE1C mRNA and protein were detected in human hearts, however PDE1A expression was conserved in rodent hearts. Moreover, PDE1A expression was significantly upregulated in vivo in the heart and myocytes from various pathological hypertrophy animal models and in vitro in isolated NRVM and ARVM treated with neurohumoral stimuli such as angiotensin II (Ang II) and ISO. Further, PDE1A plays a critical role in PE-induced reduction of intracellular cGMP and PKG activity, and thereby cardiomyocyte hypertrophy in vitro. Conclusions These results elucidate a novel role for Ca2+/CaM-stimulated PDE1, particularly PDE1A, in regulating pathological cardiomyocyte hypertrophy via a cGMP/PKG-dependent mechanism, thereby demonstrating Ca2+ and cGMP signaling cross-talk during cardiac hypertrophy. PMID:19797176

Workflows for Full Waveform Inversions

NASA Astrophysics Data System (ADS)

Boehm, Christian; Krischer, Lion; Afanasiev, Michael; van Driel, Martin; May, Dave A.; Rietmann, Max; Fichtner, Andreas

2017-04-01

Despite many theoretical advances and the increasing availability of high-performance computing clusters, full seismic waveform inversions still face considerable challenges regarding data and workflow management. While the community has access to solvers which can harness modern heterogeneous computing architectures, the computational bottleneck has fallen to these often manpower-bounded issues that need to be overcome to facilitate further progress. Modern inversions involve huge amounts of data and require a tight integration between numerical PDE solvers, data acquisition and processing systems, nonlinear optimization libraries, and job orchestration frameworks. To this end we created a set of libraries and applications revolving around Salvus (http://salvus.io), a novel software package designed to solve large-scale full waveform inverse problems. This presentation focuses on solving passive source seismic full waveform inversions from local to global scales with Salvus. We discuss (i) design choices for the aforementioned components required for full waveform modeling and inversion, (ii) their implementation in the Salvus framework, and (iii) how it is all tied together by a usable workflow system. We combine state-of-the-art algorithms ranging from high-order finite-element solutions of the wave equation to quasi-Newton optimization algorithms using trust-region methods that can handle inexact derivatives. All is steered by an automated interactive graph-based workflow framework capable of orchestrating all necessary pieces. This naturally facilitates the creation of new Earth models and hopefully sparks new scientific insights. Additionally, and even more importantly, it enhances reproducibility and reliability of the final results.

MYOCARDIAL RESPONSE TO MILRINONE IN SINGLE RIGHT VENTRICLE HEART DISEASE

PubMed Central

Nakano, Stephanie J.; Nelson, Penny; Sucharov, Carmen C.; Miyamoto, Shelley D.

2016-01-01

Objectives Empiric treatment with milrinone, a phosphodiesterase 3 inhibitor (PDE3i), has become increasingly common in patients with single ventricle heart disease of right ventricular morphology (SRV); our objective was to characterize the myocardial response to PDE3i in the pediatric population with SRV. Study design Cyclic adenosine monophosphate (cAMP) levels, phosphodiesterase (PDE) activity, and phospholamban phosphorylation (pPLN) were determined in explanted human ventricular myocardium from nonfailing pediatric donors (n=10) and pediatric patients transplanted secondary to SRV. SRV subjects were further classified by PDE3i treatment (n=13 with PDE3i and n=12 without PDE3i). Results In comparison with nonfailing RV myocardium, cAMP levels are lower in patients with SRV treated with PDE3i (p=0.021). Chronic PDE3i does not alter total PDE or PDE3 activity in SRV myocardium. When compared with nonfailing RV myocardium, SRV myocardium (both with and without PDE3i) demonstrates equivalent pPLN at the protein kinase A phosphorylation site. Conclusions As evidenced by preserved pPLN, the molecular adaptation associated with SRV differs significantly from that demonstrated in pediatric heart failure due to dilated cardiomyopathy. These alterations support a pathophysiologically distinct mechanism of heart failure in pediatric patients with SRV, which has direct implications regarding the presumed response to PDE3i treatment in this population. PMID:27181939

PDE4 as a target for cognition enhancement

PubMed Central

Richter, Wito; Menniti, Frank S.; Zhang, Han-Ting; Conti, Marco

2014-01-01

Introduction The second messengers cAMP and cGMP mediate fundamental aspects of brain function relevant to memory, learning and cognitive functions. Consequently, cyclic nucleotide phosphodiesterases (PDEs), the enzymes that inactivate the cyclic nucleotides, are promising targets for the development of cognition-enhancing drugs. Areas covered PDE4 is the largest of the eleven mammalian PDE families. This review covers the properties and functions of the PDE4 family, highlighting procognitive and memory-enhancing effects associated with their inactivation. Expert opinion PAN-selective PDE4 inhibitors exert a number of memory- and cognition-enhancing effects and have neuroprotective and neuroregenerative properties in preclinical models. The major hurdle for their clinical application is to target inhibitors to specific PDE4 isoforms relevant to particular cognitive disorders to realize the therapeutic potential while avoiding side effects, in particular emesis and nausea. The PDE4 family comprises four genes, PDE4A-D, each expressed as multiple variants. Progress to date stems from characterization of rodent models with selective ablation of individual PDE4 subtypes, revealing that individual subtypes exert unique and non-redundant functions in the brain. Thus, targeting specific PDE4 subtypes, as well as splicing variants or conformational states, represents a promising strategy to separate the therapeutic benefits from the side effects of PAN-PDE4 inhibitors. PMID:23883342

Optimizing electrostatic field calculations with the Adaptive Poisson-Boltzmann Solver to predict electric fields at protein-protein interfaces II: explicit near-probe and hydrogen-bonding water molecules.

PubMed

Ritchie, Andrew W; Webb, Lauren J

2014-07-17

We have examined the effects of including explicit, near-probe solvent molecules in a continuum electrostatics strategy using the linear Poisson-Boltzmann equation with the Adaptive Poisson-Boltzmann Solver (APBS) to calculate electric fields at the midpoint of a nitrile bond both at the surface of a monomeric protein and when docked at a protein-protein interface. Results were compared to experimental vibrational absorption energy measurements of the nitrile oscillator. We examined three methods for selecting explicit water molecules: (1) all water molecules within 5 Å of the nitrile nitrogen; (2) the water molecule closest to the nitrile nitrogen; and (3) any single water molecule hydrogen-bonding to the nitrile. The correlation between absolute field strengths with experimental absorption energies were calculated and it was observed that method 1 was only an improvement for the monomer calculations, while methods 2 and 3 were not significantly different from the purely implicit solvent calculations for all protein systems examined. Upon taking the difference in calculated electrostatic fields and comparing to the difference in absorption frequencies, we typically observed an increase in experimental correlation for all methods, with method 1 showing the largest gain, likely due to the improved absolute monomer correlations using that method. These results suggest that, unlike with quantum mechanical methods, when calculating absolute fields using entirely classical models, implicit solvent is typically sufficient and additional work to identify hydrogen-bonding or nearest waters does not significantly impact the results. Although we observed that a sphere of solvent near the field of interest improved results for relative field calculations, it should not be consider a panacea for all situations.

Conservative tightly-coupled simulations of stochastic multiscale systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Taverniers, Søren; Pigarov, Alexander Y.; Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu

2016-05-15

Multiphysics problems often involve components whose macroscopic dynamics is driven by microscopic random fluctuations. The fidelity of simulations of such systems depends on their ability to propagate these random fluctuations throughout a computational domain, including subdomains represented by deterministic solvers. When the constituent processes take place in nonoverlapping subdomains, system behavior can be modeled via a domain-decomposition approach that couples separate components at the interfaces between these subdomains. Its coupling algorithm has to maintain a stable and efficient numerical time integration even at high noise strength. We propose a conservative domain-decomposition algorithm in which tight coupling is achieved by employingmore » either Picard's or Newton's iterative method. Coupled diffusion equations, one of which has a Gaussian white-noise source term, provide a computational testbed for analysis of these two coupling strategies. Fully-converged (“implicit”) coupling with Newton's method typically outperforms its Picard counterpart, especially at high noise levels. This is because the number of Newton iterations scales linearly with the amplitude of the Gaussian noise, while the number of Picard iterations can scale superlinearly. At large time intervals between two subsequent inter-solver communications, the solution error for single-iteration (“explicit”) Picard's coupling can be several orders of magnitude higher than that for implicit coupling. Increasing the explicit coupling's communication frequency reduces this difference, but the resulting increase in computational cost can make it less efficient than implicit coupling at similar levels of solution error, depending on the communication frequency of the latter and the noise strength. This trend carries over into higher dimensions, although at high noise strength explicit coupling may be the only computationally viable option.« less

Homology modeling, docking studies and molecular dynamic simulations using graphical processing unit architecture to probe the type-11 phosphodiesterase catalytic site: a computational approach for the rational design of selective inhibitors.

PubMed

Cichero, Elena; D'Ursi, Pasqualina; Moscatelli, Marco; Bruno, Olga; Orro, Alessandro; Rotolo, Chiara; Milanesi, Luciano; Fossa, Paola

2013-12-01

Phosphodiesterase 11 (PDE11) is the latest isoform of the PDEs family to be identified, acting on both cyclic adenosine monophosphate and cyclic guanosine monophosphate. The initial reports of PDE11 found evidence for PDE11 expression in skeletal muscle, prostate, testis, and salivary glands; however, the tissue distribution of PDE11 still remains a topic of active study and some controversy. Given the sequence similarity between PDE11 and PDE5, several PDE5 inhibitors have been shown to cross-react with PDE11. Accordingly, many non-selective inhibitors, such as IBMX, zaprinast, sildenafil, and dipyridamole, have been documented to inhibit PDE11. Only recently, a series of dihydrothieno[3,2-d]pyrimidin-4(3H)-one derivatives proved to be selective toward the PDE11 isoform. In the absence of experimental data about PDE11 X-ray structures, we found interesting to gain a better understanding of the enzyme-inhibitor interactions using in silico simulations. In this work, we describe a computational approach based on homology modeling, docking, and molecular dynamics simulation to derive a predictive 3D model of PDE11. Using a Graphical Processing Unit architecture, it is possible to perform long simulations, find stable interactions involved in the complex, and finally to suggest guideline for the identification and synthesis of potent and selective inhibitors. © 2013 John Wiley & Sons A/S.

Scalable Nonlinear Solvers for Fully Implicit Coupled Nuclear Fuel Modeling. Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cai, Xiao-Chuan; Keyes, David; Yang, Chao

2014-09-29

The focus of the project is on the development and customization of some highly scalable domain decomposition based preconditioning techniques for the numerical solution of nonlinear, coupled systems of partial differential equations (PDEs) arising from nuclear fuel simulations. These high-order PDEs represent multiple interacting physical fields (for example, heat conduction, oxygen transport, solid deformation), each is modeled by a certain type of Cahn-Hilliard and/or Allen-Cahn equations. Most existing approaches involve a careful splitting of the fields and the use of field-by-field iterations to obtain a solution of the coupled problem. Such approaches have many advantages such as ease of implementationmore » since only single field solvers are needed, but also exhibit disadvantages. For example, certain nonlinear interactions between the fields may not be fully captured, and for unsteady problems, stable time integration schemes are difficult to design. In addition, when implemented on large scale parallel computers, the sequential nature of the field-by-field iterations substantially reduces the parallel efficiency. To overcome the disadvantages, fully coupled approaches have been investigated in order to obtain full physics simulations.« less

High-resolution multi-code implementation of unsteady Navier-Stokes flow solver based on paralleled overset adaptive mesh refinement and high-order low-dissipation hybrid schemes

NASA Astrophysics Data System (ADS)

Li, Gaohua; Fu, Xiang; Wang, Fuxin

2017-10-01

The low-dissipation high-order accurate hybrid up-winding/central scheme based on fifth-order weighted essentially non-oscillatory (WENO) and sixth-order central schemes, along with the Spalart-Allmaras (SA)-based delayed detached eddy simulation (DDES) turbulence model, and the flow feature-based adaptive mesh refinement (AMR), are implemented into a dual-mesh overset grid infrastructure with parallel computing capabilities, for the purpose of simulating vortex-dominated unsteady detached wake flows with high spatial resolutions. The overset grid assembly (OGA) process based on collection detection theory and implicit hole-cutting algorithm achieves an automatic coupling for the near-body and off-body solvers, and the error-and-try method is used for obtaining a globally balanced load distribution among the composed multiple codes. The results of flows over high Reynolds cylinder and two-bladed helicopter rotor show that the combination of high-order hybrid scheme, advanced turbulence model, and overset adaptive mesh refinement can effectively enhance the spatial resolution for the simulation of turbulent wake eddies.

Three dimensional modelling of earthquake rupture cycles on frictional faults

NASA Astrophysics Data System (ADS)

Simpson, Guy; May, Dave

2017-04-01

We are developing an efficient MPI-parallel numerical method to simulate earthquake sequences on preexisting faults embedding within a three dimensional viscoelastic half-space. We solve the velocity form of the elasto(visco)dynamic equations using a continuous Galerkin Finite Element Method on an unstructured pentahedral mesh, which thus permits local spatial refinement in the vicinity of the fault. Friction sliding is coupled to the viscoelastic solid via rate- and state-dependent friction laws using the split-node technique. Our coupled formulation employs a picard-type non-linear solver with a fully implicit, first order accurate time integrator that utilises an adaptive time step that efficiently evolves the system through multiple seismic cycles. The implementation leverages advanced parallel solvers, preconditioners and linear algebra from the Portable Extensible Toolkit for Scientific Computing (PETSc) library. The model can treat heterogeneous frictional properties and stress states on the fault and surrounding solid as well as non-planar fault geometries. Preliminary tests show that the model successfully reproduces dynamic rupture on a vertical strike-slip fault in a half-space governed by rate-state friction with the ageing law.

Evaluation of the effect of phosphodiesterase on equine platelet activation and the effect of antigen challenge on platelet phosphodiesterase activity in horses with recurrent airway obstruction.

PubMed

Dunkel, Bettina; Rickards, Karen J; Werling, Dirk; Page, Clive P; Cunningham, Fiona M

2010-05-01

To determine whether expression of equine platelet activation-dependent surface markers is influenced by phospodiesterase (PDE) isoenzyme activity and whether antigen challenge alters platelet PDE activity in horses with recurrent airway obstruction (RAO). 16 horses. 7 healthy horses were used for in vitro experiments, 6 horses with RAO were used for antigen challenge, and 6 healthy horses were used as control animals. Three of the healthy horses had also been used in the in vitro experiments. Effects of PDE inhibition and activation of adenylyl cyclase on CD41/61 and CD62P expression on platelets and platelet-neutrophil aggregate formation in vitro were investigated via flow cytometry. Platelet PDE activity and sensitivity to inhibition of PDE3 and PDE5 isoenzymes were examined in horses with RAO and control horses before and after antigen challenge. Inhibition of PDE or activation of adenylyl cyclase significantly inhibited stimulus-induced expression of CD41/61 and CD62P (by approx 94% and 40%, respectively) and percentage of CD62P positive cells (by approx 30%). Only the PDE3 inhibitor, trequinsin, caused a significant (53%) reduction in platelet-neutrophil aggregate formation. Platelet PDE activity decreased following antigen challenge in RAO-affected horses and control horses. In horses with RAO, a significant increase in sensitivity of platelet PDE to inhibition by the PDE5 inhibitor zaprinast was observed after 5 hours. Results provided further evidence that PDE3 is an important regulator of equine platelet activation and suggested that changes in regulation of platelet PDE5 may contribute to antigen-induced response in horses with RAO.

Defining the Phosphodiesterase Superfamily Members in Rat Brain Microvessels

PubMed Central

2011-01-01

Eleven phosphodiesterase (PDE) families are known, each having several different isoforms and splice variants. Recent evidence indicates that expression of individual PDE family members is tissue-specific. Little is known concerning detailed PDE component expression in brain microvessels where the blood-brain-barrier and the local cerebral blood flow are thought to be regulated by PDEs. The present study attempted to identify PDE family members that are expressed in brain microvessels. Adult male F344 rats were sacrificed and blocks of the cerebral cortex and infratentorial areas were dissected. Microvessels were isolated using a filtration method, and total RNA was extracted. RNA quality and quantity were determined using an Agilent bioanalyzer. The isolated cortical and infratentorial microvessel total RNA amounts were 2720 ± 750 ng (n = 2) and 250 ± 40 ng (n = 2), respectively. Microarrays with 22 000 transcripts demonstrated that there were 16 PDE transcripts in the PDE superfamily, exhibiting quantifiable density in the microvessels. An additional immunofluorescent study verified that PDE4D (cAMP-specific) and PDE5A (cGMP-specific) were colocalized with RECA-1 (an endothelial marker) in the cerebral cortex using both F344 rats and Sprague–Dawley rats (n = 3–6/strain). In addition, PDE4D and PDE5A were found to be colocalized with alpha-smooth muscle actin which delineates cerebral arteries and arterioles as well as pericytes. In conclusion, a filtration method followed by microarray analyses allows PDE components to be identified in brain microvessels, and confirmed that PDE4D and PDE5A are the primary forms expressed in rat brain microvessels. PMID:22860158

Adenoviral short hairpin RNA therapy targeting phosphodiesterase 5a relieves cardiac remodeling and dysfunction following myocardial infarction.

PubMed

Li, Longhu; Haider, Husnain Kh; Wang, Linlin; Lu, Gang; Ashraf, Muhammad

2012-05-15

We previously showed that treatment with tadalafil, a long-acting phosphodiesterase-5a (PDE5a) inhibitor, effectively prevented adverse left ventricular (LV) remodeling of the infarcted heart. We hypothesized that short-hairpin RNA (shRNA) therapy targeting PDE5a would simulate the effects of pharmacological intervention for treatment of postinfarction LV remodeling and dysfunction. Experimental model of myocardial infarction was developed in female mice by permanent ligation of left coronary artery. Immediately after that, an adenoviral vector encoding for shRNA sequence targeting PDE5a (Ad-shPDE5a) was injected intramyocardially, which specifically inhibited PDE5a in the heart. Four weeks later, Ad-shPDE5a treated mice showed significant mitigation of the left ventricle (LV) dilatation and dysfunction as indicated by smaller LV cavity and more preserved ejection fraction and fractional shortening. Infarction size and fibrosis were significantly reduced in Ad-shPDE5a-treated mice. Additionally, more salvaged cardiomyocytes, significantly reduced collagen contents, and higher blood vessel density were observed in Ad-shPDE5a-treated mice. The cytoprotective effects of Ad-shPDE5a were demonstrated in vitro in Ad-shPDE5a transfected cardiomyocytes cultured under oxygen glucose deprivation. Among downstream mediators of PDE5a signaling, cyclic GMP (cGMP) and cGMP-dependent protein kinase G (PKG) were activated with concomitant reduction in caspase-3 activity. However, no significant change in PKA and cAMP activities were observed in Ad-shPDE5a-treated hearts. Inhibition with shRNA improved cardiac remodeling and dysfunction by reducing infarction size and cardiac fibrosis and increased cGMP and PKG activity. These findings suggest that PDE5 inhibition with Ad-shPDE5a is a novel approach for treatment of myocardial infarction.

Inhibition of calmodulin-dependent phosphodiesterase induces apoptosis in human leukemic cells.

PubMed Central

Jiang, X; Li, J; Paskind, M; Epstein, P M

1996-01-01

Cytosolic extracts from a human lymphoblastoid B-cell line, RPMI-8392, established from a patient with acute lymphocytic leukemia, contain two major forms of cyclic nucleotide phosphodiesterase (PDE): Ca2+-calmodulin dependent PDE (PDE1) and cAMP-specific PDE (PDE4). In contrast, normal quiescent human peripheral blood lymphocytes (HPBL) are devoid of PDE1 activity [Epstein, P. M., Moraski, S., Jr., and Hachisu, R. (1987) Biochem. J. 243, 533-539]. Using reverse transcription-polymerase chain reaction (RT-PCR), we show that the mRNA encoding the 63-kDa form of PDE1 (PDE1B1) is expressed in RPMI-8392 cells, but not in normal, resting HPBL. This mRNA is, however, induced in HPBL following mitogenic stimulation by phytohemagglutinin (PHA). Also using RT-PCR, the full open reading frame for human PDE1B1 cDNA was cloned from RPMI-8392 cells and it encodes a protein of 536 amino acids with 96% identity to bovine, rat, and mouse species. RT-PCR also identifies the presence of PDE1B1 in other human lymphoblastoid and leukemic cell lines of B- (RPMI-1788, Daudi) and T-(MOLT-4, NA, Jurkat) cell origin. Inhibition of PDE1 or PDE4 activity by selective inhibitors induced RPMI-8392 cells, as well as the other cell lines, to undergo apoptosis. Culture of RPMI-8392 cells with an 18-bp phosphorothioate antisense oligodeoxynucleotide, targeted against the translation initiation region of the RPMI-8392 mRNA, led to a specific reduction in the amount of PDE1B1 mRNA after 1 day, and its disappearance after 2 days, and induced apoptosis in these cells in a sequence specific manner. This suggests that PDEs, particularly PDE1B1, because its expression is selective, may be useful targets for inducing the death of leukemic cells. Images Fig. 1 Fig. 3 Fig. 5 Fig. 6 PMID:8855339

Partial differential equation transform — Variational formulation and Fourier analysis

PubMed Central

Wang, Yang; Wei, Guo-Wei; Yang, Siyang

2011-01-01

Nonlinear partial differential equation (PDE) models are established approaches for image/signal processing, data analysis and surface construction. Most previous geometric PDEs are utilized as low-pass filters which give rise to image trend information. In an earlier work, we introduced mode decomposition evolution equations (MoDEEs), which behave like high-pass filters and are able to systematically provide intrinsic mode functions (IMFs) of signals and images. Due to their tunable time-frequency localization and perfect reconstruction, the operation of MoDEEs is called a PDE transform. By appropriate selection of PDE transform parameters, we can tune IMFs into trends, edges, textures, noise etc., which can be further utilized in the secondary processing for various purposes. This work introduces the variational formulation, performs the Fourier analysis, and conducts biomedical and biological applications of the proposed PDE transform. The variational formulation offers an algorithm to incorporate two image functions and two sets of low-pass PDE operators in the total energy functional. Two low-pass PDE operators have different signs, leading to energy disparity, while a coupling term, acting as a relative fidelity of two image functions, is introduced to reduce the disparity of two energy components. We construct variational PDE transforms by using Euler-Lagrange equation and artificial time propagation. Fourier analysis of a simplified PDE transform is presented to shed light on the filter properties of high order PDE transforms. Such an analysis also offers insight on the parameter selection of the PDE transform. The proposed PDE transform algorithm is validated by numerous benchmark tests. In one selected challenging example, we illustrate the ability of PDE transform to separate two adjacent frequencies of sin(x) and sin(1.1x). Such an ability is due to PDE transform’s controllable frequency localization obtained by adjusting the order of PDEs. The frequency selection is achieved either by diffusion coefficients or by propagation time. Finally, we explore a large number of practical applications to further demonstrate the utility of proposed PDE transform. PMID:22207904

Adenoviral short hairpin RNA therapy targeting phosphodiesterase 5a relieves cardiac remodeling and dysfunction following myocardial infarction

PubMed Central

Li, Longhu; Haider, Husnain Kh.; Wang, Linlin; Lu, Gang

2012-01-01

We previously showed that treatment with tadalafil, a long-acting phosphodiesterase-5a (PDE5a) inhibitor, effectively prevented adverse left ventricular (LV) remodeling of the infarcted heart. We hypothesized that short-hairpin RNA (shRNA) therapy targeting PDE5a would simulate the effects of pharmacological intervention for treatment of postinfarction LV remodeling and dysfunction. Experimental model of myocardial infarction was developed in female mice by permanent ligation of left coronary artery. Immediately after that, an adenoviral vector encoding for shRNA sequence targeting PDE5a (Ad-shPDE5a) was injected intramyocardially, which specifically inhibited PDE5a in the heart. Four weeks later, Ad-shPDE5a treated mice showed significant mitigation of the left ventricle (LV) dilatation and dysfunction as indicated by smaller LV cavity and more preserved ejection fraction and fractional shortening. Infarction size and fibrosis were significantly reduced in Ad-shPDE5a-treated mice. Additionally, more salvaged cardiomyocytes, significantly reduced collagen contents, and higher blood vessel density were observed in Ad-shPDE5a-treated mice. The cytoprotective effects of Ad-shPDE5a were demonstrated in vitro in Ad-shPDE5a transfected cardiomyocytes cultured under oxygen glucose deprivation. Among downstream mediators of PDE5a signaling, cyclic GMP (cGMP) and cGMP-dependent protein kinase G (PKG) were activated with concomitant reduction in caspase-3 activity. However, no significant change in PKA and cAMP activities were observed in Ad-shPDE5a-treated hearts. Inhibition with shRNA improved cardiac remodeling and dysfunction by reducing infarction size and cardiac fibrosis and increased cGMP and PKG activity. These findings suggest that PDE5 inhibition with Ad-shPDE5a is a novel approach for treatment of myocardial infarction. PMID:22447941

PDE1C deficiency antagonizes pathological cardiac remodeling and dysfunction

PubMed Central

Knight, Walter E.; Chen, Si; Zhang, Yishuai; Oikawa, Masayoshi; Wu, Meiping; Zhou, Qian; Miller, Clint L.; Cai, Yujun; Mickelsen, Deanne M.; Moravec, Christine; Small, Eric M.; Abe, Junichi; Yan, Chen

2016-01-01

Cyclic nucleotide phosphodiesterase 1C (PDE1C) represents a major phosphodiesterase activity in human myocardium, but its function in the heart remains unknown. Using genetic and pharmacological approaches, we studied the expression, regulation, function, and underlying mechanisms of PDE1C in the pathogenesis of cardiac remodeling and dysfunction. PDE1C expression is up-regulated in mouse and human failing hearts and is highly expressed in cardiac myocytes but not in fibroblasts. In adult mouse cardiac myocytes, PDE1C deficiency or inhibition attenuated myocyte death and apoptosis, which was largely dependent on cyclic AMP/PKA and PI3K/AKT signaling. PDE1C deficiency also attenuated cardiac myocyte hypertrophy in a PKA-dependent manner. Conditioned medium taken from PDE1C-deficient cardiac myocytes attenuated TGF-β–stimulated cardiac fibroblast activation through a mechanism involving the crosstalk between cardiac myocytes and fibroblasts. In vivo, cardiac remodeling and dysfunction induced by transverse aortic constriction, including myocardial hypertrophy, apoptosis, cardiac fibrosis, and loss of contractile function, were significantly attenuated in PDE1C-knockout mice relative to wild-type mice. These results indicate that PDE1C activation plays a causative role in pathological cardiac remodeling and dysfunction. Given the continued development of highly specific PDE1 inhibitors and the high expression level of PDE1C in the human heart, our findings could have considerable therapeutic significance. PMID:27791092

A pathophysiological role of PDE3 in allergic airway inflammation

PubMed Central

Beute, Jan; Lukkes, Melanie; Koekoek, Ewout P.; Nastiti, Hedwika; Ganesh, Keerthana; de Bruijn, Marjolein J.W.; Hockman, Steve; van Nimwegen, Menno; Braunstahl, Gert-Jan; Boon, Louis; Lambrecht, Bart N.; Manganiello, Vince C.; Hendriks, Rudi W.

2018-01-01

Phosphodiesterase 3 (PDE3) and PDE4 regulate levels of cyclic AMP, which are critical in various cell types involved in allergic airway inflammation. Although PDE4 inhibition attenuates allergic airway inflammation, reported side effects preclude its application as an antiasthma drug in humans. Case reports showed that enoximone, which is a smooth muscle relaxant that inhibits PDE3, is beneficial and lifesaving in status asthmaticus and is well tolerated. However, clinical observations also showed antiinflammatory effects of PDE3 inhibition. In this study, we investigated the role of PDE3 in a house dust mite–driven (HDM-driven) allergic airway inflammation (AAI) model that is characterized by T helper 2 cell activation, eosinophilia, and reduced mucosal barrier function. Compared with wild-type (WT) littermates, mice with a targeted deletion of the PDE3A or PDE3B gene showed significantly reduced HDM-driven AAI. Therapeutic intervention in WT mice showed that all hallmarks of HDM-driven AAI were abrogated by the PDE3 inhibitors enoximone and milrinone. Importantly, we found that enoximone also reduced the upregulation of the CD11b integrin on mouse and human eosinophils in vitro, which is crucial for their recruitment during allergic inflammation. This study provides evidence for a hitherto unknown antiinflammatory role of PDE3 inhibition in allergic airway inflammation and offers a potentially novel treatment approach. PMID:29367458

Phosphodiesterase type 4 inhibition enhances nitric oxide- and hydrogen sulfide-mediated bladder neck inhibitory neurotransmission.

PubMed

Agis-Torres, Ángel; Recio, Paz; López-Oliva, María Elvira; Martínez, María Pilar; Barahona, María Victoria; Benedito, Sara; Bustamante, Salvador; Jiménez-Cidre, Miguel Ángel; García-Sacristán, Albino; Prieto, Dolores; Fernandes, Vítor S; Hernández, Medardo

2018-03-16

Nitric oxide (NO) and hydrogen sulfide (H 2 S) play a pivotal role in nerve-mediated relaxation of the bladder outflow region. In the bladder neck, a marked phosphodiesterase type 4 (PDE4) expression has also been described and PDE4 inhibitors, as rolipram, produce smooth muscle relaxation. This study investigates the role of PDE4 isoenzyme in bladder neck gaseous inhibitory neurotransmission. We used Western blot and double immunohistochemical staining for the detection of NPP4 (PDE4) and PDE4A and organ baths for isometric force recording to roflumilast and tadalafil, PDE4 and PDE5, respectively, inhibitors in pig and human samples. Endogenous H 2 S production measurement and electrical field stimulation (EFS) were also performed. A rich PDE4 and PDE4A expression was observed mainly limited to nerve fibers of the smooth muscle layer of both species. Moreover, roflumilast produced a much more potent smooth muscle relaxation than that induced by tadalafil. In porcine samples, H 2 S generation was diminished by H 2 S and NO synthase inhibition and augmented by roflumilast. Relaxations elicited by EFS were potentiated by roflumilast. These results suggest that PDE4, mainly PDE4A, is mostly located within nerve fibers of the pig and human bladder neck, where roflumilast produces a powerful smooth muscle relaxation. In pig, the fact that roflumilast increases endogenous H 2 S production and EFS-induced relaxations suggests a modulation of PDE4 on NO- and H 2 S-mediated inhibitory neurotransmission.

A cAMP-specific phosphodiesterase (PDE8B) that is mutated in adrenal hyperplasia is expressed widely in human and mouse tissues: a novel PDE8B isoform in human adrenal cortex

PubMed Central

Horvath, Anelia; Giatzakis, Christoforos; Tsang, Kitman; Greene, Elizabeth; Osorio, Paulo; Boikos, Sosipatros; Libè, Rossella; Patronas, Yianna; Robinson-White, Audrey; Remmers, Elaine; Bertherat, Jerôme; Nesterova, Maria; Stratakis, Constantine A.

2009-01-01

Bilateral adrenocortical hyperplasia (BAH) is the second most common cause of corticotropin-independent Cushing syndrome (CS). Genetic forms of BAH have been associated with complex syndromes such as Carney Complex and McCune Albright syndrome or may present as isolated micronodular adrenocortical disease (iMAD) usually in children and young adults with CS. A genome-wide association study identified inactivating phosphodiesterase (PDE) 11A (PDE11A) sequencing defects as low-penetrance predisposing factors for iMAD and related abnormalities; we also described a mutation (c.914A>C/H305P) in cAMP-specific PDE8B, in a patient with iMAD. In this study we further characterize this mutation; we also found a novel PDE8B isoform, highly expressed in the adrenal gland. This mutation is shown to significantly affect the ability of the protein to degrade cAMP in vitro. Tumor tissues from patients with iMAD and no mutations in the coding PDE8B sequence or any other related genes (PRKAR1A, PDE11A) showed down-regulated PDE8B expression (compared to normal adrenal cortex). Pde8b is detectable in the adrenal gland of newborn mice and is widely expressed in other mouse tissues. We conclude that PDE8B is another PDE gene linked to iMAD; it is a candidate causative gene for other adrenocortical lesions linked to the cAMP-signaling pathway, and possibly for tumors in other tissues. PMID:18431404

Phosphodiesterase-1b (Pde1b) knockout mice are resistant to forced swim and tail suspension induced immobility and show upregulation of Pde10a.

PubMed

Hufgard, Jillian R; Williams, Michael T; Skelton, Matthew R; Grubisha, Olivera; Ferreira, Filipa M; Sanger, Helen; Wright, Mary E; Reed-Kessler, Tracy M; Rasmussen, Kurt; Duman, Ronald S; Vorhees, Charles V

2017-06-01

Major depressive disorder is a leading cause of suicide and disability. Despite this, current antidepressants provide insufficient efficacy in more than 60% of patients. Most current antidepressants are presynaptic reuptake inhibitors; postsynaptic signal regulation has not received as much attention as potential treatment targets. We examined the effects of disruption of the postsynaptic cyclic nucleotide hydrolyzing enzyme, phosphodiesterase (PDE) 1b, on depressive-like behavior and the effects on PDE1B protein in wild-type (WT) mice following stress. Littermate knockout (KO) and WT mice were tested in locomotor activity, tail suspension (TST), and forced swim tests (FST). FST was also used to compare the effects of two antidepressants, fluoxetine and bupropion, in KO versus WT mice. Messenger RNA (mRNA) expression changes were also determined. WT mice underwent acute or chronic stress and markers of stress and PDE1B expression were examined. Pde1b KO mice exhibited decreased TST and FST immobility. When treated with antidepressants, both WT and KO mice showed decreased FST immobility and the effect was additive in KO mice. Mice lacking Pde1b had increased striatal Pde10a mRNA expression. In WT mice, acute and chronic stress upregulated PDE1B expression while PDE10A expression was downregulated after chronic but not acute stress. PDE1B is a potential therapeutic target for depression treatment because of the antidepressant-like phenotype seen in Pde1b KO mice.

Deterministic Mean-Field Ensemble Kalman Filtering

DOE PAGES

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

2016-05-03

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

Deterministic Mean-Field Ensemble Kalman Filtering

DOE Office of Scientific and Technical Information (OSTI.GOV)

Law, Kody J. H.; Tembine, Hamidou; Tempone, Raul

The proof of convergence of the standard ensemble Kalman filter (EnKF) from Le Gland, Monbet, and Tran [Large sample asymptotics for the ensemble Kalman filter, in The Oxford Handbook of Nonlinear Filtering, Oxford University Press, Oxford, UK, 2011, pp. 598--631] is extended to non-Gaussian state-space models. In this paper, a density-based deterministic approximation of the mean-field limit EnKF (DMFEnKF) is proposed, consisting of a PDE solver and a quadrature rule. Given a certain minimal order of convergence κ between the two, this extends to the deterministic filter approximation, which is therefore asymptotically superior to standard EnKF for dimension d

Adaptive Skin Meshes Coarsening for Biomolecular Simulation

PubMed Central

Shi, Xinwei; Koehl, Patrice

2011-01-01

In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surfaces and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedral that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry. PMID:21779137

Investigation into the role of phosphodiesterase IV in bronchorelaxation, including studies with human bronchus.

PubMed Central

Cortijo, J.; Bou, J.; Beleta, J.; Cardelús, I.; Llenas, J.; Morcillo, E.; Gristwood, R. W.

1993-01-01

1. We have investigated the role of cyclic nucleotide phosphodiesterase IV (PDE IV) in the relaxation of human bronchus and guinea-pig trachea in vitro and in guinea-pigs in vivo. 2. Functional studies showed that the selective PDE IV inhibitors, rolipram and denbufylline, relaxed human and guinea-pig preparations in vitro. 3. Two clinically used xanthine non-selective PDE inhibitors, theophylline and pentoxifylline, were also effective in these preparations, but were much less potent than the selective agents used. 4. The rank order of potency for the four PDE inhibitors in both species was similar. 5. Biochemical studies indicated that PDE IV was the major PDE isoform present in the human bronchial tissue. PDEs I, II and V were also identified. 6. Theophylline and pentoxifylline were, as expected, non-selective inhibitors of the human enzymes, but there was a good correlation between PDE IV inhibitory and bronchorelaxation potencies, suggesting that PDE IV inhibition is important for the clinical bronchodilator activities of the two xanthine compounds. 7. We have confirmed the ability of selective PDE IV inhibitors to cause bronchodilatation in guinea-pigs in vivo. 8. We conclude that our study has provided further evidence that selective PDE IV inhibitors could act as bronchodilators in the clinic. PMID:8383567

Inactivation of Pde8b enhances memory, motor performance, and protects against age-induced motor coordination decay

PubMed Central

Tsai, Li-Chun Lisa; Chan, Guy Chiu-Kai; Nangle, Shannon N.; Shimizu-Albergine, Masami; Jones, Graham; Storm, Daniel R.; Beavo, Joseph A.; Zweifel, Larry S.

2012-01-01

Phosphodiesterases (PDEs) are critical regulatory enzymes in cyclic nucleotide signaling. PDEs have diverse expression patterns within the central nervous system (CNS), show differing affinities for cyclic adenosine monophosphate (cAMP) and cyclic guanosine monophosphate (cGMP), and regulate a vast array of behaviors. Here, we investigated the expression profile of the PDE8 gene family members Pde8a and Pde8b in the mouse brain. We find that Pde8a expression is largely absent in the CNS; by contrast, Pde8b is expressed in select regions of the hippocampus, ventral striatum, and cerebellum. Behavioral analysis of mice with Pde8b gene inactivation (PDE8B KO) demonstrate an enhancement in contextual fear, spatial memory, performance in an appetitive instrumental conditioning task, motor-coordination, and have an attenuation of age-induced motor coordination decline. In addition to improvements observed in select behaviors, we find basal anxiety levels to be increased in PDE8B KO mice. These findings indicate that selective antagonism of PDE8B may be an attractive target for enhancement of cognitive and motor functions; however, possible alterations in affective state will need to be weighed against potential therapeutic value. PMID:22925203

The localization and concentration of the PDE2-encoded high-affinity cAMP phosphodiesterase is regulated by cAMP-dependent protein kinase A in the yeast Saccharomyces cerevisiae.

PubMed

Hu, Yun; Liu, Enkai; Bai, Xiaojia; Zhang, Aili

2010-03-01

The genome of the yeast Saccharomyces cerevisiae encodes two cyclic AMP (cAMP) phosphodiesterases, a low-affinity one, Pde1, and a high-affinity one, Pde2. Pde1 has been ascribed a function for downregulating agonist-induced cAMP accumulation in a protein kinase A (PKA)-governed negative feedback loop, whereas Pde2 controls the basal cAMP level in the cell. Here we show that PKA regulates the localization and protein concentration of Pde2. Pde2 is accumulated in the nucleus in wild-type cells growing on glucose, or in strains with hyperactive PKA. In contrast, in derepressed wild-type cells or cells with attenuated PKA activity, Pde2 is distributed over the nucleus and cytoplasm. We also show evidence indicating that the Pde2 protein level is positively correlated with PKA activity. The increase in the Pde2 protein level in high-PKA strains and in cells growing on glucose was due to its increased half-life. These results suggest that, like its low-affinity counterpart, the high-affinity phosphodiesterase may also play an important role in the PKA-controlled feedback inhibition of intracellular cAMP.

Development of a grid-independent approximate Riemannsolver. Ph.D. Thesis - Michigan Univ.

NASA Technical Reports Server (NTRS)

Rumsey, Christopher Lockwood

1991-01-01

A grid-independent approximate Riemann solver for use with the Euler and Navier-Stokes equations was introduced and explored. The two-dimensional Euler and Navier-Stokes equations are described in Cartesian and generalized coordinates, as well as the traveling wave form of the Euler equations. The spatial and temporal discretization are described for both explicit and implicit time-marching schemes. The grid-aligned flux function of Roe is outlined, while the 5-wave grid-independent flux function is derived. The stability and monotonicity analysis of the 5-wave model are presented. Two-dimensional results are provided and extended to three dimensions. The corresponding results are presented.

Analysis of viscous transonic flow over airfoil sections

NASA Technical Reports Server (NTRS)

Huff, Dennis L.; Wu, Jiunn-Chi; Sankar, L. N.

1987-01-01

A full Navier-Stokes solver has been used to model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to be held at the AIAA 25th Aerospace Sciences Meeting. The NACA 0012, RAE 2822 and Jones airfoils have been investigated for both attached and separated transonic flows. Predictions for pressure distributions, loads, skin friction coefficients, boundary layer displacement thickness and velocity profiles are included and compared with experimental data when possible. Overall, the results are in good agreement with experimental data.

A Solution Adaptive Structured/Unstructured Overset Grid Flow Solver with Applications to Helicopter Rotor Flows

NASA Technical Reports Server (NTRS)

Duque, Earl P. N.; Biswas, Rupak; Strawn, Roger C.

1995-01-01

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor flowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid uses an explicit finite-volume method to solve the Euler equations. Solutions on a helicopter rotor in hover show the ability to accurately convect the rotor wake. However, isotropic subdivision of the tetrahedral mesh rapidly increases the overall problem size.

Discovery of a novel orally active PDE-4 inhibitor effective in an ovalbumin-induced asthma murine model.

PubMed

Kwak, Hyun Jeong; Nam, Ji Yeon; Song, Jin Sook; No, Zaesung; Yang, Sung Don; Cheon, Hyae Gyeong

2012-06-15

Phosphodiesterase-4 (PDE-4) is responsible for metabolizing adenosine 3',5'-cyclic monophosphate that reduces the activation of a wide range of inflammatory cells including eosinophils. PDE-4 inhibitors are under development for the treatment of respiratory diseases such as asthma and chronic obstructive pulmonary disease. Herein, we report a novel PDE-4 inhibitor, PDE-423 (3-[1-(3-cyclopropylmethoxy-4-difluoromethoxybenzyl)-1H-pyrazol-3-yl]-benzoic acid), which shows good in vitro and in vivo oral activities. PDE-423 exhibited in vitro IC(50)s of 140 nM and 550 nM in enzyme assay and cell-based assay, respectively. In vivo study using ovalbumin-induced asthmatic mice revealed that PDE-423 reduced methacholine-stimulated airway hyperreactivity in a dose-dependent manner by once daily oral administration (ED(50)=18.3 mg/kg), in parallel with decreased eosinophil peroxidase activity and improved lung histology. In addition, PDE-423 was effective in diminishing lipopolysaccharide-induced neutrophilia in vivo as well as in vitro. Oral administration of PDE-423 (100 mg/kg) had no effect on the duration of xylazine/ketamine-induced anesthesia and did not induce vomiting incidence in ferrets up to the dose of 1000 mg/kg. The present study indicates that a novel PDE-4 inhibitor, PDE-423, has good pharmacological profiles implicating this as a potential candidate for the development of a new anti-asthmatic drug. Copyright © 2012 Elsevier B.V. All rights reserved.

Discovery of Selective Phosphodiesterase 1 Inhibitors with Memory Enhancing Properties.

PubMed

Dyck, Brian; Branstetter, Bryan; Gharbaoui, Tawfik; Hudson, Andrew R; Breitenbucher, J Guy; Gomez, Laurent; Botrous, Iriny; Marrone, Tami; Barido, Richard; Allerston, Charles K; Cedervall, E Peder; Xu, Rui; Sridhar, Vandana; Barker, Ryan; Aertgeerts, Kathleen; Schmelzer, Kara; Neul, David; Lee, Dong; Massari, Mark Eben; Andersen, Carsten B; Sebring, Kristen; Zhou, Xianbo; Petroski, Robert; Limberis, James; Augustin, Martin; Chun, Lawrence E; Edwards, Thomas E; Peters, Marco; Tabatabaei, Ali

2017-04-27

A series of potent thienotriazolopyrimidinone-based PDE1 inhibitors was discovered. X-ray crystal structures of example compounds from this series in complex with the catalytic domain of PDE1B and PDE10A were determined, allowing optimization of PDE1B potency and PDE selectivity. Reduction of hERG affinity led to greater than a 3000-fold selectivity for PDE1B over hERG. 6-(4-Methoxybenzyl)-9-((tetrahydro-2H-pyran-4-yl)methyl)-8,9,10,11-tetrahydropyrido[4',3':4,5]thieno[3,2-e][1,2,4]triazolo[1,5-c]pyrimidin-5(6H)-one was identified as an orally bioavailable and brain penetrating PDE1B enzyme inhibitor with potent memory-enhancing effects in a rat model of object recognition memory.

Expression of phosphodiesterase 6 (PDE6) in human breast cancer cells.

PubMed

Dong, Hongli; Claffey, Kevin P; Brocke, Stefan; Epstein, Paul M

2013-01-01

Considerable epidemiological evidence demonstrates a positive association between artificial light at night (LAN) levels and incidence rates of breast cancer, suggesting that exposure to LAN is a risk factor for breast cancer. There is a 30-50% higher risk of breast cancer in the highest LAN exposed countries compared to the lowest LAN countries, and studies showing higher incidence of breast cancer among shift workers exposed to more LAN have led the International Agency for Research on Cancer to classify shift work as a probable human carcinogen. Nevertheless, the means by which light can affect breast cancer is still unknown. In this study we examined established human breast cancer cell lines and patients' primary breast cancer tissues for expression of genetic components of phosphodiesterase 6 (PDE6), a cGMP-specific PDE involved in transduction of the light signal, and previously thought to be selectively expressed in photoreceptors. By microarray analysis we find highly significant expression of mRNA for the PDE6B, PDE6C, and PDE6D genes in both the cell lines and patients' tissues, minimal expression of PDE6A and PDE6G and no expression of PDE6H. Using antibody specific for PDE6β, we find expression of PDE6B protein in a wide range of patients' tissues by immunohistochemistry, and in MCF-7 breast cancer cells by immunofluorescence and Western blot analysis. Considerable expression of key circadian genes, PERIOD 2, CLOCK, TIMELESS, CRYPTOCHROME 1, and CRYPTOCHROME 2 was also seen in all breast cancer cell lines and all patients' breast cancer tissues. These studies indicate that genes for PDE6 and control of circadian rhythm are expressed in human breast cancer cells and tissues and may play a role in transducing the effects of light on breast cancer.

Non-invasive Management Options for Erectile Dysfunction When a Phosphodiesterase Type 5 Inhibitor Fails.

PubMed

Lee, Mary; Sharifi, Roohollah

2018-03-01

Phosphodiesterase type 5 inhibitors (PDE5Is) are the drug of choice for medical management of erectile dysfunction (ED). On-demand PDE5Is have an overall efficacy of 60-70% for ED; 30-35% of patients fail to respond to a PDE5I, and 30-50% of non-responders can be salvaged with detailed counseling on proper use and physician follow-up to ensure that the patient has been prescribed an appropriate and full PDE5I clinical trial. True non-responders may be offered intracavernosal injections of erectogenic drugs, intraurethral alprostadil, or surgical insertion of a penile prosthesis. Such options are not discreet and are associated with more adverse effects than PDE5Is. Thus patients may request additional non-invasive medical management options. This review describes published literature on patients who failed to respond to an on-demand PDE5I regimen and were treated with a non-invasive PDEI-based regimen, including switching from one PDE5I to another; increasing the dose of PDE5I above the labeled dosage range; using two PDE5Is concurrently; using a daily PDE5I regimen; or combining a PDE5I with a testosterone supplement, α-adrenergic antagonist, intraurethral or intracavernosal alprostadil, vacuum erection device, or low-intensity shock wave therapy. The limitations of published clinical trials do not allow for sufficient evidence to recommend one option over another. Therefore, in PDE5I-refractory patients, the choice of a specific next step should be individualized based on the preference of the patient and his sexual partner, the advantages and disadvantages of the various options, the concurrent medical illnesses and medications of the patient, and the patient's response to treatment.

Behavioral and neurochemical characterization of mice deficient in the phosphodiesterase-1B (PDE1B) enzyme.

PubMed

Siuciak, J A; McCarthy, S A; Chapin, D S; Reed, T M; Vorhees, C V; Repaske, D R

2007-07-01

PDE1B is a calcium-dependent cyclic nucleotide phosphodiesterase that is highly expressed in the striatum. In order to investigate the physiological role of PDE1B in the central nervous system, PDE1B knockout mice (C57BL/6N background) were assessed in behavioral tests and their brains were assayed for monoamine content. In a variety of well-characterized behavioral tasks, including the elevated plus maze (anxiety-like behavior), forced swim test (depression-like behavior), hot plate (nociception) and two cognition models (passive avoidance and acquisition of conditioned avoidance responding), PDE1B knockout mice performed similarly to wild-type mice. PDE1B knockout mice showed increased baseline exploratory activity when compared to wild-type mice. When challenged with amphetamine (AMPH) and methamphetamine (METH), male and female PDE1B knockout mice showed an exaggerated locomotor response. Male PDE1B knockout mice also showed increased locomotor responses to higher doses of phencyclidine (PCP) and MK-801; however, this effect was not consistently observed in female knockout mice. In the striatum, increased dopamine turnover (DOPAC/DA and HVA/DA ratios) was found in both male and female PDE1B knockout mice. Striatal serotonin (5-HT) levels were also decreased in PDE1B knockout mice, although levels of the metabolite, 5HIAA, were unchanged. The present studies demonstrate increased striatal dopamine turnover in PDE1B knockout mice associated with increased baseline motor activity and an exaggerated locomotor response to dopaminergic stimulants such as methamphetamine and amphetamine. These data further support a role for PDE1B in striatal function.

THOR: an open-source exo-GCM

NASA Astrophysics Data System (ADS)

Grosheintz, Luc; Mendonça, João; Käppeli, Roger; Lukas Grimm, Simon; Mishra, Siddhartha; Heng, Kevin

2015-12-01

In this talk, I will present THOR, the first fully conservative, GPU-accelerated exo-GCM (general circulation model) on a nearly uniform, global grid that treats shocks and is non-hydrostatic. THOR will be freely available to the community as a standard tool.Unlike most GCMs THOR solves the full, non-hydrostatic Euler equations instead of the primitive equations. The equations are solved on a global three-dimensional icosahedral grid by a second order Finite Volume Method (FVM). Icosahedral grids are nearly uniform refinements of an icosahedron. We've implemented three different versions of this grid. FVM conserves the prognostic variables (density, momentum and energy) exactly and doesn't require a diffusion term (artificial viscosity) in the Euler equations to stabilize our solver. Historically FVM was designed to treat discontinuities correctly. Hence it excels at resolving shocks, including those present in hot exoplanetary atmospheres.Atmospheres are generally in near hydrostatic equilibrium. We therefore implement a well-balancing technique recently developed at the ETH Zurich. This well-balancing ensures that our FVM maintains hydrostatic equilibrium to machine precision. Better yet, it is able to resolve pressure perturbations from this equilibrium as small as one part in 100'000. It is important to realize that these perturbations are significantly smaller than the truncation error of the same scheme without well-balancing. If during the course of the simulation (due to forcing) the atmosphere becomes non-hydrostatic, our solver continues to function correctly.THOR just passed an important mile stone. We've implemented the explicit part of the solver. The explicit solver is useful to study instabilities or local problems on relatively short time scales. I'll show some nice properties of the explicit THOR. An explicit solver is not appropriate for climate study because the time step is limited by the sound speed. Therefore, we are working on the first fully implicit GCM. By ESS3, I hope to present results for the advection equation.THOR is part of the Exoclimes Simulation Platform (ESP), a set of open-source community codes for simulating and understanding the atmospheres of exoplanets. The ESP also includes tools for radiative transfer and retrieval (HELIOS), an opacity calculator (HELIOS-K), and a chemical kinetics solver (VULCAN). We expect to publicly release an initial version of THOR in 2016 on www.exoclime.org.

A Block Preconditioned Conjugate Gradient-type Iterative Solver for Linear Systems in Thermal Reservoir Simulation

NASA Astrophysics Data System (ADS)

Betté, Srinivas; Diaz, Julio C.; Jines, William R.; Steihaug, Trond

1986-11-01

A preconditioned residual-norm-reducing iterative solver is described. Based on a truncated form of the generalized-conjugate-gradient method for nonsymmetric systems of linear equations, the iterative scheme is very effective for linear systems generated in reservoir simulation of thermal oil recovery processes. As a consequence of employing an adaptive implicit finite-difference scheme to solve the model equations, the number of variables per cell-block varies dynamically over the grid. The data structure allows for 5- and 9-point operators in the areal model, 5-point in the cross-sectional model, and 7- and 11-point operators in the three-dimensional model. Block-diagonal-scaling of the linear system, done prior to iteration, is found to have a significant effect on the rate of convergence. Block-incomplete-LU-decomposition (BILU) and block-symmetric-Gauss-Seidel (BSGS) methods, which result in no fill-in, are used as preconditioning procedures. A full factorization is done on the well terms, and the cells are ordered in a manner which minimizes the fill-in in the well-column due to this factorization. The convergence criterion for the linear (inner) iteration is linked to that of the nonlinear (Newton) iteration, thereby enhancing the efficiency of the computation. The algorithm, with both BILU and BSGS preconditioners, is evaluated in the context of a variety of thermal simulation problems. The solver is robust and can be used with little or no user intervention.

Conjugate Compressible Fluid Flow and Heat Transfer in Ducts

NASA Technical Reports Server (NTRS)

Cross, M. F.

2011-01-01

A computational approach to modeling transient, compressible fluid flow with heat transfer in long, narrow ducts is presented. The primary application of the model is for analyzing fluid flow and heat transfer in solid propellant rocket motor nozzle joints during motor start-up, but the approach is relevant to a wide range of analyses involving rapid pressurization and filling of ducts. Fluid flow is modeled through solution of the spatially one-dimensional, transient Euler equations. Source terms are included in the governing equations to account for the effects of wall friction and heat transfer. The equation solver is fully-implicit, thus providing greater flexibility than an explicit solver. This approach allows for resolution of pressure wave effects on the flow as well as for fast calculation of the steady-state solution when a quasi-steady approach is sufficient. Solution of the one-dimensional Euler equations with source terms significantly reduces computational run times compared to general purpose computational fluid dynamics packages solving the Navier-Stokes equations with resolved boundary layers. In addition, conjugate heat transfer is more readily implemented using the approach described in this paper than with most general purpose computational fluid dynamics packages. The compressible flow code has been integrated with a transient heat transfer solver to analyze heat transfer between the fluid and surrounding structure. Conjugate fluid flow and heat transfer solutions are presented. The author is unaware of any previous work available in the open literature which uses the same approach described in this paper.

Geometry of PDE's. IV

NASA Astrophysics Data System (ADS)

Prástaro, Agostino

2008-02-01

Following our previous results on this subject [R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(I): Webs on PDE's and integral bordism groups. The general theory, Adv. Math. Sci. Appl. 17 (2007) 239-266; R.P. Agarwal, A. Prástaro, Geometry of PDE's. III(II): Webs on PDE's and integral bordism groups. Applications to Riemannian geometry PDE's, Adv. Math. Sci. Appl. 17 (2007) 267-285; A. Prástaro, Geometry of PDE's and Mechanics, World Scientific, Singapore, 1996; A. Prástaro, Quantum and integral (co)bordism in partial differential equations, Acta Appl. Math. (5) (3) (1998) 243-302; A. Prástaro, (Co)bordism groups in PDE's, Acta Appl. Math. 59 (2) (1999) 111-201; A. Prástaro, Quantized Partial Differential Equations, World Scientific Publishing Co, Singapore, 2004, 500 pp.; A. Prástaro, Geometry of PDE's. I: Integral bordism groups in PDE's, J. Math. Anal. Appl. 319 (2006) 547-566; A. Prástaro, Geometry of PDE's. II: Variational PDE's and integral bordism groups, J. Math. Anal. Appl. 321 (2006) 930-948; A. Prástaro, Th.M. Rassias, Ulam stability in geometry of PDE's, Nonlinear Funct. Anal. Appl. 8 (2) (2003) 259-278; I. Stakgold, Boundary Value Problems of Mathematical Physics, I, The MacMillan Company, New York, 1967; I. Stakgold, Boundary Value Problems of Mathematical Physics, II, Collier-MacMillan, Canada, Ltd, Toronto, Ontario, 1968], integral bordism groups of the Navier-Stokes equation are calculated for smooth, singular and weak solutions, respectively. Then a characterization of global solutions is made on this ground. Enough conditions to assure existence of global smooth solutions are given and related to nullity of integral characteristic numbers of the boundaries. Stability of global solutions are related to some characteristic numbers of the space-like Cauchy dataE Global solutions of variational problems constrained by (NS) are classified by means of suitable integral bordism groups too.

Co-possession of phosphodiesterase type-5 inhibitors (PDE5-I) with nitrates.

PubMed

Chang, Li-Ling; Ma, Mark; Allmen, Heather von; Henderson, Scott C; Harper, Kristine; Hornbuckle, Kenneth

2010-06-01

Estimate the proportion of phosphodiesterase type-5 inhibitor (PDE5-I) patients who co-possess nitrates and compare the proportion of tadalafil patients dispensed nitrates to a matched control group. Secondarily, examine the percentage of co-possession of PDE5-Is and nitrates where the products were dispensed on the same day or written by the same prescriber. Male patients aged 18+ years filling PDE5-I prescriptions between December 2003 and March 2006 were identified using a U.S. longitudinal prescription database (IMS Health LRx). Similar patients not dispensed a PDE5-I during this period were matched to the tadalafil-dispensed cohort using a propensity score approach. Co-possession, as a proxy for concurrent use, was defined as an overlap in time on therapy for a PDE5-I and nitrate and was compared for the three PDE5-Is and for tadalafil to the matched control group. Among 601,063 tadalafil patients, 3.31% were dispensed a nitrate during the study period, compared to 6.18% in control patients (n = 601,063). When co-possessed prescriptions were defined by overlapping exposure periods, the proportion of PDE5-I patients with co-possessed nitrates ranged from 1.44% (tadalafil) to 1.72% (vardenafil) and 2.13% (sildenafil). Co-possession percentages of PDE5-I prescriptions were 0.83% for tadalafil and 1.07% for sildenafil and vardenafil. The majority (54.29%) of co-possessed PDE5-I and nitrate prescriptions had the nitrate dispensed prior to the PDE5-I prescription identified in the study cohort. Keeping in mind the limitations of observational studies, these results suggest that co-dispensing of nitrates and PDE5-Is is low. Compared to control patients, the proportion of nitrate co-possession was lowest for patients filling tadalafil. Tadalafil patients also had the lowest co-possessed proportion among the three PDE5-I cohorts. While the majority of co-possessed drug pairs were prescribed by different providers, the highest percentage of co-prescribing from the same physician was among cardiologists. These results suggest that physicians adhere to contraindications and are careful about co-prescribing of nitrates with PDE-5Is.

Immunoprecipitation of PDE2 phosphorylated and inactivated by an associated protein kinase.

PubMed

Bentley, J Kelley

2005-01-01

A PDE2A2-associated protein kinase phosphorylates PDE2A2 in vivo and in vitro to inhibit its catalytic activity. Rat brain PDE2A2 may be solubilized using nona (ethylene glycol) mono dodecyl ether (Lubrol 12A9). PDE2A2 exists in a complex with a protein kinase regulating its activity in an adenosine triphosphate-dependent manner. When native or recombinant PDE2 is immunoprecipitated from PC12 cells using an antibody to the amino terminus in a buffer containing Lubrol 12A9, protease inhibitors, and phosphatase inhibitors, a coimmunoprecipitating nerve growth factor-stimulated protein kinase acts to phosphorylate it. PDE2A2 phosphoryla-tion occurs optimally at pH 6.5 in a sodium 2-(4-morpholino)-ethane sulfonate buffer with 5 mM MgCl2 and 1 mM Na3VO4. I describe protocols for producing an antibody to an amino-terminal bacterial fusion protein encoding amino acids 1-251 of PDE2A2 as well as the use of this antibody in immunoprecipitating a PDE2: tyrosine protein-kinase complex from rat brain or PC12 cells.

Technique for Calculating Solution Derivatives With Respect to Geometry Parameters in a CFD Code

NASA Technical Reports Server (NTRS)

Mathur, Sanjay

2011-01-01

A solution has been developed to the challenges of computation of derivatives with respect to geometry, which is not straightforward because these are not typically direct inputs to the computational fluid dynamics (CFD) solver. To overcome these issues, a procedure has been devised that can be used without having access to the mesh generator, while still being applicable to all types of meshes. The basic approach is inspired by the mesh motion algorithms used to deform the interior mesh nodes in a smooth manner when the surface nodes, for example, are in a fluid structure interaction problem. The general idea is to model the mesh edges and nodes as constituting a spring-mass system. Changes to boundary node locations are propagated to interior nodes by allowing them to assume their new equilibrium positions, for instance, one where the forces on each node are in balance. The main advantage of the technique is that it is independent of the volumetric mesh generator, and can be applied to structured, unstructured, single- and multi-block meshes. It essentially reduces the problem down to defining the surface mesh node derivatives with respect to the geometry parameters of interest. For analytical geometries, this is quite straightforward. In the more general case, one would need to be able to interrogate the underlying parametric CAD (computer aided design) model and to evaluate the derivatives either analytically, or by a finite difference technique. Because the technique is based on a partial differential equation (PDE), it is applicable not only to forward mode problems (where derivatives of all the output quantities are computed with respect to a single input), but it could also be extended to the adjoint problem, either by using an analytical adjoint of the PDE or a discrete analog.

A PDE Sensitivity Equation Method for Optimal Aerodynamic Design

NASA Technical Reports Server (NTRS)

Borggaard, Jeff; Burns, John

1996-01-01

The use of gradient based optimization algorithms in inverse design is well established as a practical approach to aerodynamic design. A typical procedure uses a simulation scheme to evaluate the objective function (from the approximate states) and its gradient, then passes this information to an optimization algorithm. Once the simulation scheme (CFD flow solver) has been selected and used to provide approximate function evaluations, there are several possible approaches to the problem of computing gradients. One popular method is to differentiate the simulation scheme and compute design sensitivities that are then used to obtain gradients. Although this black-box approach has many advantages in shape optimization problems, one must compute mesh sensitivities in order to compute the design sensitivity. In this paper, we present an alternative approach using the PDE sensitivity equation to develop algorithms for computing gradients. This approach has the advantage that mesh sensitivities need not be computed. Moreover, when it is possible to use the CFD scheme for both the forward problem and the sensitivity equation, then there are computational advantages. An apparent disadvantage of this approach is that it does not always produce consistent derivatives. However, for a proper combination of discretization schemes, one can show asymptotic consistency under mesh refinement, which is often sufficient to guarantee convergence of the optimal design algorithm. In particular, we show that when asymptotically consistent schemes are combined with a trust-region optimization algorithm, the resulting optimal design method converges. We denote this approach as the sensitivity equation method. The sensitivity equation method is presented, convergence results are given and the approach is illustrated on two optimal design problems involving shocks.

An optimization-based approach for high-order accurate discretization of conservation laws with discontinuous solutions

NASA Astrophysics Data System (ADS)

Zahr, M. J.; Persson, P.-O.

2018-07-01

This work introduces a novel discontinuity-tracking framework for resolving discontinuous solutions of conservation laws with high-order numerical discretizations that support inter-element solution discontinuities, such as discontinuous Galerkin or finite volume methods. The proposed method aims to align inter-element boundaries with discontinuities in the solution by deforming the computational mesh. A discontinuity-aligned mesh ensures the discontinuity is represented through inter-element jumps while smooth basis functions interior to elements are only used to approximate smooth regions of the solution, thereby avoiding Gibbs' phenomena that create well-known stability issues. Therefore, very coarse high-order discretizations accurately resolve the piecewise smooth solution throughout the domain, provided the discontinuity is tracked. Central to the proposed discontinuity-tracking framework is a discrete PDE-constrained optimization formulation that simultaneously aligns the computational mesh with discontinuities in the solution and solves the discretized conservation law on this mesh. The optimization objective is taken as a combination of the deviation of the finite-dimensional solution from its element-wise average and a mesh distortion metric to simultaneously penalize Gibbs' phenomena and distorted meshes. It will be shown that our objective function satisfies two critical properties that are required for this discontinuity-tracking framework to be practical: (1) possesses a local minima at a discontinuity-aligned mesh and (2) decreases monotonically to this minimum in a neighborhood of radius approximately h / 2, whereas other popular discontinuity indicators fail to satisfy the latter. Another important contribution of this work is the observation that traditional reduced space PDE-constrained optimization solvers that repeatedly solve the conservation law at various mesh configurations are not viable in this context since severe overshoot and undershoot in the solution, i.e., Gibbs' phenomena, may make it impossible to solve the discrete conservation law on non-aligned meshes. Therefore, we advocate a gradient-based, full space solver where the mesh and conservation law solution converge to their optimal values simultaneously and therefore never require the solution of the discrete conservation law on a non-aligned mesh. The merit of the proposed method is demonstrated on a number of one- and two-dimensional model problems including the L2 projection of discontinuous functions, Burgers' equation with a discontinuous source term, transonic flow through a nozzle, and supersonic flow around a bluff body. We demonstrate optimal O (h p + 1) convergence rates in the L1 norm for up to polynomial order p = 6 and show that accurate solutions can be obtained on extremely coarse meshes.

Implicit solution of three-dimensional internal turbulent flows

NASA Technical Reports Server (NTRS)

Michelassi, V.; Liou, M.-S.; Povinelli, Louis A.; Martelli, F.

1991-01-01

The scalar form of the approximate factorization method was used to develop a new code for the solution of three dimensional internal laminar and turbulent compressible flows. The Navier-Stokes equations in their Reynolds-averaged form were iterated in time until a steady solution was reached. Evidence was given to the implicit and explicit artificial damping schemes that proved to be particularly efficient in speeding up convergence and enhancing the algorithm robustness. A conservative treatment of these terms at the domain boundaries was proposed in order to avoid undesired mass and/or momentum artificial fluxes. Turbulence effects were accounted for by the zero-equation Baldwin-Lomax turbulence model and the q-omega two-equation model. The flow in a developing S-duct was then solved in the laminar regime in a Reynolds number (Re) of 790 and in the turbulent regime at Re equals 40,000 by using the Baldwin-Lomax model. The Stanitz elbow was then solved by using an invicid version of the same code at M sub inlet equals 0.4. Grid dependence and convergence rate were investigated, showing that for this solver the implicit damping scheme may play a critical role for convergence characteristics. The same flow at Re equals 2.5 times 10(exp 6) was solved with the Baldwin-Lomax and the q-omega models. Both approaches show satisfactory agreement with experiments, although the q-omega model was slightly more accurate.

Inhibition of phosphodiesterase 4 reduces ethanol intake and preference in C57BL/6J mice

PubMed Central

Blednov, Yuri A.; Benavidez, Jillian M.; Black, Mendy; Harris, R. Adron

2014-01-01

Some anti-inflammatory medications reduce alcohol consumption in rodent models. Inhibition of phosphodiesterases (PDE) increases cAMP and reduces inflammatory signaling. Rolipram, an inhibitor of PDE4, markedly reduced ethanol intake and preference in mice and reduced ethanol seeking and consumption in alcohol-preferring fawn-hooded rats (Hu et al., 2011; Wen et al., 2012). To determine if these effects were specific for PDE4, we compared nine PDE inhibitors with different subtype selectivity: propentofylline (nonspecific), vinpocetine (PDE1), olprinone, milrinone (PDE3), zaprinast (PDE5), rolipram, mesopram, piclamilast, and CDP840 (PDE4). Alcohol intake was measured in C57BL/6J male mice using 24-h two-bottle choice and two-bottle choice with limited (3-h) access to alcohol. Only the selective PDE4 inhibitors reduced ethanol intake and preference in the 24-h two-bottle choice test. For rolipram, piclamilast, and CDP840, this effect was observed after the first 6 h but not after the next 18 h. Mesopram, however, produced a long-lasting reduction of ethanol intake and preference. In the limited access test, rolipram, piclamilast, and mesopram reduced ethanol consumption and total fluid intake and did not change preference for ethanol, whereas CDP840 reduced both consumption and preference without altering total fluid intake. Our results provide novel evidence for a selective role of PDE4 in regulating ethanol drinking in mice. We suggest that inhibition of PDE4 may be an unexplored target for medication development to reduce excessive alcohol consumption. PMID:24904269

Phosphodiesterase-10A Inverse Changes in Striatopallidal and Striatoentopeduncular Pathways of a Transgenic Mouse Model of DYT1 Dystonia.

PubMed

D'Angelo, Vincenza; Castelli, Valentina; Giorgi, Mauro; Cardarelli, Silvia; Saverioni, Ilaria; Palumbo, Francesca; Bonsi, Paola; Pisani, Antonio; Giampà, Carmela; Sorge, Roberto; Biagioni, Stefano; Fusco, Francesca R; Sancesario, Giuseppe

2017-02-22

We report that changes of phosphodiesterase-10A (PDE10A) can map widespread functional imbalance of basal ganglia circuits in a mouse model of DYT1 dystonia overexpressing mutant torsinA. PDE10A is a key enzyme in the catabolism of second messenger cAMP and cGMP, whose synthesis is stimulated by D1 receptors and inhibited by D2 receptors preferentially expressed in striatoentopeducuncular/substantia nigra or striatopallidal pathways, respectively. PDE10A was studied in control mice (NT) and in mice carrying human wild-type torsinA (hWT) or mutant torsinA (hMT). Quantitative analysis of PDE10A expression was assessed in different brain areas by rabbit anti-PDE10A antibody immunohistochemistry and Western blotting. PDE10A-dependent cAMP hydrolyzing activity and PDE10A mRNA were also assessed. Striatopallidal neurons were identified by rabbit anti-enkephalin antibody.In NT mice, PDE10A is equally expressed in medium spiny striatal neurons and in their projections to entopeduncular nucleus/substantia nigra and to external globus pallidus. In hMT mice, PDE10A content selectively increases in enkephalin-positive striatal neuronal bodies; moreover, PDE10A expression and activity in hMT mice, compared with NT mice, significantly increase in globus pallidus but decrease in entopeduncular nucleus/substantia nigra. Similar changes of PDE10A occur in hWT mice, but such changes are not always significant. However, PDE10A mRNA expression appears comparable among NT, hWT, and hMT mice.In DYT1 transgenic mice, the inverse changes of PDE10A in striatoentopeduncular and striatopallidal projections might result over time in an imbalance between direct and indirect pathways for properly focusing movement. The decrease of PDE10A in the striatoentopeduncular/nigral projections might lead to increased intensity and duration of D1-stimulated cAMP/cGMP signaling; conversely, the increase of PDE10A in the striatopallidal projections might lead to increased intensity and duration of D2-inhibited cAMP/cGMP signaling. SIGNIFICANCE STATEMENT In DYT1 transgenic mouse model of dystonia, PDE10A, a key enzyme in cAMP and cGMP catabolism, is downregulated in striatal projections to entopeduncular nucleus/substantia nigra, preferentially expressing D1 receptors that stimulate cAMP/cGMP synthesis. Conversely, in DYT1 mice, PDE10A is upregulated in striatal projections to globus pallidus, preferentially expressing D2 receptors that inhibit cAMP/cGMP synthesis. The inverse changes to PDE10A in striatoentopeduncular/substantia nigra and striatopallidal pathways might tightly interact downstream to dopamine receptors, likely resulting over time to increased intensity and duration respectively of D1-stimulated and D2-inhibited cAMP/cGMP signals. Therefore, PDE10A changes in the DYT1 model of dystonia can upset the functional balance of basal ganglia circuits, affecting direct and indirect pathways simultaneously. Copyright © 2017 the authors 0270-6474/17/372113-13$15.00/0.

Visualization of Unsteady Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Haimes, Robert

1997-01-01

The current compute environment that most researchers are using for the calculation of 3D unsteady Computational Fluid Dynamic (CFD) results is a super-computer class machine. The Massively Parallel Processors (MPP's) such as the 160 node IBM SP2 at NAS and clusters of workstations acting as a single MPP (like NAS's SGI Power-Challenge array and the J90 cluster) provide the required computation bandwidth for CFD calculations of transient problems. If we follow the traditional computational analysis steps for CFD (and we wish to construct an interactive visualizer) we need to be aware of the following: (1) Disk space requirements. A single snap-shot must contain at least the values (primitive variables) stored at the appropriate locations within the mesh. For most simple 3D Euler solvers that means 5 floating point words. Navier-Stokes solutions with turbulence models may contain 7 state-variables. (2) Disk speed vs. Computational speeds. The time required to read the complete solution of a saved time frame from disk is now longer than the compute time for a set number of iterations from an explicit solver. Depending, on the hardware and solver an iteration of an implicit code may also take less time than reading the solution from disk. If one examines the performance improvements in the last decade or two, it is easy to see that depending on disk performance (vs. CPU improvement) may not be the best method for enhancing interactivity. (3) Cluster and Parallel Machine I/O problems. Disk access time is much worse within current parallel machines and cluster of workstations that are acting in concert to solve a single problem. In this case we are not trying to read the volume of data, but are running the solver and the solver outputs the solution. These traditional network interfaces must be used for the file system. (4) Numerics of particle traces. Most visualization tools can work upon a single snap shot of the data but some visualization tools for transient problems require dealing with time.

Algorithm and code development for unsteady three-dimensional Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Obayashi, Shigeru

1991-01-01

A streamwise upwind algorithm for solving the unsteady 3-D Navier-Stokes equations was extended to handle the moving grid system. It is noted that the finite volume concept is essential to extend the algorithm. The resulting algorithm is conservative for any motion of the coordinate system. Two extensions to an implicit method were considered and the implicit extension that makes the algorithm computationally efficient is implemented into Ames's aeroelasticity code, ENSAERO. The new flow solver has been validated through the solution of test problems. Test cases include three-dimensional problems with fixed and moving grids. The first test case shown is an unsteady viscous flow over an F-5 wing, while the second test considers the motion of the leading edge vortex as well as the motion of the shock wave for a clipped delta wing. The resulting algorithm has been implemented into ENSAERO. The upwind version leads to higher accuracy in both steady and unsteady computations than the previously used central-difference method does, while the increase in the computational time is small.

The Magnetic Reconnection Code: an AMR-based fully implicit simulation suite

NASA Astrophysics Data System (ADS)

Germaschewski, K.; Bhattacharjee, A.; Ng, C.-S.

2006-12-01

Extended MHD models, which incorporate two-fluid effects, are promising candidates to enhance understanding of collisionless reconnection phenomena in laboratory, space and astrophysical plasma physics. In this paper, we introduce two simulation codes in the Magnetic Reconnection Code suite which integrate reduced and full extended MHD models. Numerical integration of these models comes with two challenges: Small-scale spatial structures, e.g. thin current sheets, develop and must be well resolved by the code. Adaptive mesh refinement (AMR) is employed to provide high resolution where needed while maintaining good performance. Secondly, the two-fluid effects in extended MHD give rise to dispersive waves, which lead to a very stringent CFL condition for explicit codes, while reconnection happens on a much slower time scale. We use a fully implicit Crank--Nicholson time stepping algorithm. Since no efficient preconditioners are available for our system of equations, we instead use a direct solver to handle the inner linear solves. This requires us to actually compute the Jacobian matrix, which is handled by a code generator that calculates the derivative symbolically and then outputs code to calculate it.

Multiscale Failure Analysis of Laminated Composite Panels Subjected to Blast Loading Using FEAMAC/Explicit

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.; Berdnarcyk, Brett A.; Arnold, Steven M.; Collier, Craig S.

2009-01-01

This preliminary report demonstrates the capabilities of the recently developed software implementation that links the Generalized Method of Cells to explicit finite element analysis by extending a previous development which tied the generalized method of cells to implicit finite elements. The multiscale framework, which uses explicit finite elements at the global-scale and the generalized method of cells at the microscale is detailed. This implementation is suitable for both dynamic mechanics problems and static problems exhibiting drastic and sudden changes in material properties, which often encounter convergence issues with commercial implicit solvers. Progressive failure analysis of stiffened and un-stiffened fiber-reinforced laminates subjected to normal blast pressure loads was performed and is used to demonstrate the capabilities of this framework. The focus of this report is to document the development of the software implementation; thus, no comparison between the results of the models and experimental data is drawn. However, the validity of the results are assessed qualitatively through the observation of failure paths, stress contours, and the distribution of system energies.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacon, Luis; Stanier, Adam John

Here, we demonstrate a scalable fully implicit algorithm for the two-field low-β extended MHD model. This reduced model describes plasma behavior in the presence of strong guide fields, and is of significant practical impact both in nature and in laboratory plasmas. The model displays strong hyperbolic behavior, as manifested by the presence of fast dispersive waves, which make a fully implicit treatment very challenging. In this study, we employ a Jacobian-free Newton–Krylov nonlinear solver, for which we propose a physics-based preconditioner that renders the linearized set of equations suitable for inversion with multigrid methods. As a result, the algorithm ismore » shown to scale both algorithmically (i.e., the iteration count is insensitive to grid refinement and timestep size) and in parallel in a weak-scaling sense, with the wall-clock time scaling weakly with the number of cores for up to 4096 cores. For a 4096 × 4096 mesh, we demonstrate a wall-clock-time speedup of ~6700 with respect to explicit algorithms. The model is validated linearly (against linear theory predictions) and nonlinearly (against fully kinetic simulations), demonstrating excellent agreement.« less

Computations of Wall Distances Based on Differential Equations

NASA Technical Reports Server (NTRS)

Tucker, Paul G.; Rumsey, Chris L.; Spalart, Philippe R.; Bartels, Robert E.; Biedron, Robert T.

2004-01-01

The use of differential equations such as Eikonal, Hamilton-Jacobi and Poisson for the economical calculation of the nearest wall distance d, which is needed by some turbulence models, is explored. Modifications that could palliate some turbulence-modeling anomalies are also discussed. Economy is of especial value for deforming/adaptive grid problems. For these, ideally, d is repeatedly computed. It is shown that the Eikonal and Hamilton-Jacobi equations can be easy to implement when written in implicit (or iterated) advection and advection-diffusion equation analogous forms, respectively. These, like the Poisson Laplacian term, are commonly occurring in CFD solvers, allowing the re-use of efficient algorithms and code components. The use of the NASA CFL3D CFD program to solve the implicit Eikonal and Hamilton-Jacobi equations is explored. The re-formulated d equations are easy to implement, and are found to have robust convergence. For accurate Eikonal solutions, upwind metric differences are required. The Poisson approach is also found effective, and easiest to implement. Modified distances are not found to affect global outputs such as lift and drag significantly, at least in common situations such as airfoil flows.

Fully-Implicit Orthogonal Reconstructed Discontinuous Galerkin for Fluid Dynamics with Phase Change

DOE PAGES

Nourgaliev, R.; Luo, H.; Weston, B.; ...

2015-11-11

A new reconstructed Discontinuous Galerkin (rDG) method, based on orthogonal basis/test functions, is developed for fluid flows on unstructured meshes. Orthogonality of basis functions is essential for enabling robust and efficient fully-implicit Newton-Krylov based time integration. The method is designed for generic partial differential equations, including transient, hyperbolic, parabolic or elliptic operators, which are attributed to many multiphysics problems. We demonstrate the method’s capabilities for solving compressible fluid-solid systems (in the low Mach number limit), with phase change (melting/solidification), as motivated by applications in Additive Manufacturing (AM). We focus on the method’s accuracy (in both space and time), as wellmore » as robustness and solvability of the system of linear equations involved in the linearization steps of Newton-based methods. The performance of the developed method is investigated for highly-stiff problems with melting/solidification, emphasizing the advantages from tight coupling of mass, momentum and energy conservation equations, as well as orthogonality of basis functions, which leads to better conditioning of the underlying (approximate) Jacobian matrices, and rapid convergence of the Krylov-based linear solver.« less

An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Thomas, J. L.; Bonhaus, D. L.; Anderson, W. K.; Rumsey, C. L.; Biedron, R. T.

1999-01-01

A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.

Comparison of Implicit Schemes for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1995-01-01

For a computational flow simulation tool to be useful in a design environment, it must be very robust and efficient. To develop such a tool for incompressible flow applications, a number of different implicit schemes are compared for several two-dimensional flow problems in the current study. The schemes include Point-Jacobi relaxation, Gauss-Seidel line relaxation, incomplete lower-upper decomposition, and the generalized minimum residual method preconditioned with each of the three other schemes. The efficiency of the schemes is measured in terms of the computing time required to obtain a steady-state solution for the laminar flow over a backward-facing step, the flow over a NACA 4412 airfoil, and the flow over a three-element airfoil using overset grids. The flow solver used in the study is the INS2D code that solves the incompressible Navier-Stokes equations using the method of artificial compressibility and upwind differencing of the convective terms. The results show that the generalized minimum residual method preconditioned with the incomplete lower-upper factorization outperforms all other methods by at least a factor of 2.

Design, optimization, and biological evaluation of novel keto-benzimidazoles as potent and selective inhibitors of phosphodiesterase 10A (PDE10A).

PubMed

Hu, Essa; Kunz, Roxanne K; Chen, Ning; Rumfelt, Shannon; Siegmund, Aaron; Andrews, Kristin; Chmait, Samer; Zhao, Sharon; Davis, Carl; Chen, Hang; Lester-Zeiner, Dianna; Ma, Ji; Biorn, Christopher; Shi, Jianxia; Porter, Amy; Treanor, James; Allen, Jennifer R

2013-11-14

Our development of PDE10A inhibitors began with an HTS screening hit (1) that exhibited both high p-glycoprotein (P-gp) efflux ratios in rat and human and poor metabolic stability. On the basis of cocrystal structure of 1 in human PDE10A enzyme, we designed a novel keto-benzimidazole 26 with comparable PDE10A potency devoid of efflux liabilities. On target in vivo coverage of PDE10A in rat brain was assessed using our previously reported LC-MS/MS receptor occupancy (RO) technology. Compound 26 achieved 55% RO of PDE10A at 30 mg/kg po and covered PDE10A receptors in rat brain in a dose-dependent manner. Cocrystal structure of 26 in PDE10A confirmed the binding mode of the novel scaffold. Further optimization resulted in the identification of keto-benzimidazole 34, which showed an increased in vivo efficacy of 57% RO in rats at 10 mg/kg po and an improved in vivo rat clearance and oral bioavailability.

Cyclic Nucleotide Phosphodiesterases: important signaling modulators and therapeutic targets

PubMed Central

Ahmad, Faiyaz; Murata, Taku; Simizu, Kasumi; Degerman, Eva; Maurice, Donald; Manganiello, Vincent

2014-01-01

By catalyzing hydrolysis of cAMP and cGMP, cyclic nucleotide phosphodiesterases are critical regulators of their intracellular concentrations and their biological effects. Since these intracellular second messengers control many cellular homeostatic processes, dysregulation of their signals and signaling pathways initiate or modulate pathophysiological pathways related to various disease states, including erectile dysfunction, pulmonary hypertension, acute refractory cardiac failure, intermittent claudication, chronic obstructive pulmonary disease, and psoriasis. Alterations in expression of PDEs and PDE-gene mutations (especially mutations in PDE6, PDE8B, PDE11A and PDE4) have been implicated in various diseases and cancer pathologies. PDEs also play important role in formation and function of multi-molecular signaling/regulatory complexes called signalosomes. At specific intracellular locations, individual PDEs, together with pathway-specific signaling molecules, regulators, and effectors, are incorporated into specific signalosomes, where they facilitate and regulate compartmentalization of cyclic nucleotide signaling pathways and specific cellular functions. Currently, only a limited number of PDE inhibitors (PDE3, PDE4, PDE5 inhibitors) are used in clinical practice. Future paths to novel drug discovery include the crystal structure-based design approach, which has resulted in generation of more effective family-selective inhibitors, as well as burgeoning development of strategies to alter compartmentalized cyclic nucleotide signaling pathways by selectively targeting individual PDEs and their signalosome partners. PMID:25056711

Evolution and expression of the phosphodiesterase 6 genes unveils vertebrate novelty to control photosensitivity.

PubMed

Lagman, David; Franzén, Ilkin E; Eggert, Joel; Larhammar, Dan; Abalo, Xesús M

2016-06-13

Phosphodiesterase 6 (PDE6) is a protein complex that hydrolyses cGMP and acts as the effector of the vertebrate phototransduction cascade. The PDE6 holoenzyme consists of catalytic and inhibitory subunits belonging to two unrelated gene families. Rods and cones express distinct genes from both families: PDE6A and PDE6B code for the catalytic and PDE6G the inhibitory subunits in rods while PDE6C codes for the catalytic and PDE6H the inhibitory subunits in cones. We performed phylogenetic and comparative synteny analyses for both gene families in genomes from a broad range of animals. Furthermore, gene expression was investigated in zebrafish. We found that both gene families expanded from one to three members in the two rounds of genome doubling (2R) that occurred at the base of vertebrate evolution. The PDE6 inhibitory subunit gene family appears to be unique to vertebrates and expanded further after the teleost-specific genome doubling (3R). We also describe a new family member that originated in 2R and has been lost in amniotes, which we have named pde6i. Zebrafish has retained two additional copies of the PDE6 inhibitory subunit genes after 3R that are highly conserved, have high amino acid sequence identity, are coexpressed in the same photoreceptor type as their amniote orthologs and, interestingly, show strikingly different daily oscillation in gene expression levels. Together, these data suggest specialisation related to the adaptation to different light intensities during the day-night cycle, most likely maintaining the regulatory function of the PDE inhibitory subunits in the phototransduction cascade.

Recreational Use of Phosphodiesterase 5 Inhibitors and Its Associated Factors among Undergraduate Male Students in an Ethiopian University: A Cross-Sectional Study.

PubMed

Gebreyohannes, Eyob Alemayehu; Bhagavathula, Akshaya Srikanth; Gebresillassie, Begashaw Melaku; Tefera, Yonas Getaye; Belachew, Sewunet Admasu; Erku, Daniel Asfaw

2016-12-01

To assess the prevalence of phosphodiesterase 5 (PDE5) inhibitor use and associated factors among University of Gondar undergraduate students. An institution-based, cross-sectional study, using a survey questionnaire, was conducted from October to December 2015 to assess PDE5 inhibitor use and associated factors among male students at the University of Gondar. A Self-Esteem and Relationship questionnaire (14 items), an International Index of Erectile Function questionnaire (15 items) and a questionnaire on PDE5 inhibitor use (14 items) were included in the survey. Across all respondents (age, 21.9±1.88 years), more than half (55.7%, n=233) had heard about PDE5 inhibitors, but only 23 men (5.5%) reported trying a PDE5 inhibitor drug at least once. Older students were more likely to use PDE5 inhibitors compared to younger students (adjusted odds ratio [AOR], 1.40; 95% confidence interval [CI], 1.109~1.768). Those students who were smokers were 5.15 times more likely to use PDE5 inhibitors as compared to their non-smoking counterparts (AOR, 5.15; 95% CI, 2.096~12.687). In addition, multivariate logistic regression showed that being in a relationship, alcohol use, greater number of cigarettes smoked per day, and more sexual partners were significantly associated with PDE5 inhibitor use. The prevalence of PDE5 inhibitor use among undergraduate students was 5.5%. Cigarette smoking and other substance use, older age, and greater number of sexual partners were significantly associated factors for PDE5 inhibitor use. These findings suggest that restricting access to PDE5 inhibitor drugs is essential to curtailing misuse among university students.

Recreational Use of Phosphodiesterase 5 Inhibitors and Its Associated Factors among Undergraduate Male Students in an Ethiopian University: A Cross-Sectional Study

PubMed Central

Bhagavathula, Akshaya Srikanth; Gebresillassie, Begashaw Melaku; Tefera, Yonas Getaye; Belachew, Sewunet Admasu; Erku, Daniel Asfaw

2016-01-01

Purpose To assess the prevalence of phosphodiesterase 5 (PDE5) inhibitor use and associated factors among University of Gondar undergraduate students. Materials and Methods An institution-based, cross-sectional study, using a survey questionnaire, was conducted from October to December 2015 to assess PDE5 inhibitor use and associated factors among male students at the University of Gondar. A Self-Esteem and Relationship questionnaire (14 items), an International Index of Erectile Function questionnaire (15 items) and a questionnaire on PDE5 inhibitor use (14 items) were included in the survey. Results Across all respondents (age, 21.9±1.88 years), more than half (55.7%, n=233) had heard about PDE5 inhibitors, but only 23 men (5.5%) reported trying a PDE5 inhibitor drug at least once. Older students were more likely to use PDE5 inhibitors compared to younger students (adjusted odds ratio [AOR], 1.40; 95% confidence interval [CI], 1.109~1.768). Those students who were smokers were 5.15 times more likely to use PDE5 inhibitors as compared to their non-smoking counterparts (AOR, 5.15; 95% CI, 2.096~12.687). In addition, multivariate logistic regression showed that being in a relationship, alcohol use, greater number of cigarettes smoked per day, and more sexual partners were significantly associated with PDE5 inhibitor use. Conclusions The prevalence of PDE5 inhibitor use among undergraduate students was 5.5%. Cigarette smoking and other substance use, older age, and greater number of sexual partners were significantly associated factors for PDE5 inhibitor use. These findings suggest that restricting access to PDE5 inhibitor drugs is essential to curtailing misuse among university students. PMID:28053948

The oligomerization state determines regulatory properties and inhibitor sensitivity of type 4 cAMP-specific phosphodiesterases.

PubMed

Richter, Wito; Conti, Marco

2004-07-16

PDE4 splice variants are classified into long and short forms depending on the presence or absence of two unique N-terminal domains termed upstream conserved regions 1 and 2 (UCR1 and -2). We have shown previously that the UCR module mediates dimerization of PDE4 long forms, whereas short forms, which lack UCR1, behave as monomers. In the present study, we demonstrate that dimerization is an essential structural element that determines the regulatory properties and inhibitor sensitivities of PDE4 enzymes. Comparing the properties of the dimeric wild type PDE4D3 with several monomeric mutant PDE4D3 constructs revealed that disruption of dimerization ablates the activation of PDE4 long forms by either protein kinase A phosphorylation or phosphatidic acid binding. Moreover, the analysis of heterodimers consisting of a catalytically active and a catalytically inactive PDE4D3 subunit indicates that protein kinase A phosphorylation of both subunits is essential to fully activate PDE4 enzymes. In addition to affecting enzyme regulation, disruption of dimerization reduces the sensitivity of the enzymes toward the prototypical PDE4 inhibitor rolipram. Parallel binding assays indicated that this shift in rolipram sensitivity is likely mediated by a decrease in the number of inhibitor binding sites in the high affinity rolipram binding state. Thus, although dimerization is not a requirement for high affinity rolipram binding, it functions to stabilize PDE4 long forms in their high affinity rolipram binding conformation. Taken together, our data indicate that dimerization defines the properties of PDE4 enzymes and suggest a common structural and functional organization for all PDEs.

Behavioral characterization of mice deficient in the phosphodiesterase-10A (PDE10A) enzyme on a C57/Bl6N congenic background.

PubMed

Siuciak, Judith A; McCarthy, Sheryl A; Chapin, Douglas S; Martin, Ashley N; Harms, John F; Schmidt, Christopher J

2008-02-01

The phenotype of genetically modified animals is strongly influenced by both the genetic background of the animal as well as environmental factors. We have previously reported the behavioral and neurochemical characterization of PDE10A knockout mice maintained on a DBA1LacJ (PDE10A(DBA)) genetic background. The aim of the present studies was to assess the behavioral and neurochemical phenotype of PDE10A knockout mice on an alternative congenic C57BL/6N (PDE10A(C57)) genetic background. Consistent with our previous results, PDE10A(C57) knockout mice showed a decrease in exploratory locomotor activity and a delay in the acquisition of conditioned avoidance responding. Also consistent with previous studies, the elimination of PDE10A did not alter basal levels of striatal cGMP or cAMP or affect behavior in several other well-characterized behavioral assays. PDE10A(C57) knockout mice showed a blunted response to MK-801, although to a lesser degree than previously observed in the PDE10A(DBA) knockout mice, and no differences were observed following a PCP challenge. PDE10A(C57) knockout mice showed a significant change in striatal dopamine turnover, which was accompanied by an enhanced locomotor response to AMPH, These studies demonstrate that while many of the behavioral effects of the PDE10A gene deletion appear to be independent of genetic background, the impact of the deletion on behavior can vary in magnitude. Furthermore, the effects on the dopaminergic system appear to be background-dependent, with significant effects observed only in knockout mice on the C57BL6N genetic background.

Angiotensin II increases phosphodiesterase 5A expression in vascular smooth muscle cells: A mechanism by which angiotensin II antagonizes cGMP signaling

PubMed Central

Kim, Dongsoo; Aizawa, Toru; Wei, Heng; Pi, Xinchun; Rybalkin, Sergei D.; Berk, Bradford C.; Yan, Chen

2014-01-01

Angiotensin II (Ang II) and nitric oxide (NO)/natriuretic peptide (NP) signaling pathways mutually regulate each other. Imbalance of Ang II and NO/NP has been implicated in the pathophysiology of many vascular diseases. cGMP functions as a key mediator in the interaction between Ang II and NO/NP. Cyclic nucleotide phosphodiesterase 5A (PDE5A) is important in modulating cGMP signaling by hydrolyzing cGMP in vascular smooth muscle cells (VSMC). Therefore, we examined whether Ang II negatively modulates intracellular cGMP signaling in VSMC by regulating PDE5A. Ang II rapidly and transiently increased PDE5A mRNA levels in rat aortic VSMC. Upregulation of PDE5A mRNA was associated with a time-dependent increase of both PDE5 protein expression and activity. Increased PDE5A mRNA level was transcription-dependent and mediated by the Ang II type 1 receptor. Ang II-mediated activation of extracellular signal-regulated kinases 1/2 (ERK1/2) was essential for Ang II-induced PDE5A upregulation. Pretreatment of VSMC with Ang II inhibited C-type NP (CNP) stimulated cGMP signaling, such as cGMP dependent protein kinase (PKG)-mediated phosphorylation of vasodilator-stimulated-phosphoprotein (VASP). Ang II-mediated inhibition of PKG was blocked when PDE5 activity was decreased by selective PDE5 inhibitors, suggesting that upregulation of PDE5A expression is an important mechanism for Ang II to attenuate cGMP signaling. PDE5A may also play a critical role in the growth promoting effects of Ang II because inhibition of PDE5A activity significantly decreased Ang II-stimulated VSMC growth. These observations establish a new mechanism by which Ang II antagonizes cGMP signaling and stimulates VSMC growth. PMID:15623434

Distinct phosphodiesterase 5A-containing compartments allow selective regulation of cGMP-dependent signalling in human arterial smooth muscle cells.

PubMed

Wilson, Lindsay S; Guo, Manhong; Umana, M Bibiana; Maurice, Donald H

2017-08-01

Cyclic GMP (cGMP) translates and integrates much of the information encoded by nitric oxide (NO · ) and several natriuretic peptides, including the atrial natriuretic peptide (ANP). Previously, we reported that integration of a cGMP-specific cyclic nucleotide phosphodiesterase, namely phosphodiesterase 5A (PDE5A), into a protein kinase G (PKG)- and inositol-1,4,5-trisphosphate receptor (IP 3 R)-containing endoplasmic reticulum (ER) signalosome allows localized control of PDE5A activity and of PKG-dependent inhibition of IP 3 -mediated release of ER Ca 2+ in human platelets. Herein, we report that PDE5A integrates into an analogous signalosome in human arterial smooth muscle cells (HASMC), wherein it regulates muscarinic agonist-dependent Ca 2+ release and is activated selectively by PKG-dependent phosphorylation. In addition, we report that PDE5A also regulates HASMC functions via events independent of PKG, but rather through actions coordinated by competitive cGMP-mediated inhibition of cAMP hydrolysis by the so-called cGMP-inhibited cAMP PDE, namely phosphodiesterase 3A (PDE3A). Indeed, we show that ANP increases both cGMP and cAMP levels in HASMC and promotes phosphorylation of vasodilator-stimulated phospho-protein (VASP) at each the PKG and PKA phospho-acceptor sites. Since selective inhibition of PDE5 decreased DNA synthesis and chemotaxis of HASMC, and that PDE3A knockdown obviated these effects, our findings are consistent with a role for a PDE5A-PDE3A-PKA axis in their regulation. Our findings provide insight into the existence of distinct "pools" of PDE5A in HASMC and support the idea that these discrete compartments regulate distinct cGMP-dependent events. As a corollary, we suggest that it may be possible to target these distinct PDE5A-regulated pools and in so-doing differentially impact selected cGMP-regulated functions in these cells. Copyright © 2017. Published by Elsevier Inc.

Synthesis, Pharmacological Profile and Docking Studies of New Sulfonamides Designed as Phosphodiesterase-4 Inhibitors

PubMed Central

Cardozo, Suzana Vanessa S.; Carvalho, Vinicius de Frias; Romeiro, Nelilma Correia; Silva, Patrícia Machado Rodrigues e; Martins, Marco Aurélio; Barreiro, Eliezer J.; Lima, Lídia Moreira

2016-01-01

Prior investigations showed that increased levels of cyclic AMP down-regulate lung inflammatory changes, stimulating the interest in phosphodiesterase (PDE)4 as therapeutic target. Here, we described the synthesis, pharmacological profile and docking properties of a novel sulfonamide series (5 and 6a-k) designed as PDE4 inhibitors. Compounds were screened for their selectivity against the four isoforms of human PDE4 using an IMAP fluorescence polarized protocol. The effect on allergen- or LPS-induced lung inflammation and airway hyper-reactivity (AHR) was studied in A/J mice, while the xylazine/ketamine-induced anesthesia test was employed as a behavioral correlate of emesis in rodents. As compared to rolipram, the most promising screened compound, 6a (LASSBio-448) presented a better inhibitory index concerning PDE4D/PDE4A or PDE4D/PDE4B. Accordingly, docking analyses of the putative interactions of LASSBio-448 revealed similar poses in the active site of PDE4A and PDE4C, but slight unlike orientations in PDE4B and PDE4D. LASSBio-448 (100 mg/kg, oral), 1 h before provocation, inhibited allergen-induced eosinophil accumulation in BAL fluid and lung tissue samples. Under an interventional approach, LASSBio-448 reversed ongoing lung eosinophilic infiltration, mucus exacerbation, peribronchiolar fibrosis and AHR by allergen provocation, in a mechanism clearly associated with blockade of pro-inflammatory mediators such as IL-4, IL-5, IL-13 and eotaxin-2. LASSBio-448 (2.5 and 10 mg/kg) also prevented inflammation and AHR induced by LPS. Finally, the sulfonamide derivative was shown to be less pro-emetic than rolipram and cilomilast in the assay employed. These findings suggest that LASSBio-448 is a new PDE4 inhibitor with marked potential to prevent and reverse pivotal pathological features of diseases characterized by lung inflammation, such as asthma. PMID:27695125

Exact charge and energy conservation in implicit PIC with mapped computational meshes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Guangye; Barnes, D. C.

This paper discusses a novel fully implicit formulation for a one-dimensional electrostatic particle-in-cell (PIC) plasma simulation approach. Unlike earlier implicit electrostatic PIC approaches (which are based on a linearized Vlasov Poisson formulation), ours is based on a nonlinearly converged Vlasov Amp re (VA) model. By iterating particles and fields to a tight nonlinear convergence tolerance, the approach features superior stability and accuracy properties, avoiding most of the accuracy pitfalls in earlier implicit PIC implementations. In particular, the formulation is stable against temporal (Courant Friedrichs Lewy) and spatial (aliasing) instabilities. It is charge- and energy-conserving to numerical round-off for arbitrary implicitmore » time steps (unlike the earlier energy-conserving explicit PIC formulation, which only conserves energy in the limit of arbitrarily small time steps). While momentum is not exactly conserved, errors are kept small by an adaptive particle sub-stepping orbit integrator, which is instrumental to prevent particle tunneling (a deleterious effect for long-term accuracy). The VA model is orbit-averaged along particle orbits to enforce an energy conservation theorem with particle sub-stepping. As a result, very large time steps, constrained only by the dynamical time scale of interest, are possible without accuracy loss. Algorithmically, the approach features a Jacobian-free Newton Krylov solver. A main development in this study is the nonlinear elimination of the new-time particle variables (positions and velocities). Such nonlinear elimination, which we term particle enslavement, results in a nonlinear formulation with memory requirements comparable to those of a fluid computation, and affords us substantial freedom in regards to the particle orbit integrator. Numerical examples are presented that demonstrate the advertised properties of the scheme. In particular, long-time ion acoustic wave simulations show that numerical accuracy does not degrade even with very large implicit time steps, and that significant CPU gains are possible.« less

Rotor cascade shape optimization with unsteady passing wakes using implicit dual time stepping method

NASA Astrophysics Data System (ADS)

Lee, Eun Seok

2000-10-01

An improved aerodynamics performance of a turbine cascade shape can be achieved by an understanding of the flow-field associated with the stator-rotor interaction. In this research, an axial gas turbine airfoil cascade shape is optimized for improved aerodynamic performance by using an unsteady Navier-Stokes solver and a parallel genetic algorithm. The objective of the research is twofold: (1) to develop a computational fluid dynamics code having faster convergence rate and unsteady flow simulation capabilities, and (2) to optimize a turbine airfoil cascade shape with unsteady passing wakes for improved aerodynamic performance. The computer code solves the Reynolds averaged Navier-Stokes equations. It is based on the explicit, finite difference, Runge-Kutta time marching scheme and the Diagonalized Alternating Direction Implicit (DADI) scheme, with the Baldwin-Lomax algebraic and k-epsilon turbulence modeling. Improvements in the code focused on the cascade shape design capability, convergence acceleration and unsteady formulation. First, the inverse shape design method was implemented in the code to provide the design capability, where a surface transpiration concept was employed as an inverse technique to modify the geometry satisfying the user specified pressure distribution on the airfoil surface. Second, an approximation storage multigrid method was implemented as an acceleration technique. Third, the preconditioning method was adopted to speed up the convergence rate in solving the low Mach number flows. Finally, the implicit dual time stepping method was incorporated in order to simulate the unsteady flow-fields. For the unsteady code validation, the Stokes's 2nd problem and the Poiseuille flow were chosen and compared with the computed results and analytic solutions. To test the code's ability to capture the natural unsteady flow phenomena, vortex shedding past a cylinder and the shock oscillation over a bicircular airfoil were simulated and compared with experiments and other research results. The rotor cascade shape optimization with unsteady passing wakes was performed to obtain an improved aerodynamic performance using the unsteady Navier-Stokes solver. Two objective functions were defined as minimization of total pressure loss and maximization of lift, while the mass flow rate was fixed. A parallel genetic algorithm was used as an optimizer and the penalty method was introduced. Each individual's objective function was computed simultaneously by using a 32 processor distributed memory computer. One optimization took about four days.

Phosphodiesterase 4 Inhibitor Therapies for Atopic Dermatitis: Progress and Outlook.

PubMed

Ahluwalia, Jusleen; Udkoff, Jeremy; Waldman, Andrea; Borok, Jenna; Eichenfield, Lawrence F

2017-09-01

Phosphodiesterase 4 (PDE4) is a cyclic AMP degrading enzyme in leukocytes. Several decades ago, increased PDE activity was demonstrated in patients with atopic dermatitis (AD). Currently, several PDE4 inhibitors in both topical and oral formulation have been developed to target the inflammatory cascade of AD. This review shows the pathogenic rationale behind these inhibitors, and discusses multiple PDE4 inhibitors that are under evaluation or in the market. PDE4 inhibitors may be considered as favorable agents in the repertoire of current interventions for AD.

New findings on phosphodiesterases, MoPdeH and MoPdeL, in Magnaporthe oryzae revealed by structural analysis.

PubMed

Yang, Li-Na; Yin, Ziyi; Zhang, Xi; Feng, Wanzhen; Xiao, Yuhan; Zhang, Haifeng; Zheng, Xiaobo; Zhang, Zhengguang

2018-05-01

The cyclic adenosine monophosphate (cAMP) signalling pathway mediates signal communication and sensing during infection-related morphogenesis in eukaryotes. Many studies have implicated cAMP as a critical mediator of appressorium development in the rice blast fungus, Magnaporthe oryzae. The cAMP phosphodiesterases, MoPdeH and MoPdeL, as key regulators of intracellular cAMP levels, play pleiotropic roles in cell wall integrity, cellular morphology, appressorium formation and infectious growth in M. oryzae. Here, we analysed the roles of domains of MoPdeH and MoPdeL separately or in chimeras. The results indicated that the HD and EAL domains of MoPdeH are indispensable for its phosphodiesterase activity and function. Replacement of the MoPdeH HD domain with the L1 and L2 domains of MoPdeL, either singly or together, resulted in decreased cAMP hydrolysis activity of MoPdeH. All of the transformants exhibited phenotypes similar to that of the ΔMopdeH mutant, but also revealed that EAL and L1 play additional roles in conidiation, and that L1 is involved in infectious growth. We further found that the intracellular cAMP level is important for surface signal recognition and hyphal autolysis. The intracellular cAMP level negatively regulates Mps1-MAPK and positively regulates Pmk1-MAPK in the rice blast fungus. Our results provide new information to better understand the cAMP signalling pathway in the development, differentiation and plant infection of the fungus. © 2017 BSPP AND JOHN WILEY & SONS LTD.

Phosphodiesterase 9A regulates central cGMP and modulates responses to cholinergic and monoaminergic perturbation in vivo.

PubMed

Kleiman, Robin J; Chapin, Douglas S; Christoffersen, Curt; Freeman, Jody; Fonseca, Kari R; Geoghegan, Kieran F; Grimwood, Sarah; Guanowsky, Victor; Hajós, Mihály; Harms, John F; Helal, Christopher J; Hoffmann, William E; Kocan, Geralyn P; Majchrzak, Mark J; McGinnis, Dina; McLean, Stafford; Menniti, Frank S; Nelson, Fredrick; Roof, Robin; Schmidt, Anne W; Seymour, Patricia A; Stephenson, Diane T; Tingley, Francis David; Vanase-Frawley, Michelle; Verhoest, Patrick R; Schmidt, Christopher J

2012-05-01

Cyclic nucleotides are critical regulators of synaptic plasticity and participate in requisite signaling cascades implicated across multiple neurotransmitter systems. Phosphodiesterase 9A (PDE9A) is a high-affinity, cGMP-specific enzyme widely expressed in the rodent central nervous system. In the current study, we observed neuronal staining with antibodies raised against PDE9A protein in human cortex, cerebellum, and subiculum. We have also developed several potent, selective, and brain-penetrant PDE9A inhibitors and used them to probe the function of PDE9A in vivo. Administration of these compounds to animals led to dose-dependent accumulation of cGMP in brain tissue and cerebrospinal fluid, producing a range of biological effects that implied functional significance for PDE9A-regulated cGMP in dopaminergic, cholinergic, and serotonergic neurotransmission and were consistent with the widespread distribution of PDE9A. In vivo effects of PDE9A inhibition included reversal of the respective disruptions of working memory by ketamine, episodic and spatial memory by scopolamine, and auditory gating by amphetamine, as well as potentiation of risperidone-induced improvements in sensorimotor gating and reversal of the stereotypic scratching response to the hallucinogenic 5-hydroxytryptamine 2A agonist mescaline. The results suggested a role for PDE9A in the regulation of monoaminergic circuitry associated with sensory processing and memory. Thus, PDE9A activity regulates neuronal cGMP signaling downstream of multiple neurotransmitter systems, and inhibition of PDE9A may provide therapeutic benefits in psychiatric and neurodegenerative diseases promoted by the dysfunction of these diverse neurotransmitter systems.

The dangers of sexual enhancement supplements and counterfeit drugs to "treat" erectile dysfunction.

PubMed

Chiang, Jason; Yafi, Faysal A; Dorsey, Philip J; Hellstrom, Wayne J G

2017-02-01

Counterfeit phosphodiesterase-5 inhibitors (PDE-5i) are an increasing problem. Already in widespread use, the market for PDE-5i is steadily growing as the population ages. Counterfeiters are taking advantage of this growing market by developing illicit and counterfeit PDE-5i products. Many factors are contributing to the rapid growth of the illicit market, such as the low risk of prosecution, potentially high financial reward, and ease of distribution via Internet pharmacies. Consumers of illicit PDE-5i often do not realize they are using counterfeit products and placing themselves at an unnecessary health risk. Others seek to bypass the legitimate healthcare system due to either embarrassment of the underlying condition or desire for cheaper alternatives. However, taking illicit PDE-5i may harm consumers directly, as many illicit products contain detrimental contaminants and inaccurate amounts of the active ingredient without the appropriate warnings. Bypassing the legitimate healthcare system also endangers consumers indirectly, as erectile dysfunction (ED) is often associated with other medical comorbidities that patients should be screened for. Furthermore, PDE-5i can have potentially dangerous interactions with other pharmaceuticals that are rarely warned against with counterfeit PDE-5i. This communication reviews the literature regarding counterfeit PDE-5i, and summarizes both the scope and dangers of the illicit PDE-5i market.

A novel thermoregulatory role for PDE10A in mouse and human adipocytes.

PubMed

Hankir, Mohammed K; Kranz, Mathias; Gnad, Thorsten; Weiner, Juliane; Wagner, Sally; Deuther-Conrad, Winnie; Bronisch, Felix; Steinhoff, Karen; Luthardt, Julia; Klöting, Nora; Hesse, Swen; Seibyl, John P; Sabri, Osama; Heiker, John T; Blüher, Matthias; Pfeifer, Alexander; Brust, Peter; Fenske, Wiebke K

2016-07-01

Phosphodiesterase type 10A (PDE10A) is highly enriched in striatum and is under evaluation as a drug target for several psychiatric/neurodegenerative diseases. Preclinical studies implicate PDE10A in the regulation of energy homeostasis, but the mechanisms remain unclear. By utilizing small-animal PET/MRI and the novel radioligand [(18)F]-AQ28A, we found marked levels of PDE10A in interscapular brown adipose tissue (BAT) of mice. Pharmacological inactivation of PDE10A with the highly selective inhibitor MP-10 recruited BAT and potentiated thermogenesis in vivo In diet-induced obese mice, chronic administration of MP-10 caused weight loss associated with increased energy expenditure, browning of white adipose tissue, and improved insulin sensitivity. Analysis of human PET data further revealed marked levels of PDE10A in the supraclavicular region where brown/beige adipocytes are clustered in adults. Finally, the inhibition of PDE10A with MP-10 stimulated thermogenic gene expression in human brown adipocytes and induced browning of human white adipocytes. Collectively, our findings highlight a novel thermoregulatory role for PDE10A in mouse and human adipocytes and promote PDE10A inhibitors as promising candidates for the treatment of obesity and diabetes. © 2016 The Authors. Published under the terms of the CC BY 4.0 license.

PDE7B is involved in nandrolone decanoate hydrolysis in liver cytosol and its transcription is up-regulated by androgens in HepG2.

PubMed

Strahm, Emmanuel; Rane, Anders; Ekström, Lena

2014-01-01

Most androgenic drugs are available as esters for a prolonged depot action. However, the enzymes involved in the hydrolysis of the esters have not been identified. There is one study indicating that PDE7B may be involved in the activation of testosterone enanthate. The aims are to identify the cellular compartments where the hydrolysis of testosterone enanthate and nandrolone decanoate occurs, and to investigate the involvement of PDE7B in the activation. We also determined if testosterone and nandrolone affect the expression of the PDE7B gene. The hydrolysis studies were performed in isolated human liver cytosolic and microsomal preparations with and without specific PDE7B inhibitor. The gene expression was studied in human hepatoma cells (HepG2) exposed to testosterone and nandrolone. We show that PDE7B serves as a catalyst of the hydrolysis of testosterone enanthate and nandrolone decanoate in liver cytosol. The gene expression of PDE7B was significantly induced 3- and 5- fold after 2 h exposure to 1 μM testosterone enanthate and nandrolone decanoate, respectively. These results show that PDE7B is involved in the activation of esterified nandrolone and testosterone and that the gene expression of PDE7B is induced by supra-physiological concentrations of androgenic drugs.

Identification of cancer cytotoxic modulators of PDE3A by predictive chemogenomics

PubMed Central

de Waal, Luc; Lewis, Timothy A.; Rees, Matthew G.; Tsherniak, Aviad; Wu, Xiaoyun; Choi, Peter S.; Gechijian, Lara; Hartigan, Christina; Faloon, Patrick W.; Hickey, Mark J.; Tolliday, Nicola; Carr, Steven A.; Clemons, Paul A.; Munoz, Benito; Wagner, Bridget K.; Shamji, Alykhan F.; Koehler, Angela N.; Schenone, Monica; Burgin, Alex B.; Schreiber, Stuart L.; Greulich, Heidi; Meyerson, Matthew

2015-01-01

High cancer death rates indicate the need for new anti-cancer therapeutic agents. Approaches to discover new cancer drugs include target-based drug discovery and phenotypic screening. Here, we identified phosphodiesterase 3A modulators as cell-selective cancer cytotoxic compounds by phenotypic compound library screening and target deconvolution by predictive chemogenomics. We found that sensitivity to 6-(4-(diethylamino)-3-nitrophenyl)-5-methyl-4,5-dihydropyridazin-3(2H)-one, or DNMDP, across 766 cancer cell lines correlates with expression of the phosphodiesterase 3A gene, PDE3A. Like DNMDP, a subset of known PDE3A inhibitors kill selected cancer cells while others do not. Furthermore, PDE3A depletion leads to DNMDP resistance. We demonstrated that DNMDP binding to PDE3A promotes an interaction between PDE3A and Schlafen 12 (SLFN12), suggesting a neomorphic activity. Co-expression of SLFN12 with PDE3A correlates with DNMDP sensitivity, while depletion of SLFN12 results in decreased DNMDP sensitivity. Our results implicate PDE3A modulators as candidate cancer therapeutic agents and demonstrate the power of predictive chemogenomics in small-molecule discovery. PMID:26656089

DISC1, PDE4B, and NDE1 at the centrosome and synapse

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bradshaw, Nicholas J.; Ogawa, Fumiaki; Antolin-Fontes, Beatriz

Disrupted-In-Schizophrenia 1 (DISC1) is a risk factor for schizophrenia and other major mental illnesses. Its protein binding partners include the Nuclear Distribution Factor E Homologs (NDE1 and NDEL1), LIS1, and phosphodiesterases 4B and 4D (PDE4B and PDE4D). We demonstrate that NDE1, NDEL1 and LIS1, together with their binding partner dynein, associate with DISC1, PDE4B and PDE4D within the cell, and provide evidence that this complex is present at the centrosome. LIS1 and NDEL1 have been previously suggested to be synaptic, and we now demonstrate localisation of DISC1, NDE1, and PDE4B at synapses in cultured neurons. NDE1 is phosphorylated by cAMP-dependantmore » Protein Kinase A (PKA), whose activity is, in turn, regulated by the cAMP hydrolysis activity of phosphodiesterases, including PDE4. We propose that DISC1 acts as an assembly scaffold for all of these proteins and that the NDE1/NDEL1/LIS1/dynein complex is modulated by cAMP levels via PKA and PDE4.« less

A positivity preserving and conservative variational scheme for phase-field modeling of two-phase flows

NASA Astrophysics Data System (ADS)

Joshi, Vaibhav; Jaiman, Rajeev K.

2018-05-01

We present a positivity preserving variational scheme for the phase-field modeling of incompressible two-phase flows with high density ratio. The variational finite element technique relies on the Allen-Cahn phase-field equation for capturing the phase interface on a fixed Eulerian mesh with mass conservative and energy-stable discretization. The mass conservation is achieved by enforcing a Lagrange multiplier which has both temporal and spatial dependence on the underlying solution of the phase-field equation. To make the scheme energy-stable in a variational sense, we discretize the spatial part of the Lagrange multiplier in the phase-field equation by the mid-point approximation. The proposed variational technique is designed to reduce the spurious and unphysical oscillations in the solution while maintaining the second-order accuracy of both spatial and temporal discretizations. We integrate the Allen-Cahn phase-field equation with the incompressible Navier-Stokes equations for modeling a broad range of two-phase flow and fluid-fluid interface problems. The coupling of the implicit discretizations corresponding to the phase-field and the incompressible flow equations is achieved via nonlinear partitioned iterative procedure. Comparison of results between the standard linear stabilized finite element method and the present variational formulation shows a remarkable reduction of oscillations in the solution while retaining the boundedness of the phase-indicator field. We perform a standalone test to verify the accuracy and stability of the Allen-Cahn two-phase solver. We examine the convergence and accuracy properties of the coupled phase-field solver through the standard benchmarks of the Laplace-Young law and a sloshing tank problem. Two- and three-dimensional dam break problems are simulated to assess the capability of the phase-field solver for complex air-water interfaces involving topological changes on unstructured meshes. Finally, we demonstrate the phase-field solver for a practical offshore engineering application of wave-structure interaction.

Finite element simulations of the Portevin Le Chatelier effect in aluminium alloy

NASA Astrophysics Data System (ADS)

Hopperstad, O. S.; Børvik, T.; Berstad, T.; Benallal, A.

2006-08-01

Finite element simulations of the Portevin-Le Chatelier effect in aluminium alloy 5083-H116 are presented and evaluated against existing experimental results. The constitutive model of McCormick (1988) for materials exhibiting negative steady-state strain-rate sensitivity is incorporated into an elastic-viscoplastic model for large plastic deformations and implemented in LS-DYNA for use with the explicit or implicit solver. Axisymmetric tensile specimens loaded at different strain rates are studied numerically, and it is shown that the model predicts the experimental behaviour with reasonable accuracy; including serrated yielding and propagating bands of localized plastic deformation along the gauge length of the specimen at intermediate strain rates.

Juncture flow improvement for wing/pylon configurations by using CFD methodology

NASA Technical Reports Server (NTRS)

Gea, Lie-Mine; Chyu, Wei J.; Stortz, Michael W.; Chow, Chuen-Yen

1993-01-01

Transonic flow field around a fighter wing/pylon configuration was simulated by using an implicit upwinding Navier-Stokes flow solver (F3D) and overset grid technology (Chimera). Flow separation and local shocks near the wing/pylon junction were observed in flight and predicted by numerical calculations. A new pylon/fairing shape was proposed to improve the flow quality. Based on numerical results, the size of separation area is significantly reduced and the onset of separation is delayed farther downstream. A smoother pressure gradient is also obtained near the junction area. This paper demonstrates that computational fluid dynamics (CFD) methodology can be used as a practical tool for aircraft design.

A hierarchical uniformly high order DG-IMEX scheme for the 1D BGK equation

NASA Astrophysics Data System (ADS)

Xiong, Tao; Qiu, Jing-Mei

2017-05-01

A class of high order nodal discontinuous Galerkin implicit-explicit (DG-IMEX) schemes with asymptotic preserving (AP) property has been developed for the one-dimensional (1D) BGK equation in Xiong et al. (2015) [40], based on a micro-macro reformulation. The schemes are globally stiffly accurate and asymptotically consistent, and as the Knudsen number becomes small or goes to zero, they recover first the compressible Navier-Stokes (CNS) and then the Euler limit. Motivated by the recent work of Filbet and Rey (2015) [27] and the references therein, in this paper, we propose a hierarchical high order AP method, namely kinetic, CNS and Euler solvers are automatically applied in regions where their corresponding models are appropriate. The numerical solvers for different regimes are coupled naturally by interface conditions. To the best of our knowledge, the resulting scheme is the very first hierarchical one being proposed in the literature, that enjoys AP property as well as uniform high order accuracy. Numerical experiments demonstrate the efficiency and effectiveness of the proposed approach. As time evolves, three different regimes are dynamically identified and naturally coupled, leading to significant CPU time savings (more than 80% for some of our test problems).

MPSalsa Version 1.5: A Finite Element Computer Program for Reacting Flow Problems: Part 1 - Theoretical Development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Devine, K.D.; Hennigan, G.L.; Hutchinson, S.A.

1999-01-01

The theoretical background for the finite element computer program, MPSalsa Version 1.5, is presented in detail. MPSalsa is designed to solve laminar or turbulent low Mach number, two- or three-dimensional incompressible and variable density reacting fluid flows on massively parallel computers, using a Petrov-Galerkin finite element formulation. The code has the capability to solve coupled fluid flow (with auxiliary turbulence equations), heat transport, multicomponent species transport, and finite-rate chemical reactions, and to solve coupled multiple Poisson or advection-diffusion-reaction equations. The program employs the CHEMKIN library to provide a rigorous treatment of multicomponent ideal gas kinetics and transport. Chemical reactions occurringmore » in the gas phase and on surfaces are treated by calls to CHEMKIN and SURFACE CHEMK3N, respectively. The code employs unstructured meshes, using the EXODUS II finite element database suite of programs for its input and output files. MPSalsa solves both transient and steady flows by using fully implicit time integration, an inexact Newton method and iterative solvers based on preconditioned Krylov methods as implemented in the Aztec. solver library.« less

A new finite element and finite difference hybrid method for computing electrostatics of ionic solvated biomolecule

NASA Astrophysics Data System (ADS)

Ying, Jinyong; Xie, Dexuan

2015-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.

An implementation of a chemical and thermal nonequilibrium flow solver on unstructured meshes and application to blunt bodies

NASA Technical Reports Server (NTRS)

Prabhu, Ramadas K.

1994-01-01

This paper presents a nonequilibrium flow solver, implementation of the algorithm on unstructured meshes, and application to hypersonic flow past blunt bodies. Air is modeled as a mixture of five chemical species, namely O2, N2, O, NO, and N, having two temperatures namely translational and vibrational. The solution algorithm is a cell centered, point implicit upwind scheme that employs Roe's flux difference splitting technique. Implementation of this algorithm on unstructured meshes is described. The computer code is applied to solve Mach 15 flow with and without a Type IV shock interference on a cylindrical body of 2.5mm radius representing a cowl lip. Adaptively generated meshes are employed, and the meshes are refined several times until the solution exhibits detailed flow features and surface pressure and heat flux distributions. Effects of a catalytic wall on surface heat flux distribution are studied. For the Mach 15 Type IV shock interference flow, present results showed a peak heat flux of 544 MW/m2 for a fully catalytic wall and 431 MW/m(exp 2) for a noncatalytic wall. Some of the results are compared with available computational data.

Numerical analysis of the three-dimensional swirling flow in centrifugal compressor volutes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ayder, E.; Van den Braembussche, R.

1994-07-01

The improvement of centrifugal compressor performance and the control of the radial forces acting on the impeller due to the circumferential variation of the static pressure caused by the volute require a good understanding of the flow mechanisms and an accurate prediction of the flow pattern inside the volute. A three-dimensional volute calculation method has been developed for this purpose. The volute is discretized by means of hexahedral elements. A cell vertex finite volume approach is used in combination with a time-marching procedure. The numerical procedure makes use of a central space discretization and a four-step Runge-Kutta time-stepping scheme. Themore » artificial dissipation used in the solver is based on the fourth-order differences of the conservative variables. Implicit residual smoothing improves the convergence rate. The loss model implemented in the code accounts for the losses due to internal shear and friction losses on the walls. A comparison of the calculated and measured results inside a volute with elliptical cross section reveals that the modified Euler solver accurately predicts the velocity and pressure distribution inside and upstream of the volute.« less

An Evaluation of a Phase-Lag Boundary Condition for Francis Hydroturbine Simulations Using a Pressure-Based Solver

NASA Astrophysics Data System (ADS)

Wouden, Alex; Cimbala, John; Lewis, Bryan

2014-11-01

While the periodic boundary condition is useful for handling rotational symmetry in many axisymmetric geometries, its application fails for analysis of rotor-stator interaction (RSI) in multi-stage turbomachinery flow. The inadequacy arises from the underlying geometry where the blade counts per row differ, since the blade counts are crafted to deter the destructive harmonic forces of synchronous blade passing. Therefore, to achieve the computational advantage of modeling a single blade passage per row while preserving the integrity of the RSI, a phase-lag boundary condition is adapted to OpenFOAM® software's incompressible pressure-based solver. The phase-lag construct is accomplished through restating the implicit periodic boundary condition as a constant boundary condition that is updated at each time step with phase-shifted data from the coupled cells adjacent to the boundary. Its effectiveness is demonstrated using a typical Francis hydroturbine modeled as single- and double-passages with phase-lag boundary conditions. The evaluation of the phase-lag condition is based on the correspondence of the overall computational performance and the calculated flow parameters of the phase-lag simulations with those of a baseline full-wheel simulation. Funded in part by DOE Award Number: DE-EE0002667.

H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

NASA Technical Reports Server (NTRS)

Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.

1993-01-01

The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

Development of iterative techniques for the solution of unsteady compressible viscous flows

NASA Technical Reports Server (NTRS)

Hixon, Duane; Sankar, L. N.

1993-01-01

During the past two decades, there has been significant progress in the field of numerical simulation of unsteady compressible viscous flows. At present, a variety of solution techniques exist such as the transonic small disturbance analyses (TSD), transonic full potential equation-based methods, unsteady Euler solvers, and unsteady Navier-Stokes solvers. These advances have been made possible by developments in three areas: (1) improved numerical algorithms; (2) automation of body-fitted grid generation schemes; and (3) advanced computer architectures with vector processing and massively parallel processing features. In this work, the GMRES scheme has been considered as a candidate for acceleration of a Newton iteration time marching scheme for unsteady 2-D and 3-D compressible viscous flow calculation; from preliminary calculations, this will provide up to a 65 percent reduction in the computer time requirements over the existing class of explicit and implicit time marching schemes. The proposed method has ben tested on structured grids, but is flexible enough for extension to unstructured grids. The described scheme has been tested only on the current generation of vector processor architecture of the Cray Y/MP class, but should be suitable for adaptation to massively parallel machines.

Verification of continuum drift kinetic equation solvers in NIMROD

DOE Office of Scientific and Technical Information (OSTI.GOV)

Held, E. D.; Ji, J.-Y.; Kruger, S. E.

Verification of continuum solutions to the electron and ion drift kinetic equations (DKEs) in NIMROD [C. R. Sovinec et al., J. Comp. Phys. 195, 355 (2004)] is demonstrated through comparison with several neoclassical transport codes, most notably NEO [E. A. Belli and J. Candy, Plasma Phys. Controlled Fusion 54, 015015 (2012)]. The DKE solutions use NIMROD's spatial representation, 2D finite-elements in the poloidal plane and a 1D Fourier expansion in toroidal angle. For 2D velocity space, a novel 1D expansion in finite elements is applied for the pitch angle dependence and a collocation grid is used for the normalized speedmore » coordinate. The full, linearized Coulomb collision operator is kept and shown to be important for obtaining quantitative results. Bootstrap currents, parallel ion flows, and radial particle and heat fluxes show quantitative agreement between NIMROD and NEO for a variety of tokamak equilibria. In addition, velocity space distribution function contours for ions and electrons show nearly identical detailed structure and agree quantitatively. A Θ-centered, implicit time discretization and a block-preconditioned, iterative linear algebra solver provide efficient electron and ion DKE solutions that ultimately will be used to obtain closures for NIMROD's evolving fluid model.« less

Inhibition of PDE4B suppresses inflammation by increasing expression of the deubiquitinase CYLD

PubMed Central

Komatsu, Kensei; Lee, Ji-Yun; Miyata, Masanori; Hyang Lim, Jae; Jono, Hirofumi; Koga, Tomoaki; Xu, Haidong; Yan, Chen; Kai, Hirofumi; Li, Jian-Dong

2013-01-01

The deubiquitinase CYLD acts as a key negative regulator to tightly control overactive inflammation. Most anti-inflammatory strategies have focused on directly targeting the positive regulator, which often results in significant side effects such as suppression of the host defence response. Here, we show that inhibition of phosphodiesterase 4B (PDE4B) markedly enhances upregulation of CYLD expression in response to bacteria, thereby suggesting that PDE4B acts as a negative regulator for CYLD. Interestingly, in Cyld-deficient mice, inhibition of PDE4B no longer suppresses inflammation. Moreover, PDE4B negatively regulates CYLD via specific activation of JNK2 but not JNK1. Importantly, ototopical post-inoculation administration of a PDE4 inhibitor suppresses inflammation in this animal model, thus demonstrating the therapeutic potential of targeting PDE4. These studies provide insights into how inflammation is tightly regulated via the inhibition of its negative regulator and may also lead to the development of new anti-inflammatory therapeutics that upregulate CYLD expression. PMID:23575688

Identification of a Phosphodiesterase-Inhibiting Fraction from Roasted Coffee (Coffea arabica) through Activity-Guided Fractionation.

PubMed

Röhrig, Teresa; Liesenfeld, David; Richling, Elke

2017-05-17

Recent reports that coffee can significantly inhibit cAMP phosphodiesterases (PDEs) in vitro, as well as in vivo, have described another beneficial effect of coffee consumption. However, the PDE-inhibiting substances remain mostly unknown. We chose activity-guided fractionation and an in vitro test system to identify the coffee components that are responsible for PDE inhibition. This approach indicated that a fraction of melanoidins reveals strong PDE-inhibiting potential (IC 50 = 130 ± 42 μg/mL). These melanoidins were characterized as water-soluble, low-molecular weight melanoidins (<3 kDa) with a nitrogen content of 4.2% and a carbohydrate content lower than those of other melanoidins. Fractions containing known PDE inhibitors such as chlorogenic acids, alkylpyrazines, or trigonelline as well as N-caffeoyl-tryptophan and N-p-coumaroyl-tryptophan did not exert PDE-inhibiting activity. We also observed that the known PDE inhibitor caffeine does not contribute to the PDE-inhibiting effects of coffee.

Effect of phosphodiesterase inhibitors in the bladder.

PubMed

Chughtai, Bilal; Ali, Aizaz; Dunphy, Claire; Kaplan, Steven A

2015-01-01

Many aging men will experience lower urinary tract symptoms (LUTS). Phosphodiesterase type 5 (PDE5) inhibitors have shown promise in treating LUTS in these patients. PDE5 inhibitors mediate their effects through several pathways including cAMP, NO/cGMP, K-channel modulated pathways, and the l -cysteine/H 2 S pathway. PDE5 inhibitors exert their effect in muscle cells, nerve fibers, and interstitial cells (ICs). The use of PDE5 inhibitors led to improvement in LUTS. This included urodynamic parameters. PDE5 inhibitors may play a significant role in LUTS due to their effect on the bladder rather than the prostate.

Detonation Propagation Through Ducts in a Pulsed Detonation Engine

DTIC Science & Technology

2011-03-01

PDE head. This convention is used based on the fill and purge flow directions, not the detonation direction. Figure 21. Adapter used to rotate ...presented for the development of a continuously operating pulsed detonation engine ( PDE ). A PDE without a high energy ignition system or a... detonation wave. Propagation is left to right in the bottom tube. ..... 19  Figure 15. Research PDE head

Frequent phosphodiesterase 11A gene (PDE11A) defects in patients with Carney complex (CNC) caused by PRKAR1A mutations: PDE11A may contribute to adrenal and testicular tumors in CNC as a modifier of the phenotype.

PubMed

Libé, Rossella; Horvath, Anelia; Vezzosi, Delphine; Fratticci, Amato; Coste, Joel; Perlemoine, Karine; Ragazzon, Bruno; Guillaud-Bataille, Marine; Groussin, Lionel; Clauser, Eric; Raffin-Sanson, Marie-Laure; Siegel, Jennifer; Moran, Jason; Drori-Herishanu, Limor; Faucz, Fabio Rueda; Lodish, Maya; Nesterova, Maria; Bertagna, Xavier; Bertherat, Jerome; Stratakis, Constantine A

2011-01-01

Carney complex (CNC) is an autosomal dominant multiple neoplasia, caused mostly by inactivating mutations of the regulatory subunit 1A of the protein kinase A (PRKAR1A). Primary pigmented nodular adrenocortical disease (PPNAD) is the most frequent endocrine manifestation of CNC with a great inter-individual variability. Germline, protein-truncating mutations of phosphodiesterase type 11A (PDE11A) have been described to predispose to a variety of endocrine tumors, including adrenal and testicular tumors. Our objective was to investigate the role of PDE11A as a possible gene modifier of the phenotype in a series of 150 patients with CNC. A higher frequency of PDE11A variants in patients with CNC compared with healthy controls was found (25.3 vs. 6.8%, P < 0.0001). Among CNC patients, those with PPNAD were significantly more frequently carriers of PDE11A variants compared with patients without PPNAD (30.8 vs. 13%, P = 0.025). Furthermore, men with PPNAD were significantly more frequently carriers of PDE11A sequence variants (40.7%) than women with PPNAD (27.3%) (P < 0.001). A higher frequency of PDE11A sequence variants was also found in patients with large-cell calcifying Sertoli cell tumors (LCCSCT) compared with those without LCCSCT (50 vs. 10%, P = 0.0056). PDE11A variants were significantly associated with the copresence of PPNAD and LCCSCT in men: 81 vs. 20%, P < 0.004). The simultaneous inactivation of PRKAR1A and PDE11A by small inhibitory RNA led to an increase in cAMP-regulatory element-mediated transcriptional activity under basal conditions and after stimulation by forskolin. We demonstrate, in a large cohort of CNC patients, a high frequency of PDE11A variants, suggesting that PDE11A is a genetic modifying factor for the development of testicular and adrenal tumors in patients with germline PRKAR1A mutation.

Biomolecular surface construction by PDE transform

PubMed Central

Zheng, Qiong; Yang, Siyang; Wei, Guo-Wei

2011-01-01

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high order PDE transforms. The fast Fourier transform is utilized to accomplish the PDE transform so as to avoid stringent stability constraints in solving high order PDEs. As a consequence, the time integration of high order PDEs can be done efficiently with the fast Fourier transform. The present approach is validated with a variety of test examples in two and three-dimensional settings. We explore the impact of the PDE transform parameters, such as the PDE order and propagation time, on the quality of resulting surfaces. Additionally, we utilize a set of 10 proteins to compare the computational efficiency of the present surface generation method and the MSMS approach in Cartesian meshes. Moreover, we analyze the present method by examining some benchmark indicators of biomolecular surface, i.e., surface area, surface enclosed volume, solvation free energy and surface electrostatic potential. A test set of 13 protein molecules is used in the present investigation. The electrostatic analysis is carried out via the Poisson-Boltzmann equation model. To further demonstrate the utility of the present PDE transform based surface method, we solve the Poisson-Nernst-Planck (PNP) equations with a PDE transform surface of a protein. Second order convergence is observed for the electrostatic potential and concentrations. Finally, to test the capability and efficiency of the present PDE transform based surface generation method, we apply it to the construction of an excessively large biomolecule, a virus surface capsid. Virus surface morphologies of different resolutions are attained by adjusting the propagation time. Therefore, the present PDE transform provides a multiresolution analysis in the surface visualization. Extensive numerical experiment and comparison with an established surface model indicate that the present PDE transform is a robust, stable and efficient approach for biomolecular surface generation in Cartesian meshes. PMID:22582140

Powerful relaxation of phosphodiesterase type 4 inhibitor rolipram in the pig and human bladder neck.

PubMed

Ribeiro, Ana S F; Fernandes, Vítor S; Martínez-Sáenz, Ana; Martínez, Pilar; Barahona, María Victoria; Orensanz, Luis M; Blaha, Igor; Serrano-Margüello, Daniel; Bustamante, Salvador; Carballido, Joaquín; García-Sacristán, Albino; Prieto, Dolores; Hernández, Medardo

2014-04-01

Phosphodiesterase type 5 (PDE5) inhibitors act as effective drugs for the treatment of lower urinary tract symptom (LUTS). There is a poor information, however, about the role of the PDE4 inhibitors on the bladder outflow region contractility. To investigate PDE4 expression and the relaxation induced by the PDE4 inhibitor rolipram versus that induced by the PDE5 blockers sildenafil and vardenafil, in the pig and human bladder neck. Immunohistochemistry for PDE4 expression, myographs for isometric force recordings and fura-2 fluorescence for simultaneous measurements of intracellular Ca2+ concentration ([Ca2+]i ) and tension for rolipram in bladder neck samples were used. PDE4 expression and relaxations to PDE4 and PDE5 inhibitors and simultaneous measurements of [Ca2+]i and tension. PDE4 expression was observed widely distributed in the smooth muscle layer of the pig and human bladder neck. On urothelium-denuded phenylephrine (PhE)-precontracted strips of pig and human, rolipram, sildenafil and vardenafil produced concentration-dependent relaxations with the following order of potency: rolipram> > sildenafil>vardenafil. In pig, the adenylyl cyclase activator forskolin potentiated rolipram-elicited relaxation, whereas protein kinase A (PKA) blockade reduced such effect. On potassium-enriched physiological saline solution (KPSS)-precontracted strips, rolipram evoked a lower relaxation than that obtained on PhE-stimulated preparations. Inhibition of large (BKCa ) and intermediate (IKCa ) conductance Ca2+ -activated K+ channels, neuronal voltage-gated Ca2+ channels, nitric oxide (NO) and hydrogen sulfide (H2 S) synthases reduced rolipram responses. Rolipram inhibited the contractions induced by PhE without reducing the PhE-evoked [Ca2+]i increase. PDE4 is present in the pig and human bladder neck smooth muscle, where rolipram exerts a much more potent relaxation than that elicited by PDE5 inhibitors. In pig, rolipram-induced response is produced through the PKA pathway involving BKCa and IKCa channel activation and [Ca2+]i desensitization-dependent mechanisms, this relaxation also being due to neuronal NO and H2S release. © 2014 International Society for Sexual Medicine.

A multiple hypotheses uncertainty analysis in hydrological modelling: about model structure, landscape parameterization, and numerical integration

NASA Astrophysics Data System (ADS)

Pilz, Tobias; Francke, Till; Bronstert, Axel

2016-04-01

Until today a large number of competing computer models has been developed to understand hydrological processes and to simulate and predict streamflow dynamics of rivers. This is primarily the result of a lack of a unified theory in catchment hydrology due to insufficient process understanding and uncertainties related to model development and application. Therefore, the goal of this study is to analyze the uncertainty structure of a process-based hydrological catchment model employing a multiple hypotheses approach. The study focuses on three major problems that have received only little attention in previous investigations. First, to estimate the impact of model structural uncertainty by employing several alternative representations for each simulated process. Second, explore the influence of landscape discretization and parameterization from multiple datasets and user decisions. Third, employ several numerical solvers for the integration of the governing ordinary differential equations to study the effect on simulation results. The generated ensemble of model hypotheses is then analyzed and the three sources of uncertainty compared against each other. To ensure consistency and comparability all model structures and numerical solvers are implemented within a single simulation environment. First results suggest that the selection of a sophisticated numerical solver for the differential equations positively affects simulation outcomes. However, already some simple and easy to implement explicit methods perform surprisingly well and need less computational efforts than more advanced but time consuming implicit techniques. There is general evidence that ambiguous and subjective user decisions form a major source of uncertainty and can greatly influence model development and application at all stages.

Study of the adaptive refinement on an open source 2D shallow-water flow solver using quadtree grid for flash flood simulations.

NASA Astrophysics Data System (ADS)

Kirstetter, G.; Popinet, S.; Fullana, J. M.; Lagrée, P. Y.; Josserand, C.

2015-12-01

The full resolution of shallow-water equations for modeling flash floods may have a high computational cost, so that majority of flood simulation softwares used for flood forecasting uses a simplification of this model : 1D approximations, diffusive or kinematic wave approximations or exotic models using non-physical free parameters. These kind of approximations permit to save a lot of computational time by sacrificing in an unquantified way the precision of simulations. To reduce drastically the cost of such 2D simulations by quantifying the lost of precision, we propose a 2D shallow-water flow solver built with the open source code Basilisk1, which is using adaptive refinement on a quadtree grid. This solver uses a well-balanced central-upwind scheme, which is at second order in time and space, and treats the friction and rain terms implicitly in finite volume approach. We demonstrate the validity of our simulation on the case of the flood of Tewkesbury (UK) occurred in July 2007, as shown on Fig. 1. On this case, a systematic study of the impact of the chosen criterium for adaptive refinement is performed. The criterium which has the best computational time / precision ratio is proposed. Finally, we present the power law giving the computational time in respect to the maximum resolution and we show that this law for our 2D simulation is close to the one of 1D simulation, thanks to the fractal dimension of the topography. [1] http://basilisk.fr/

A synthetic cGMP-sensitive gene switch providing Viagra(®)-controlled gene expression in mammalian cells and mice.

PubMed

Kim, Taeuk; Folcher, Marc; Charpin-El Hamri, Ghislaine; Fussenegger, Martin

2015-05-01

Cyclic guanosine monophosphate (cGMP) is a universal second messenger that is synthesized from guanosine triphosphate (GTP) by guanylyl cyclases (GCs) and hydrolyzed into guanosine monophosphate (GMP) by phosphodiesterases (PDEs). Small-molecule drugs that induce high cGMP levels in specialized tissues by boosting GC activity or inhibiting PDE activity have become the predominant treatment strategy for a wide range of medical conditions, including congestive heart failure, pulmonary hypertension, atherosclerosis-based claudication and erectile dysfunction. By fusing the cGMP receptor protein (CRP) of Rhodospirillum centenum to the Herpes simplex-derived transactivation domain VP16, we created a novel synthetic mammalian cGMP-sensing transcription factor (GTA) that activates synthetic promoters (PGTA) containing newly identified GTA-specific operator sites in a concentration-dependent manner. In cell lines expressing endogenous natriuretic peptide receptor A (NPR-A) (HeLa), GTA/PGTA-driven transgene expression was induced by B-type natriuretic peptide (BNP; Nesiritide(®)) in a concentration-dependent manner, which activated NPR-A׳s intracellular GC domain and triggered a corresponding cGMP surge. Ectopic expression of NPR-A in NPR-A-negative cell lines (HEK-293T) produced high cGMP levels and mediated maximum GTA/PGTA-driven transgene expression, which was suppressed by co-expression of PDEs (PDE-3A, PDE-5A and PDE-9A) and was re-triggered by the corresponding PDE inhibitor drugs (Pletal(®), Perfan(®), Primacor(®) (PDE-3A), Viagra(®), Levitra(®), Cialis(®) (PDE-5A) and BAY73-6691 (PDE-9A)). Mice implanted with microencapsulated designer cells co-expressing the GTA/PGTA device with NPR-A and PDE-5A showed control of blood SEAP levels through administration of sildenafil (Viagra(®)). Designer cells engineered for PDE inhibitor-modulated transgene expression may provide a cell-based PDE-targeting drug discovery platform and enable drug-adjusted gene- and cell-based therapies. Copyright © 2015 International Metabolic Engineering Society. Published by Elsevier Inc. All rights reserved.

Phosphodiesterase 5a Inhibition with Adenoviral Short Hairpin RNA Benefits Infarcted Heart Partially through Activation of Akt Signaling Pathway and Reduction of Inflammatory Cytokines.

PubMed

Li, Longhu; Zhao, Dong; Jin, Zhe; Zhang, Jian; Paul, Christian; Wang, Yigang

2015-01-01

Treatment with short hairpin RNA (shRNA) interference therapy targeting phosphodiesterase 5a after myocardial infarction (MI) has been shown to mitigate post-MI heart failure. We investigated the mechanisms that underpin the beneficial effects of PDE5a inhibition through shRNA on post-MI heart failure. An adenoviral vector with an shRNA sequence inserted was adopted for the inhibition of phosphodiesterase 5a (Ad-shPDE5a) in vivo and in vitro. Myocardial infarction (MI) was induced in male C57BL/6J mice by left coronary artery ligation, and immediately after that, the Ad-shPDE5a was injected intramyocardially around the MI region and border areas. Four weeks post-MI, the Ad-shPDE5a-treated mice showed significant mitigation of the left ventricular (LV) dilatation and dysfunction compared to control mice. Infarction size and fibrosis were also significantly reduced in Ad-shPDE5a-treated mice. Additionally, Ad-shPDE5a treatment decreased the MI-induced inflammatory cytokines interleukin (IL)-1β, IL-6, tumor necrosis factor-α, and transforming growth factor-β1, which was confirmed in vitro in Ad-shPDE5a transfected myofibroblasts cultured under oxygen glucose deprivation. Finally, Ad-shPDE5a treatment was found to activate the myocardial Akt signaling pathway in both in vivo and in vitro experiments. These findings indicate that PDE5a inhibition by Ad-shPDE5a via the Akt signal pathway could be of significant value in the design of future therapeutics for post-MI heart failure.

Erectile dysfunction and phosphodiesterase type 5 inhibitor use: associations with sexual activities, function and satisfaction in a population sample of older men.

PubMed

Lee, D M; Nazroo, J; Pendleton, N

2015-07-01

The objective of this study was to examine the association between sexual activities, problems and satisfaction, and ED and PDE5 inhibitor (PDE5i) use. A nationally representative sample of men (n=2612) aged 51-87 years from the English Longitudinal Study of Ageing completed an in-depth Sexual Relationships and Activities Questionnaire. Associations between ED and/or PDE5i use and sexual outcomes were explored using logistic regression models adjusted for age, health and lifestyle factors. PDE5i use in the preceding 3 months was reported by a total of 191 (7%) men, whereas 542 (21%) reported ED but no PDE5i use (untreated ED). Compared with men without ED, PDE5i users were more likely to be sexually active and report more frequent sexual intercourse. Men with untreated ED reported the lowest frequency of sexual activities. Compared with men without ED, both PDE5i users and those with untreated ED were more likely to report being concerned about their level of sexual desire, frequency of sexual activities, erectile function, waking erections and orgasmic experience. PDE5i users were also more concerned about and dissatisfied with their overall sex life than men without ED. This population-based study shows that while PDE5i use is associated with improved sexual functioning, this is not equally reflected in decreased levels of concern and dissatisfaction with their overall sexual health. Clinicians should be aware of this disparity between functional gains and continuing sexual concerns and dissatisfaction, and, where appropriate, offer psychosexual counselling as an adjunct to PDE5i medication.

Parameter Estimation of Partial Differential Equation Models.

PubMed

Xun, Xiaolei; Cao, Jiguo; Mallick, Bani; Carroll, Raymond J; Maity, Arnab

2013-01-01

Partial differential equation (PDE) models are commonly used to model complex dynamic systems in applied sciences such as biology and finance. The forms of these PDE models are usually proposed by experts based on their prior knowledge and understanding of the dynamic system. Parameters in PDE models often have interesting scientific interpretations, but their values are often unknown, and need to be estimated from the measurements of the dynamic system in the present of measurement errors. Most PDEs used in practice have no analytic solutions, and can only be solved with numerical methods. Currently, methods for estimating PDE parameters require repeatedly solving PDEs numerically under thousands of candidate parameter values, and thus the computational load is high. In this article, we propose two methods to estimate parameters in PDE models: a parameter cascading method and a Bayesian approach. In both methods, the underlying dynamic process modeled with the PDE model is represented via basis function expansion. For the parameter cascading method, we develop two nested levels of optimization to estimate the PDE parameters. For the Bayesian method, we develop a joint model for data and the PDE, and develop a novel hierarchical model allowing us to employ Markov chain Monte Carlo (MCMC) techniques to make posterior inference. Simulation studies show that the Bayesian method and parameter cascading method are comparable, and both outperform other available methods in terms of estimation accuracy. The two methods are demonstrated by estimating parameters in a PDE model from LIDAR data.

Prenatal Drug Exposure and Adolescent Cortisol Reactivity: Association with Behavioral Concerns.

PubMed

Buckingham-Howes, Stacy; Mazza, Dayna; Wang, Yan; Granger, Douglas A; Black, Maureen M

2016-09-01

To examine stress reactivity in a sample of adolescents with prenatal drug exposure (PDE) by examining the consequences of PDE on stress-related adrenocortical reactivity, behavioral problems, and drug experimentation during adolescence. Participants (76 PDE, 61 non-drug exposed [NE]; 99% African-American; 50% male; mean age = 14.17 yr, SD = 1.17) provided a urine sample, completed a drug use questionnaire, and provided saliva samples (later assayed for cortisol) before and after a mild laboratory stress task. Caregivers completed the Behavior Assessment System for Children, Second Edition (BASC II) and reported their relationship to the adolescent. The NE group was more likely to exhibit task-related cortisol reactivity compared to the PDE group. Overall behavior problems and drug experimentation were comparable across groups with no differences between PDE and NE groups. In unadjusted mediation analyses, cortisol reactivity mediated the association between PDE and BASC II aggression scores (95% bootstrap confidence interval [CI], 0.04-4.28), externalizing problems scores (95% bootstrap CI, 0.03-4.50), and drug experimentation (95% bootstrap CI, 0.001-0.54). The associations remain with the inclusion of gender as a covariate but not when age is included. Findings support and expand current research in cortisol reactivity and PDE by demonstrating that cortisol reactivity attenuates the association between PDE and behavioral problems (aggression) and drug experimentation. If replicated, PDE may have long-lasting effects on stress-sensitive physiological mechanisms associated with behavioral problems (aggression) and drug experimentation in adolescence.

Applications of Laser Diagnostics

DTIC Science & Technology

2005-03-01

Heat Transfer and Thermal Management of PDE . . . . 39 5.1.2 Application of Optical and Numerical Diagnostic Methods to PDE...in Reno, NV. The paper is included in the Appendix. 5.1.1.16 Heat Transfer and Thermal Management in PDE The unsteady nature of the PDE cycle...January 2003, Reno, NV. 57 “Heat Transfer and Thermal Management in a Pulsed Detonation Engine,” J. Hoke, R. Bradley, and F. Schauer, AIAA Paper No

PDE4 and PDE5 regulate cyclic nucleotide contents and relaxing effects on carbachol-induced contraction in the bovine abomasum.

PubMed

Kaneda, Takeharu; Kido, Yuuki; Tajima, Tsuyoshi; Urakawa, Norimoto; Shimizu, Kazumasa

2015-01-01

The effects of various selective phosphodiesterase (PDE) inhibitors on carbachol (CCh)-induced contraction in the bovine abomasum were investigated. Various selective PDE inhibitors, vinpocetine (type 1), erythro-9-(2-hydroxy-3-nonyl) adenine (EHNA, type 2), milrinone (type 3), Ro20-1724 (type 4), vardenafil (type 5), BRL-50481 (type 7) and BAY73-6691 (type 9), inhibited CCh-induced contractions in a concentration-dependent manner. Among the PDE inhibitors, Ro20-1724 and vardenafil induced more relaxation than the other inhibitors based on the data for the IC50 or maximum relaxation. In smooth muscle of the bovine abomasum, we showed the expression of PDE4B, 4C, 4D and 5 by RT-PCR analysis. In the presence of CCh, Ro20-1724 increased the cAMP content, but not the cGMP content. By contrast, vardenafil increased the cGMP content, but not the cAMP content. These results suggest that Ro20-1724-induced relaxation was correlated with cAMP and that vardenafil-induced relaxation was correlated with cGMP in the bovine abomasum. In conclusion, PDE4 and PDE5 are the enzymes involved in regulation of the relaxation associated with cAMP and cGMP, respectively, in the bovine abomasum.

Robust parallel iterative solvers for linear and least-squares problems, Final Technical Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Saad, Yousef

2014-01-16

The primary goal of this project is to study and develop robust iterative methods for solving linear systems of equations and least squares systems. The focus of the Minnesota team is on algorithms development, robustness issues, and on tests and validation of the methods on realistic problems. 1. The project begun with an investigation on how to practically update a preconditioner obtained from an ILU-type factorization, when the coefficient matrix changes. 2. We investigated strategies to improve robustness in parallel preconditioners in a specific case of a PDE with discontinuous coefficients. 3. We explored ways to adapt standard preconditioners formore » solving linear systems arising from the Helmholtz equation. These are often difficult linear systems to solve by iterative methods. 4. We have also worked on purely theoretical issues related to the analysis of Krylov subspace methods for linear systems. 5. We developed an effective strategy for performing ILU factorizations for the case when the matrix is highly indefinite. The strategy uses shifting in some optimal way. The method was extended to the solution of Helmholtz equations by using complex shifts, yielding very good results in many cases. 6. We addressed the difficult problem of preconditioning sparse systems of equations on GPUs. 7. A by-product of the above work is a software package consisting of an iterative solver library for GPUs based on CUDA. This was made publicly available. It was the first such library that offers complete iterative solvers for GPUs. 8. We considered another form of ILU which blends coarsening techniques from Multigrid with algebraic multilevel methods. 9. We have released a new version on our parallel solver - called pARMS [new version is version 3]. As part of this we have tested the code in complex settings - including the solution of Maxwell and Helmholtz equations and for a problem of crystal growth.10. As an application of polynomial preconditioning we considered the problem of evaluating f(A)v which arises in statistical sampling. 11. As an application to the methods we developed, we tackled the problem of computing the diagonal of the inverse of a matrix. This arises in statistical applications as well as in many applications in physics. We explored probing methods as well as domain-decomposition type methods. 12. A collaboration with researchers from Toulouse, France, considered the important problem of computing the Schur complement in a domain-decomposition approach. 13. We explored new ways of preconditioning linear systems, based on low-rank approximations.« less

Scalable implicit incompressible resistive MHD with stabilized FE and fully-coupled Newton–Krylov-AMG

DOE PAGES

Shadid, J. N.; Pawlowski, R. P.; Cyr, E. C.; ...

2016-02-10

Here, we discuss that the computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method,more » and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton–Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin–Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.« less

A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Taverniers, Søren; Tartakovsky, Daniel M., E-mail: dmt@ucsd.edu

2017-02-01

Multiphysics simulations often involve nonlinear components that are driven by internally generated or externally imposed random fluctuations. When used with a domain-decomposition (DD) algorithm, such components have to be coupled in a way that both accurately propagates the noise between the subdomains and lends itself to a stable and cost-effective temporal integration. We develop a conservative DD approach in which tight coupling is obtained by using a Jacobian-free Newton–Krylov (JfNK) method with a generalized minimum residual iterative linear solver. This strategy is tested on a coupled nonlinear diffusion system forced by a truncated Gaussian noise at the boundary. Enforcement ofmore » path-wise continuity of the state variable and its flux, as opposed to continuity in the mean, at interfaces between subdomains enables the DD algorithm to correctly propagate boundary fluctuations throughout the computational domain. Reliance on a single Newton iteration (explicit coupling), rather than on the fully converged JfNK (implicit) coupling, may increase the solution error by an order of magnitude. Increase in communication frequency between the DD components reduces the explicit coupling's error, but makes it less efficient than the implicit coupling at comparable error levels for all noise strengths considered. Finally, the DD algorithm with the implicit JfNK coupling resolves temporally-correlated fluctuations of the boundary noise when the correlation time of the latter exceeds some multiple of an appropriately defined characteristic diffusion time.« less

A three-dimensional finite-volume Eulerian-Lagrangian Localized Adjoint Method (ELLAM) for solute-transport modeling

USGS Publications Warehouse

Heberton, C.I.; Russell, T.F.; Konikow, Leonard F.; Hornberger, G.Z.

2000-01-01

This report documents the U.S. Geological Survey Eulerian-Lagrangian Localized Adjoint Method (ELLAM) algorithm that solves an integral form of the solute-transport equation, incorporating an implicit-in-time difference approximation for the dispersive and sink terms. Like the algorithm in the original version of the U.S. Geological Survey MOC3D transport model, ELLAM uses a method of characteristics approach to solve the transport equation on the basis of the velocity field. The ELLAM algorithm, however, is based on an integral formulation of conservation of mass and uses appropriate numerical techniques to obtain global conservation of mass. The implicit procedure eliminates several stability criteria required for an explicit formulation. Consequently, ELLAM allows large transport time increments to be used. ELLAM can produce qualitatively good results using a small number of transport time steps. A description of the ELLAM numerical method, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. The ELLAM algorithm was evaluated for the same set of problems used to test and evaluate Version 1 and Version 2 of MOC3D. These test results indicate that ELLAM offers a viable alternative to the explicit and implicit solvers in MOC3D. Its use is desirable when mass balance is imperative or a fast, qualitative model result is needed. Although accurate solutions can be generated using ELLAM, its efficiency relative to the two previously documented solution algorithms is problem dependent.

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

NASA Astrophysics Data System (ADS)

Veerapaneni, Shravan K.; Gueyffier, Denis; Biros, George; Zorin, Denis

2009-10-01

We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334-2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spectral approximation in space, semi-implicit time-stepping scheme—the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.

Preclinical Characterization of the Phosphodiesterase 10A PET Tracer [(11)C]MK-8193.

PubMed

Hostetler, Eric D; Fan, Hong; Joshi, Aniket D; Zeng, Zhizhen; Eng, Waisi; Gantert, Liza; Holahan, Marie; Meng, Xianjun; Miller, Patricia; O'Malley, Stacey; Purcell, Mona; Riffel, Kerry; Salinas, Cristian; Williams, Mangay; Ma, Bennett; Buist, Nicole; Smith, Sean M; Coleman, Paul J; Cox, Christopher D; Flores, Brock A; Raheem, Izzat T; Cook, Jacquelynn J; Evelhoch, Jeffrey L

2016-08-01

A positron emission tomography (PET) tracer for the enzyme phosphodiesterase 10A (PDE10A) is desirable to guide the discovery and development of PDE10A inhibitors as potential therapeutics. The preclinical characterization of the PDE10A PET tracer [(11)C]MK-8193 is described. In vitro binding studies with [(3)H]MK-8193 were conducted in rat, monkey, and human brain tissue. PET studies with [(11)C]MK-8193 were conducted in rats and rhesus monkeys at baseline and following administration of a PDE10A inhibitor. [(3)H]MK-8193 is a high-affinity, selective PDE10A radioligand in rat, monkey, and human brain tissue. In vivo, [(11)C]MK-8193 displays rapid kinetics, low test-retest variability, and a large specific signal that is displaced by a structurally diverse PDE10A inhibitor, enabling the determination of pharmacokinetic/enzyme occupancy relationships. [(11)C]MK-8193 is a useful PET tracer for the preclinical characterization of PDE10A therapeutic candidates in rat and monkey. Further evaluation of [(11)C]MK-8193 in humans is warranted.

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

NASA Technical Reports Server (NTRS)

White, Jeffery A.; Baurle, Robert A.; Passe, Bradley J.; Spiegel, Seth C.; Nishikawa, Hiroaki

2017-01-01

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

Pharmacologic therapy for erectile dysfunction and its interaction with the cardiovascular system.

PubMed

Ioakeimidis, Nikolaos; Kostis, John B

2014-01-01

Phosphodiesterase (PDE) enzymes are widely distributed throughout the body, having numerous effects and functions. The PDE type 5 (PDE5) inhibitors are widely used to treat erectile dysfunction (ED). Recent, intense preclinical and clinical research with PDE5 inhibitors has shed light on new mechanisms and has revealed a number of pleiotropic effects on the cardiovascular (CV) system. To date, PDE5 inhibition has been shown to be effective for the treatment of idiopathic pulmonary arterial hypertension, and both sildenafil and tadalafil are approved for this indication. However, current or future PDE5 inhibitors have the potential of becoming clinically useful in a variety of CV conditions such as heart failure, coronary artery disease, and hypertension. The present review discusses recent findings regarding pharmacologic treatment of ED and its interaction with the CV system and highlights current and future clinical applications beyond ED.

Active site similarity between human and Plasmodium falciparum phosphodiesterases: considerations for antimalarial drug design

NASA Astrophysics Data System (ADS)

Howard, Brittany L.; Thompson, Philip E.; Manallack, David T.

2011-08-01

The similarity between Plasmodium falciparum phosphodiesterase enzymes ( PfPDEs) and their human counterparts have been examined and human PDE9A was found to be a suitable template for the construction of homology models for each of the four PfPDE isoforms. In contrast, the architecture of the active sites of each model was most similar to human PDE1. Molecular docking was able to model cyclic guanosine monophosphate (cGMP) substrate binding in each case but a docking mode supporting cyclic adenosine monophosphate (cAMP) binding could not be found. Anticipating the potential of PfPDE inhibitors as anti-malarial drugs, a range of reported PDE inhibitors including zaprinast and sildenafil were docked into the model of PfPDEα. The results were consistent with their reported biological activities, and the potential of PDE1/9 inhibitor analogues was also supported by docking.

Expression of three mammalian cDNAs that interfere with RAS function in Saccharomyces cerevisiae.

PubMed Central

Colicelli, J; Nicolette, C; Birchmeier, C; Rodgers, L; Riggs, M; Wigler, M

1991-01-01

Saccharomyces cerevisiae strains expressing the activated RAS2Val19 gene or lacking both cAMP phosphodiesterase genes, PDE1 and PDE2, have impaired growth control and display an acute sensitivity to heat shock. We have isolated two classes of mammalian cDNAs from yeast expression libraries that suppress the heat shock-sensitive phenotype of RAS2Val19 strain. Members of the first class of cDNAs also suppress the heat shock-sensitive phenotype of pde1- pde2- strains and encode cAMP phosphodiesterases. Members of the second class fail to suppress the phenotype of pde1- pde2- strains and therefore are candidate cDNAs encoding proteins that interact with RAS proteins. We report the nucleotide sequence of three members of this class. Two of these cDNAs share considerable sequence similarity, but none are clearly similar to previously isolated genes. Images PMID:1849280

Phosphodiesterase Type 5 Inhibitors, Sport and Doping.

PubMed

Di Luigi, Luigi; Sansone, Massimiliano; Sansone, Andrea; Ceci, Roberta; Duranti, Guglielmo; Borrione, Paolo; Crescioli, Clara; Sgrò, Paolo; Sabatini, Stefania

Phosphodiesterase type 5 inhibitors (PDE5i) (e.g., sildenafil, tadalafil, vardenafil, and avanafil) are drugs commonly used to treat erectile dysfunction, pulmonary arterial hypertension, and benign prostatic hyperplasia. PDE5i are not prohibited by the World Anti-Doping Agency (WADA) but are alleged to be frequently misused by healthy athletes to improve sporting performance. In vitro and in vivo studies have reported various effects of PDE5i on cardiovascular, muscular, metabolic, and neuroendocrine systems and the potential, therefore, to enhance performance of healthy athletes during training and competition. This suggests well-controlled research studies to examine the ergogenic effects of PDE5i on performance during activities that simulate real sporting situations are warranted to determine if PDE5i should be included on the prohibited WADA list. In the meantime, there is concern that some otherwise healthy athletes will continue to misuse PDE5i to gain an unfair competitive advantage over their competitors.

Compartmentalized PDE4A5 Signaling Impairs Hippocampal Synaptic Plasticity and Long-Term Memory.

PubMed

Havekes, Robbert; Park, Alan J; Tolentino, Rosa E; Bruinenberg, Vibeke M; Tudor, Jennifer C; Lee, Yool; Hansen, Rolf T; Guercio, Leonardo A; Linton, Edward; Neves-Zaph, Susana R; Meerlo, Peter; Baillie, George S; Houslay, Miles D; Abel, Ted

2016-08-24

Alterations in cAMP signaling are thought to contribute to neurocognitive and neuropsychiatric disorders. Members of the cAMP-specific phosphodiesterase 4 (PDE4) family, which contains >25 different isoforms, play a key role in determining spatial cAMP degradation so as to orchestrate compartmentalized cAMP signaling in cells. Each isoform binds to a different set of protein complexes through its unique N-terminal domain, thereby leading to targeted degradation of cAMP in specific intracellular compartments. However, the functional role of specific compartmentalized PDE4 isoforms has not been examined in vivo Here, we show that increasing protein levels of the PDE4A5 isoform in mouse hippocampal excitatory neurons impairs a long-lasting form of hippocampal synaptic plasticity and attenuates hippocampus-dependent long-term memories without affecting anxiety. In contrast, viral expression of a truncated version of PDE4A5, which lacks the unique N-terminal targeting domain, does not affect long-term memory. Further, overexpression of the PDE4A1 isoform, which targets a different subset of signalosomes, leaves memory undisturbed. Fluorescence resonance energy transfer sensor-based cAMP measurements reveal that the full-length PDE4A5, in contrast to the truncated form, hampers forskolin-mediated increases in neuronal cAMP levels. Our study indicates that the unique N-terminal localization domain of PDE4A5 is essential for the targeting of specific cAMP-dependent signaling underlying synaptic plasticity and memory. The development of compounds to disrupt the compartmentalization of individual PDE4 isoforms by targeting their unique N-terminal domains may provide a fruitful approach to prevent cognitive deficits in neuropsychiatric and neurocognitive disorders that are associated with alterations in cAMP signaling. Neurons exhibit localized signaling processes that enable biochemical cascades to be activated selectively in specific subcellular compartments. The phosphodiesterase 4 (PDE4) family coordinates the degradation of cAMP, leading to the local attenuation of cAMP-dependent signaling pathways. Sleep deprivation leads to increased hippocampal expression of the PDE4A5 isoform. Here, we explored whether PDE4A5 overexpression mimics behavioral and synaptic plasticity phenotypes associated with sleep deprivation. Viral expression of PDE4A5 in hippocampal neurons impairs long-term potentiation and attenuates the formation of hippocampus-dependent long-term memories. Our findings suggest that PDE4A5 is a molecular constraint on cognitive processes and may contribute to the development of novel therapeutic approaches to prevent cognitive deficits in neuropsychiatric and neurocognitive disorders that are associated with alterations in cAMP signaling. Copyright © 2016 Havekes et al.

GPU surface extraction using the closest point embedding

NASA Astrophysics Data System (ADS)

Kim, Mark; Hansen, Charles

2015-01-01

Isosurface extraction is a fundamental technique used for both surface reconstruction and mesh generation. One method to extract well-formed isosurfaces is a particle system; unfortunately, particle systems can be slow. In this paper, we introduce an enhanced parallel particle system that uses the closest point embedding as the surface representation to speedup the particle system for isosurface extraction. The closest point embedding is used in the Closest Point Method (CPM), a technique that uses a standard three dimensional numerical PDE solver on two dimensional embedded surfaces. To fully take advantage of the closest point embedding, it is coupled with a Barnes-Hut tree code on the GPU. This new technique produces well-formed, conformal unstructured triangular and tetrahedral meshes from labeled multi-material volume datasets. Further, this new parallel implementation of the particle system is faster than any known methods for conformal multi-material mesh extraction. The resulting speed-ups gained in this implementation can reduce the time from labeled data to mesh from hours to minutes and benefits users, such as bioengineers, who employ triangular and tetrahedral meshes

Grid generation for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.; Erlebacher, Gordon

1989-01-01

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

Grid generation for the solution of partial differential equations

NASA Technical Reports Server (NTRS)

Eiseman, Peter R.; Erlebacher, Gordon

1987-01-01

A general survey of grid generators is presented with a concern for understanding why grids are necessary, how they are applied, and how they are generated. After an examination of the need for meshes, the overall applications setting is established with a categorization of the various connectivity patterns. This is split between structured grids and unstructured meshes. Altogether, the categorization establishes the foundation upon which grid generation techniques are developed. The two primary categories are algebraic techniques and partial differential equation techniques. These are each split into basic parts, and accordingly are individually examined in some detail. In the process, the interrelations between the various parts are accented. From the established background in the primary techniques, consideration is shifted to the topic of interactive grid generation and then to adaptive meshes. The setting for adaptivity is established with a suitable means to monitor severe solution behavior. Adaptive grids are considered first and are followed by adaptive triangular meshes. Then the consideration shifts to the temporal coupling between grid generators and PDE-solvers. To conclude, a reflection upon the discussion, herein, is given.

Dynamic one-dimensional modeling of secondary settling tanks and design impacts of sizing decisions.

PubMed

Li, Ben; Stenstrom, Michael K

2014-03-01

As one of the most significant components in the activated sludge process (ASP), secondary settling tanks (SSTs) can be investigated with mathematical models to optimize design and operation. This paper takes a new look at the one-dimensional (1-D) SST model by analyzing and considering the impacts of numerical problems, especially the process robustness. An improved SST model with Yee-Roe-Davis technique as the PDE solver is proposed and compared with the widely used Takács model to show its improvement in numerical solution quality. The improved and Takács models are coupled with a bioreactor model to reevaluate ASP design basis and several popular control strategies for economic plausibility, contaminant removal efficiency and system robustness. The time-to-failure due to rising sludge blanket during overloading, as a key robustness indicator, is analyzed to demonstrate the differences caused by numerical issues in SST models. The calculated results indicate that the Takács model significantly underestimates time to failure, thus leading to a conservative design. Copyright © 2013 Elsevier Ltd. All rights reserved.

cAMP Catalyzing Phosphodiesterases Control Cholinergic Muscular Activity But Their Inhibition Does Not Enhance 5-HT4 Receptor-Mediated Facilitation of Cholinergic Contractions in the Murine Gastrointestinal Tract

PubMed Central

Pauwelyn, Vicky; Lefebvre, Romain A.

2018-01-01

Background: As the signal transduction of 5-HT4 receptors on cholinergic neurons innervating smooth muscle is controlled by phosphodiesterase (PDE) 4 in porcine stomach and colon, and human large intestine, the in vivo gastroprokinetic effects of a 5-HT4 receptor agonist might be enhanced by combination with a selective PDE4 inhibitor. The presence of 5-HT4 receptors on cholinergic neurons towards murine gastrointestinal circular muscle was recently shown. If the control of this receptor pathway by PDE4 is also present in mice, this might be a good model for in vivo testing of the combination therapy. Therefore this study investigates the role of cAMP catalyzing PDEs in smooth muscle cell activity and in the intraneuronal signal transduction of the 5-HT4 receptors in the gastrointestinal tract of C57Bl/6J mice. Methods: In circular smooth muscle strips from murine fundus, jejunum, and colon, submaximal cholinergic contractions were induced by either electrical field stimulation (EFS) or by carbachol (muscarinic receptor agonist). The influence of the PDE inhibitors IBMX (non-selective), vinpocetine (PDE1), EHNA (PDE2), cilostamide (PDE3), and rolipram (PDE4) was tested on these contractions and on the facilitating effect of a submaximal concentration of prucalopride (5-HT4 receptor agonist) on EFS-induced contractions. Results: In the three gastrointestinal regions, IBMX and cilostamide concentration-dependently decreased carbachol- as well as EFS-induced contractions. Some inhibitory effect was also observed with rolipram. In the fundus a non-significant trend for an enhancement of the facilitating effect of prucalopride on EFS-induced contractions was observed with IBMX, but none of the selective PDE inhibitors enhanced the facilitating effect of prucalopride in fundus, jejunum or colon. Conclusion: In analogy with the porcine gastrointestinal tract, in murine fundus, jejunum, and colon circular smooth muscle PDE3 is the main regulator of the cAMP turnover, with some contribution of PDE4. In contrast to the porcine gastrointestinal tract, the in vitro facilitation of electrically induced cholinergic contractions by 5-HT4 receptor stimulation could not be enhanced by specific PDE inhibition. The C57Bl/6J murine model is thus not suitable for in vivo testing of a 5-HT4 receptor agonist combined with a selective PDE4 inhibitor. PMID:29568269

Economic analysis of use of counterfeit drugs: health impairment risk of counterfeit phosphodiesterase type 5 inhibitor taken as an example.

PubMed

Sugita, Minoru; Miyakawa, Michiko

2010-07-01

The size of the market for counterfeit drugs throughout the world is considerable. Many cases of health impairment due to counterfeits have been reported. The market share of counterfeits in drug markets in developed countries is smaller than that in developing countries. However, the size of the market for counterfeits of phosphodiesterase type 5 inhibitors (PDE5Is) used as anti-erectile-dysfunction drugs is not small. The purpose of the present study was to analyze the health impairment risk of taking the counterfeit PDE5Is and the convenience of obtaining the counterfeits in Japan, using an economic methodology in order to work out countermeasures for reducing the health impairment risk. Information was obtained by interviewing employees of pharmaceutical and chemical corporations in Japan. The size of the market for counterfeit PDE5Is in Japan was recently estimated to be about 2.5 times larger than that of genuine PDE5Is. The price of the counterfeits in their market is reported to be nearly equal to that of the genuine PDE5Is. An outbreak of severe hypoglycemia among users of counterfeit PDE5Is containing an antidiabetic drug in Singapore was reported in 2008, and seven patients remained comatose as a result of prolonged neuroglycopenia. Four of them subsequently died, so the health impairment risk due to counterfeit PDE5Is should not be ignored. In order to obtain a genuine PDE5I in Japan, a patient must be examined and have a prescription written at a medical institution, and buy it at a dispensing pharmacy. Focusing on the health impairment risk due to counterfeit PDE5Is and the convenience of obtaining the counterfeits in Japan, we analyzed the effects on the prices and quantities of PDE5Is in the market from demand and supply curves, using an economic methodology. From the analysis, it was shown that the health impairment risk due to the counterfeits is underestimated in the market in Japan. Physicians should warn their patients not to buy counterfeit PDE5Is, and when they write a prescription for purchasing genuine PDE5Is, should inform their patients of the severe health problems that occurred in Singapore. The present economic analysis indicates that the health impairment risk due to counterfeit PDE5Is is underestimated in the market in Japan. Clarification of the underestimation of the severe health impairment risk due to counterfeits is important.

In vivo effects of phosphodiesterase inhibition on basal cyclic guanosine monophosphate levels in the prefrontal cortex, hippocampus and cerebellum of freely moving rats.

PubMed

Marte, Antonella; Pepicelli, Olimpia; Cavallero, Anna; Raiteri, Maurizio; Fedele, Ernesto

2008-11-15

We have characterized the various phosphodiesterases (PDE) that degrade cyclic GMP in the prefrontal cortex, hippocampus, and cerebellum using the microdialysis technique to measure in vivo extracellular cyclic GMP in awake rats. The following PDE blockers were used (100 and 1,000 microM): 8-methoxymethyl-IBMX (8-MM-IBMX), erythro-9-(2-hydroxy-3-nonyl)adenine (EHNA), milrinone, rolipram, and zaprinast. For solubility reasons, sildenafil was tested only at 100 microM. All drugs were administered locally in the brain regions through the dialysis probe. At 100 microM, 8-MM-IBMX enhanced the cyclic nucleotide extracellular levels in the prefrontal cortex and hippocampus but not in the cerebellum; EHNA and milrinone were active only in the hippocampus; rolipram was devoid of any effect; zaprinast and sildenafil were effective in all three brain areas. At 1 mM, 8-MM-IBMX, milrinone, and zaprinast increased extracellular cyclic GMP in all the brain regions examined, EHNA became active also in the prefrontal cortex and rolipram showed a significant effect only in the cerebellum. This is the first in vivo functional study showing that, in cortex, PDE1, -2, and -5/9 degrade cGMP, with PDE9 probably playing a major role; in hippocampus, PDE5/9 and PDE1 are mainly involved and seem almost equally active, but PDE2 and -3 also contribute; in cerebellum, PDE5/9 are the main cGMP hydrolyzing enzymes, but also PDE1 and -4 significantly operate.

Biomolecular surface construction by PDE transform.

PubMed

Zheng, Qiong; Yang, Siyang; Wei, Guo-Wei

2012-03-01

This work proposes a new framework for the surface generation based on the partial differential equation (PDE) transform. The PDE transform has recently been introduced as a general approach for the mode decomposition of images, signals, and data. It relies on the use of arbitrarily high-order PDEs to achieve the time-frequency localization, control the spectral distribution, and regulate the spatial resolution. The present work provides a new variational derivation of high-order PDE transforms. The fast Fourier transform is utilized to accomplish the PDE transform so as to avoid stringent stability constraints in solving high-order PDEs. As a consequence, the time integration of high-order PDEs can be done efficiently with the fast Fourier transform. The present approach is validated with a variety of test examples in two-dimensional and three-dimensional settings. We explore the impact of the PDE transform parameters, such as the PDE order and propagation time, on the quality of resulting surfaces. Additionally, we utilize a set of 10 proteins to compare the computational efficiency of the present surface generation method and a standard approach in Cartesian meshes. Moreover, we analyze the present method by examining some benchmark indicators of biomolecular surface, that is, surface area, surface-enclosed volume, solvation free energy, and surface electrostatic potential. A test set of 13 protein molecules is used in the present investigation. The electrostatic analysis is carried out via the Poisson-Boltzmann equation model. To further demonstrate the utility of the present PDE transform-based surface method, we solve the Poisson-Nernst-Planck equations with a PDE transform surface of a protein. Second-order convergence is observed for the electrostatic potential and concentrations. Finally, to test the capability and efficiency of the present PDE transform-based surface generation method, we apply it to the construction of an excessively large biomolecule, a virus surface capsid. Virus surface morphologies of different resolutions are attained by adjusting the propagation time. Therefore, the present PDE transform provides a multiresolution analysis in the surface visualization. Extensive numerical experiment and comparison with an established surface model indicate that the present PDE transform is a robust, stable, and efficient approach for biomolecular surface generation in Cartesian meshes. Copyright © 2012 John Wiley & Sons, Ltd.

Frontiers in Numerical Relativity

NASA Astrophysics Data System (ADS)

Evans, Charles R.; Finn, Lee S.; Hobill, David W.

2011-06-01

Preface; Participants; Introduction; 1. Supercomputing and numerical relativity: a look at the past, present and future David W. Hobill and Larry L. Smarr; 2. Computational relativity in two and three dimensions Stuart L. Shapiro and Saul A. Teukolsky; 3. Slowly moving maximally charged black holes Robert C. Ferrell and Douglas M. Eardley; 4. Kepler's third law in general relativity Steven Detweiler; 5. Black hole spacetimes: testing numerical relativity David H. Bernstein, David W. Hobill and Larry L. Smarr; 6. Three dimensional initial data of numerical relativity Ken-ichi Oohara and Takashi Nakamura; 7. Initial data for collisions of black holes and other gravitational miscellany James W. York, Jr.; 8. Analytic-numerical matching for gravitational waveform extraction Andrew M. Abrahams; 9. Supernovae, gravitational radiation and the quadrupole formula L. S. Finn; 10. Gravitational radiation from perturbations of stellar core collapse models Edward Seidel and Thomas Moore; 11. General relativistic implicit radiation hydrodynamics in polar sliced space-time Paul J. Schinder; 12. General relativistic radiation hydrodynamics in spherically symmetric spacetimes A. Mezzacappa and R. A. Matzner; 13. Constraint preserving transport for magnetohydrodynamics John F. Hawley and Charles R. Evans; 14. Enforcing the momentum constraints during axisymmetric spacelike simulations Charles R. Evans; 15. Experiences with an adaptive mesh refinement algorithm in numerical relativity Matthew W. Choptuik; 16. The multigrid technique Gregory B. Cook; 17. Finite element methods in numerical relativity P. J. Mann; 18. Pseudo-spectral methods applied to gravitational collapse Silvano Bonazzola and Jean-Alain Marck; 19. Methods in 3D numerical relativity Takashi Nakamura and Ken-ichi Oohara; 20. Nonaxisymmetric rotating gravitational collapse and gravitational radiation Richard F. Stark; 21. Nonaxisymmetric neutron star collisions: initial results using smooth particle hydrodynamics Christopher S. Kochanek and Charles R. Evans; 22. Relativistic hydrodynamics James R. Wilson and Grant J. Mathews; 23. Computational dynamics of U(1) gauge strings: probability of reconnection of cosmic strings Richard A. Matzner; 24. Dynamically inhomogenous cosmic nucleosynthesis Hannu Kurki-Suonio; 25. Initial value solutions in planar cosmologies Peter Anninos, Joan Centrella and Richard Matzner; 26. An algorithmic overview of an Einstein solver Roger Ove; 27. A PDE compiler for full-metric numerical relativity Jonathan Thornburg; 28. Numerical evolution on null cones R. Gomez and J. Winicour; 29. Normal modes coupled to gravitational waves in a relativistic star Yasufumi Kojima; 30. Cosmic censorship and numerical relativity Dalia S. Goldwirth, Amos Ori and Tsvi Piran.

Schlieren Imaging of a Single-Ejector, Multi-Tube Pulsed Detonation Engine (Postprint)

DTIC Science & Technology

2009-01-01

studies have shown the potential of an ejector to almost double the thrust of a pulsed detonation engine ( PDE ) tube [1-3]. Axial misalignment of the... Detonation Research Facility in the Air Force Research Laboratory were used for this study. The PDE utilizes automotive valving to feed up to four... detonation tubes. The damped thrust stand was setup to measure PDE thrust alone for baseline tests or total thrust from ejector and PDE . This

Superoxide from NADPH oxidase upregulates type 5 phosphodiesterase in human vascular smooth muscle cells: inhibition with iloprost and NONOate.

PubMed

Muzaffar, S; Shukla, N; Bond, M; Sala-Newby, G B; Newby, A C; Angelini, G D; Jeremy, J Y

2008-11-01

To determine whether there is an association between vascular NADPH oxidase (NOX), superoxide, the small GTPase Rac(1) and PDE type 5 (PDE5) in human vascular smooth muscle cell (hVSMCs). hVSMCs were incubated with xanthine-xanthine oxidase (X-XO; a superoxide generating system) or the thromboxane A(2) analogue, U46619 (+/-superoxide dismutase (SOD) or apocynin) for 16 h. The expression of PDE5 and NOX-1 was assessed using Western blotting and superoxide measured. The role of Rac(1) in superoxide generation was assessed by overexpressing either the dominant-negative or constitutively active Rac isoforms. The effects of iloprost, DETA-NONOate and the Rho-kinase inhibitor, Y27632, on PDE5 and NOX-1 expression were also studied. Following 16 h incubation, U46619 and X-XO promoted the expression of PDE5 and NOX-1, an effect blocked by SOD or apocynin when co-incubated over the same time course. X-XO and U46619 both promoted the formation of superoxide. Overexpression of dominant-negative Rac(1) or addition of iloprost, DETA-NONOate or Y27632 completely blocked both superoxide release and PDE5 protein expression and activity. These data demonstrate that superoxide derived from NOX upregulates the expression of PDE5 in human VSMCs. As PDE5 hydrolyses cyclic GMP, this effect may blunt the vasculoprotective actions of NO.

Reasons and predictive factors for discontinuation of PDE-5 inhibitors despite successful intercourse in erectile dysfunction patients

PubMed Central

Kim, S-C; Lee, Y-S; Seo, K-K; Jung, G-W; Kim, T-H

2014-01-01

This study was aimed to identify characteristics of ED patients who discontinued PDE5i despite successful intercourse. Data were collected using a questionnaire from 34 urologic clinics regardless of the effect (success or failure) of PDE5i treatment by visiting the clinics (717), e-mail (64) or post (101) for 882 ED patients who had previously taken any kind of PDE5i on demand four or more times. Discontinuation of PDE5i was defined if the patient had never taken PDE5i for the previous 1 year despite successful intercourse. Of the 882 patients, 485 were included in the final analysis. Difference in the socio-demographic, ED- and partner-related data between the continuation and discontinuation group and factors influencing discontinuation of the PDE5i were analyzed. Among 485 respondents (mean age, 53.6), 116 (23.9%) had discontinued PDE5i use despite successful intercourse. Most common reasons for the discontinuation were ‘reluctant medication-dependent intercourse' (31.0%), ‘spontaneous recovery of erectile function without further treatment' (30.2%), and ‘high cost' (26.7%). In multiple logistic regression analysis, independent factors influencing discontinuation of the drug were cause of ED (psychogenic), short duration of ED, low education (⩽ middle school), and religion (Catholic). In partner-related compliance, only partner's religion (Catholic) was a significant factor. PMID:24305610

Comparison of the Pharmacological Profiles of Selective PDE4B and PDE4D Inhibitors in the Central Nervous System

PubMed Central

Zhang, Chong; Xu, Ying; Zhang, Han-Ting; Gurney, Mark E.; O’Donnell, James M.

2017-01-01

Inhibition of cyclic AMP (cAMP)-specific phosphodiesterase 4 (PDE4) has been proposed as a potential treatment for a series of neuropsychological conditions such as depression, anxiety and memory loss. However, the specific involvement of each of the PDE4 subtypes (PDE4A, 4B and 4C) in different categories of behavior has yet to be elucidated. In the present study, we compared the possible pharmacological effects of PDE4B and PDE4D selective inhibitors, A-33 and D159687, in mediating neurological function in mice. Both compounds were equally potent in stimulating cAMP signaling in the mouse hippocampal cell line HT-22 leading to an increase in CREB phosphorylation. In contrast, A-33 and D159687 displayed distinct neuropharmacological effects in mouse behavioral tests. A-33 has an antidepressant-like profile as indicated by reduced immobility time in the forced swim and tail suspension tasks, as well as reduced latency to feed in the novelty suppressed feeding test. D159687, on the other hand, had a procognitive profile as it improved memory in the novel object recognition test but had no antidepressant or anxiolytic benefit. The present data suggests that inhibitors targeting specific subtypes of PDE4 may exhibit differential pharmacological effects and aid a more efficient pharmacotherapy towards neuropsychological conditions. PMID:28054669

Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows

DOE Office of Scientific and Technical Information (OSTI.GOV)

HyeongKae Park; Robert Nourgaliev; Vincent Mousseau

2008-07-01

A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” familymore » of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.« less

Diablo 2.0: A modern DNS/LES code for the incompressible NSE leveraging new time-stepping and multigrid algorithms

NASA Astrophysics Data System (ADS)

Cavaglieri, Daniele; Bewley, Thomas; Mashayek, Ali

2015-11-01

We present a new code, Diablo 2.0, for the simulation of the incompressible NSE in channel and duct flows with strong grid stretching near walls. The code leverages the fractional step approach with a few twists. New low-storage IMEX (implicit-explicit) Runge-Kutta time-marching schemes are tested which are superior to the traditional and widely-used CN/RKW3 (Crank-Nicolson/Runge-Kutta-Wray) approach; the new schemes tested are L-stable in their implicit component, and offer improved overall order of accuracy and stability with, remarkably, similar computational cost and storage requirements. For duct flow simulations, our new code also introduces a new smoother for the multigrid solver for the pressure Poisson equation. The classic approach, involving alternating-direction zebra relaxation, is replaced by a new scheme, dubbed tweed relaxation, which achieves the same convergence rate with roughly half the computational cost. The code is then tested on the simulation of a shear flow instability in a duct, a classic problem in fluid mechanics which has been the object of extensive numerical modelling for its role as a canonical pathway to energetic turbulence in several fields of science and engineering.

A finite element solver for 3-D compressible viscous flows

NASA Technical Reports Server (NTRS)

Reddy, K. C.; Reddy, J. N.; Nayani, S.

1990-01-01

Computation of the flow field inside a space shuttle main engine (SSME) requires the application of state of the art computational fluid dynamic (CFD) technology. Several computer codes are under development to solve 3-D flow through the hot gas manifold. Some algorithms were designed to solve the unsteady compressible Navier-Stokes equations, either by implicit or explicit factorization methods, using several hundred or thousands of time steps to reach a steady state solution. A new iterative algorithm is being developed for the solution of the implicit finite element equations without assembling global matrices. It is an efficient iteration scheme based on a modified nonlinear Gauss-Seidel iteration with symmetric sweeps. The algorithm is analyzed for a model equation and is shown to be unconditionally stable. Results from a series of test problems are presented. The finite element code was tested for couette flow, which is flow under a pressure gradient between two parallel plates in relative motion. Another problem that was solved is viscous laminar flow over a flat plate. The general 3-D finite element code was used to compute the flow in an axisymmetric turnaround duct at low Mach numbers.

Implicit LES using adaptive filtering

NASA Astrophysics Data System (ADS)

Sun, Guangrui; Domaradzki, Julian A.

2018-04-01

In implicit large eddy simulations (ILES) numerical dissipation prevents buildup of small scale energy in a manner similar to the explicit subgrid scale (SGS) models. If spectral methods are used the numerical dissipation is negligible but it can be introduced by applying a low-pass filter in the physical space, resulting in an effective ILES. In the present work we provide a comprehensive analysis of the numerical dissipation produced by different filtering operations in a turbulent channel flow simulated using a non-dissipative, pseudo-spectral Navier-Stokes solver. The amount of numerical dissipation imparted by filtering can be easily adjusted by changing how often a filter is applied. We show that when the additional numerical dissipation is close to the subgrid-scale (SGS) dissipation of an explicit LES the overall accuracy of ILES is also comparable, indicating that periodic filtering can replace explicit SGS models. A new method is proposed, which does not require any prior knowledge of a flow, to determine the filtering period adaptively. Once an optimal filtering period is found, the accuracy of ILES is significantly improved at low implementation complexity and computational cost. The method is general, performing well for different Reynolds numbers, grid resolutions, and filter shapes.

Spacecraft charging analysis with the implicit particle-in-cell code iPic3D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Deca, J.; Lapenta, G.; Marchand, R.

2013-10-15

We present the first results on the analysis of spacecraft charging with the implicit particle-in-cell code iPic3D, designed for running on massively parallel supercomputers. The numerical algorithm is presented, highlighting the implementation of the electrostatic solver and the immersed boundary algorithm; the latter which creates the possibility to handle complex spacecraft geometries. As a first step in the verification process, a comparison is made between the floating potential obtained with iPic3D and with Orbital Motion Limited theory for a spherical particle in a uniform stationary plasma. Second, the numerical model is verified for a CubeSat benchmark by comparing simulation resultsmore » with those of PTetra for space environment conditions with increasing levels of complexity. In particular, we consider spacecraft charging from plasma particle collection, photoelectron and secondary electron emission. The influence of a background magnetic field on the floating potential profile near the spacecraft is also considered. Although the numerical approaches in iPic3D and PTetra are rather different, good agreement is found between the two models, raising the level of confidence in both codes to predict and evaluate the complex plasma environment around spacecraft.« less

Development of intra-strain self-cloning procedure for breeding baker's yeast strains.

PubMed

Nakagawa, Youji; Ogihara, Hiroyuki; Mochizuki, Chisato; Yamamura, Hideki; Iimura, Yuzuru; Hayakawa, Masayuki

2017-03-01

Previously reported self-cloning procedures for breeding of industrial yeast strains require DNA from other strains, plasmid DNA, or mutagenesis. Therefore, we aimed to construct a self-cloning baker's yeast strain that exhibits freeze tolerance via an improved self-cloning procedure. We first disrupted the URA3 gene of a prototrophic baker's yeast strain without the use of any marker gene, resulting in a Δura3 homozygous disruptant. Then, the URA3 gene of the parental baker's yeast strain was used as a selection marker to introduce the constitutive TDH3 promoter upstream of the PDE2 gene encoding high-affinity cyclic AMP phosphodiesterase. This self-cloning procedure was performed without using DNA from other Saccharomyces cerevisiae strains, plasmid DNA, or mutagenesis and was therefore designated an intra-strain self-cloning procedure. Using this self-cloning procedure, we succeeded in producing self-cloning baker's yeast strains that harbor the TDH3p-PDE2 gene heterozygously and homozygously, designated TDH3p-PDE2 hetero and TDH3p-PDE2 homo strains, respectively. These self-cloning strains expressed much higher levels of PDE2 mRNA than the parental strain and exhibited higher viability after freeze stress, as well as higher fermentation ability in frozen dough, when compared with the parental strain. The TDH3p-PDE2 homo strain was genetically more stable than the TDH3p-PDE2 hetero strain. These results indicate that both heterozygous and homozygous strains of self-cloning PDE2-overexpressing freeze-tolerant strains of industrial baker's yeast can be prepared using the intra-strain self-cloning procedure, and, from a practical viewpoint, the TDH3p-PDE2 homo strain constructed in this study is preferable to the TDH3p-PDE2 hetero strain for frozen dough baking. Copyright © 2016 The Society for Biotechnology, Japan. Published by Elsevier B.V. All rights reserved.

In permanent atrial fibrillation, PDE3 reduces force responses to 5‐HT, but PDE3 and PDE4 do not cause the blunting of atrial arrhythmias

PubMed Central

Schwarz, Simon; Ravens, Ursula; Knaut, Michael

2016-01-01

Abstract Background and Purpose 5‐HT increases force and L‐type Ca2 + current (ICa,L) and causes arrhythmias through 5‐HT4 receptors in human atrium. In permanent atrial fibrillation (peAF), atrial force responses to 5‐HT are blunted, arrhythmias abolished but ICa,L responses only moderately attenuated. We investigated whether, in peAF, this could be due to an increased function of PDE3 and/or PDE4, using the inhibitors cilostamide (300 nM) and rolipram (1 μM) respectively. Experimental Approach Contractile force, arrhythmic contractions and ICa,L were assessed in right atrial trabeculae and myocytes, obtained from patients with sinus rhythm (SR), paroxysmal atrial fibrillation (pAF) and peAF. Key Results Maximum force responses to 5‐HT were reduced to 15% in peAF, but not in pAF. Cilostamide, but not rolipram, increased both the blunted force responses to 5‐HT in peAF and the inotropic potency of 5‐HT fourfold to sevenfold in trabeculae of patients with SR, pAF and peAF. Lusitropic responses to 5‐HT were not decreased in peAF. Responses of ICa,L to 5‐HT did not differ and were unaffected by cilostamide or rolipram in myocytes from patients with SR or peAF. Concurrent cilostamide and rolipram increased 5‐HT's propensity to elicit arrhythmias in trabeculae from patients with SR, but not with peAF. Conclusions and Implications PDE3, but not PDE4, reduced inotropic responses to 5‐HT in peAF, independently of lusitropy and ICa,L, but PDE3 activity was the same as that in patients with SR and pAF. Atrial remodelling in peAF abolished the facilitation of 5‐HT to induce arrhythmias by inhibition of PDE3 plus PDE4. PMID:27238373

Use of the KlADH3 promoter for the quantitative production of the murine PDE5A isoforms in the yeast Kluyveromyces lactis.

PubMed

Cardarelli, Silvia; Giorgi, Mauro; Naro, Fabio; Malatesta, Francesco; Biagioni, Stefano; Saliola, Michele

2017-09-22

Phosphodiesterases (PDE) are a superfamily of enzymes that hydrolyse cyclic nucleotides (cAMP/cGMP), signal molecules in transduction pathways regulating crucial aspects of cell life. PDEs regulate the intensity and duration of the cyclic nucleotides signal modulating the downstream biological effect. Due to this critical role associated with the extensive distribution and multiplicity of isozymes, the 11 mammalian families (PDE1 to PDE11) constitute key therapeutic targets. PDE5, one of these cGMP-specific hydrolysing families, is the molecular target of several well known drugs used to treat erectile dysfunction and pulmonary hypertension. Kluyveromyces lactis, one of the few yeasts capable of utilizing lactose, is an attractive host alternative to Saccharomyces cerevisiae for heterologous protein production. Here we established K. lactis as a powerful host for the quantitative production of the murine PDE5 isoforms. Using the promoter of the highly expressed KlADH3 gene, multicopy plasmids were engineered to produce the native and recombinant Mus musculus PDE5 in K. lactis. Yeast cells produced large amounts of the purified A1, A2 and A3 isoforms displaying K m , V max and Sildenafil inhibition values similar to those of the native murine enzymes. PDE5 whose yield was nearly 1 mg/g wet weight biomass for all three isozymes (30 mg/L culture), is well tolerated by K. lactis cells without major growth deficiencies and interferences with the endogenous cAMP/cGMP signal transduction pathways. To our knowledge, this is the first time that the entire PDE5 isozymes family containing both regulatory and catalytic domains has been produced at high levels in a heterologous eukaryotic organism. K. lactis has been shown to be a very promising host platform for large scale production of mammalian PDEs for biochemical and structural studies and for the development of new specific PDE inhibitors for therapeutic applications in many pathologies.

In silico design of novel hERG-neutral sildenafil-like PDE5 inhibitors.

PubMed

Kayık, Gülru; Tüzün, Nurcan Ş; Durdagi, Serdar

2017-10-01

Cyclic nucleotide phosphodiesterase enzymes (PDEs) have functions in regulating the levels of intracellular second messengers, 3', 5'-cyclic adenosine monophosphate (cAMP) and 3', 5'-cyclic guanosine monophosphate (cGMP), via hydrolysis and decomposing mechanisms in cells. They take essential roles in modulating various cellular activities such as memory and smooth muscle functions. PDE type 5 (PDE5) inhibitors enhance the vasodilatory effects of cGMP in the corpus cavernosum and they are used to treat erectile dysfunction. Patch clamp experiments showed that the IC 50 values of the human ether-à-go-go-related gene (hERG1) potassium (K) ion channel blocking affinity of PDE5 inhibitors sildenafil, vardenafil, and tadalafil as 33, 12, and 100 μM, respectively. hERG1 channel is responsible for the regulation of the action potential of human ventricular myocyte by contributing the rapid component of delayed rectifier K + current (I Kr ) component of the cardiac action potential. In this work, interaction patterns and binding affinity predictions of selected PDE5 inhibitors against the hERG1 channel are studied. It is attempted to develop PDE5 inhibitor analogs with lower binding affinity to hERG1 ion channel while keeping their pharmacological activity against their principal target PDE5 using in silico methods. Based on detailed analyses of docking poses and predicted interaction energies, novel analogs of PDE5 inhibitors with lower predicted binding affinity to hERG1 channels without loosing their principal target activity were proposed. Moreover, molecular dynamics (MD) simulations and post-processing MD analyses (i.e. Molecular Mechanics/Generalized Born Surface Area calculations) were performed. Detailed analysis of molecular simulations helped us to better understand the PDE5 inhibitor-target binding interactions in the atomic level. Results of this study can be useful for designing of novel and safe PDE5 inhibitors with enhanced activity and other tailored properties.

Engineered stabilization and structural analysis of the autoinhibited conformation of PDE4

DOE PAGES

Cedervall, Peder; Aulabaugh, Ann; Geoghegan, Kieran F.; ...

2015-03-09

Phosphodiesterase 4 (PDE4) is an essential contributor to intracellular signaling and an important drug target. The four members of this enzyme family (PDE4A to -D) are functional dimers in which each subunit contains two upstream conserved regions (UCR), UCR1 and -2, which precede the C-terminal catalytic domain. Alternative promoters, transcriptional start sites, and mRNA splicing lead to the existence of over 25 variants of PDE4, broadly classified as long, short, and supershort forms. We report the X-ray crystal structure of long form PDE4B containing UCR1, UCR2, and the catalytic domain, crystallized as a dimer in which a disulfide bond cross-linksmore » cysteines engineered into UCR2 and the catalytic domain. Biochemical and mass spectrometric analyses showed that the UCR2-catalytic domain interaction occurs in trans, and established that this interaction regulates the catalytic activity of PDE4. By elucidating the key structural determinants of dimerization, we show that only long forms of PDE4 can be regulated by this mechanism. The results also provide a structural basis for the long-standing observation of high- and low-affinity binding sites for the prototypic inhibitor rolipram.« less

Flowfield analysis of helicopter rotor in hover and forward flight based on CFD

NASA Astrophysics Data System (ADS)

Zhao, Qinghe; Li, Xiaodong

2018-05-01

The helicopter rotor field is simulated in hover and forward flight based on Computational Fluid Dynamics(CFD). In hover case only one rotor is simulated with the periodic boundary condition in the rotational coordinate system and the grid is fixed. In the non-lift forward flight case, the total rotor is simulated in inertia coordinate system and the whole grid moves rigidly. The dual-time implicit scheme is applied to simulate the unsteady flowfield on the movement grids. The k – ω turbulence model is employed in order to capture the effects of turbulence. To verify the solver, the flowfield around the Caradonna-Tung rotor is computed. The comparison shows a good agreement between the numerical results and the experimental data.

Transition and Turbulence Modeling for Blunt-Body Wake Flows

NASA Technical Reports Server (NTRS)

Nance, Robert P.; Horvath, Thomas J.; Hassan, H. A.

1997-01-01

This study attempts t o improve the modeling and computational prediction of high- speed transitional wake flows. The recently developed kappa - zeta (Enstrophy) turbulence model is coupled with a newly developed transition prediction method and implemented in an implicit flow solver well-suited to hypersonic flows. In this model, transition onset is determined as part of the solution. Results obtained using the new model for a 70- deg blunted cone/sting geometry demonstrate better agreement with experimental heat- transfer measurements when compared to laminar calculations as well as solutions using the kappa - omega model. Results are also presented for the situation where transition onset is preselected. It is shown that, in this case, results are quite sensitive to location of the transition point.

First-generation phosphodiesterase type 5 inhibitors dropout: a comprehensive review and meta-analysis.

PubMed

Corona, G; Rastrelli, G; Burri, A; Serra, E; Gianfrilli, D; Mannucci, E; Jannini, E A; Maggi, M

2016-11-01

The discontinuation rate with phosphodiesterase type 5 inhibitors (PDE5i) remains very high. The aim of this study was to review and meta-analyze currently available data regarding dropout of the first-generation of PDE5i including sildenafil, vardenafil, and tadalafil. An extensive Medline Embase and Cochrane search was performed including the following words: 'PDE5i', 'discontinuation'. All observational studies reporting the dropout rate of PDE5i and its specific causes without any arbitrary restrictions were included. Out of 103 retrieved articles, 22 were included in the study. Retrieved trials included a total of 162,936 patients with a mean age of 58.8 ± 7.9 years. Prevalence of reported comorbid diabetes and hypertension were 27.7% and 36.9%, respectively. PDE5i were associated with a mean discontinuation rate of 4% per month (almost 50% after one year). This rate was higher in younger subjects and in those reporting a higher prevalence of associated morbidities. Six main reasons of PDE5i dropout were identified in the evaluated trials. Partner-related problems and lack of efficacy represented the most important reasons for PDE5i discontinuation, although no significant difference among factors was detected. In conclusion, despite their high efficacy and easy administration, the discontinuation rate and dissatisfaction with PDE5i are still very high. Our data showed that no single factor plays a major role in PDE5i dropout, suggesting that the discontinuation rate is usually because of a combination of both medical problems and psychosocial and relational factors. © 2016 American Society of Andrology and European Academy of Andrology.

Anchored PDE4 regulates chloride conductance in wild-type and ΔF508-CFTR human airway epithelia

PubMed Central

Blanchard, Elise; Zlock, Lorna; Lao, Anna; Mika, Delphine; Namkung, Wan; Xie, Moses; Scheitrum, Colleen; Gruenert, Dieter C.; Verkman, Alan S.; Finkbeiner, Walter E.; Conti, Marco; Richter, Wito

2014-01-01

Cystic fibrosis (CF) is caused by mutations in the gene encoding the cystic fibrosis transmembrane conductance regulator (CFTR) that impair its expression and/or chloride channel function. Here, we provide evidence that type 4 cyclic nucleotide phosphodiesterases (PDE4s) are critical regulators of the cAMP/PKA-dependent activation of CFTR in primary human bronchial epithelial cells. In non-CF cells, PDE4 inhibition increased CFTR activity under basal conditions (ΔISC 7.1 μA/cm2) and after isoproterenol stimulation (increased ΔISC from 13.9 to 21.0 μA/cm2) and slowed the return of stimulated CFTR activity to basal levels by >3-fold. In cells homozygous for ΔF508-CFTR, the most common mutation found in CF, PDE4 inhibition alone produced minimal channel activation. However, PDE4 inhibition strongly amplified the effects of CFTR correctors, drugs that increase expression and membrane localization of CFTR, and/or CFTR potentiators, drugs that increase channel gating, to reach ∼25% of the chloride conductance observed in non-CF cells. Biochemical studies indicate that PDE4s are anchored to CFTR and mediate a local regulation of channel function. Taken together, our results implicate PDE4 as an important determinant of CFTR activity in airway epithelia, and support the use of PDE4 inhibitors to potentiate the therapeutic benefits of CFTR correctors and potentiators.—Blanchard, E., Zlock, L., Lao, A., Mika, D., Namkung, W., Xie, M., Scheitrum, C., Gruenert, D.C., Verkman, A.S., Finkbeiner, W.E., Conti, M., Richter, W. Anchored PDE4 regulates chloride conductance in wild type and ΔF508-CFTR human airway epithelia. PMID:24200884

Functional phosphodiesterase 11A mutations may modify the risk of familial and bilateral testicular germ cell tumors

PubMed Central

Horvath, Anelia; Korde, Larissa; Greene, Mark H.; Libe, Rosella; Osorio, Paulo; Faucz, Fabio Rueda; Raffin-Sanson, Marie Laure; Tsang, Kit Man; Drori-Herishanu, Limor; Patronas, Yianna; Remmers, Elaine F; Nikita, Maria-Elena; Moran, Jason; Greene, Joseph; Nesterova, Maria; Merino, Maria; Bertherat, Jerome; Stratakis, Constantine A.

2009-01-01

Inactivating germline mutations in phosphodiesterase 11A (PDE11A) have been implicated in adrenal tumor susceptibility. PDE11A is highly-expressed in endocrine steroidogenic tissues, especially the testis, and mice with inactivated Pde11a exhibit male infertility, a known testicular germ cell tumor (TGCT) risk factor. We sequenced the PDE11A gene-coding region in 95 patients with TGCT from 64 unrelated kindreds. We identified 8 non-synonymous substitutions in 20 patients from 15 families: four (R52T; F258Y; G291R; V820M) were newly-recognized, three (R804H; R867G; M878V) were functional variants previously implicated in adrenal tumor predisposition, and one (Y727C) was a known polymorphism. We compared the frequency of these variants in our patients to unrelated controls that had been screened and found negative for any endocrine diseases: only the two previously-reported variants, R804H and R867G, known to be frequent in general population, were detected in these controls. The frequency of all PDE11A-gene variants (combined) was significantly higher among patients with TGCT (P=0.0002), present in 19% of the families of our cohort. Most variants were detected in the general population, but functional studies showed that all these mutations reduced PDE activity, and that PDE11A protein expression was decreased (or absent) in TGCT samples from carriers. This is the first demonstration of a PDE gene’s involvement in TGCT, although the cAMP signaling pathway has been investigated extensively in other reproductive organs and their diseases. In conclusion, we report that PDE11A-inactivating sequence variants may modify the risk of familial and bilateral TGCT. PMID:19549888

Effects of Alanyl-Glutamine Treatment on the Peritoneal Dialysis Effluent Proteome Reveal Pathomechanism-Associated Molecular Signatures*

PubMed Central

Herzog, Rebecca; Boehm, Michael; Unterwurzacher, Markus; Wagner, Anja; Parapatics, Katja; Májek, Peter; Mueller, André C.; Lichtenauer, Anton; Bennett, Keiryn L.; Alper, Seth L.; Vychytil, Andreas; Aufricht, Christoph; Kratochwill, Klaus

2018-01-01

Peritoneal dialysis (PD) is a modality of renal replacement therapy in which the high volumes of available PD effluent (PDE) represents a rich source of biomarkers for monitoring disease and therapy. Although this information could help guide the management of PD patients, little is known about the potential of PDE to define pathomechanism-associated molecular signatures in PD. We therefore subjected PDE to a high-performance multiplex proteomic analysis after depletion of highly-abundant plasma proteins and enrichment of low-abundance proteins. A combination of label-free and isobaric labeling strategies was applied to PDE samples from PD patients (n = 20) treated in an open-label, randomized, two-period, cross-over clinical trial with standard PD fluid or with a novel PD fluid supplemented with alanyl-glutamine (AlaGln). With this workflow we identified 2506 unique proteins in the PDE proteome, greatly increasing coverage beyond the 171 previously-reported proteins. The proteins identified range from high abundance plasma proteins to low abundance cellular proteins, and are linked to larger numbers of biological processes and pathways, some of which are novel for PDE. Interestingly, proteins linked to membrane remodeling and fibrosis are overrepresented in PDE compared with plasma, whereas the proteins underrepresented in PDE suggest decreases in host defense, immune-competence and response to stress. Treatment with AlaGln-supplemented PD fluid is associated with reduced activity of membrane injury-associated mechanisms and with restoration of biological processes involved in stress responses and host defense. Our study represents the first application of the PDE proteome in a randomized controlled prospective clinical trial of PD. This novel proteomic workflow allowed detection of low abundance biomarkers to define pathomechanism-associated molecular signatures in PD and their alterations by a novel therapeutic intervention. PMID:29208752

[Analysis and identification of illegal constituents in health food products implicitly advertizing tonic or slimming effect in the National Institute of Health Sciences in Japan].

PubMed

Goda, Yukihiro

2014-01-01

With the prefectural governments' aid of the purchase, the Division of Pharmacognosy, Phytochemistry and Narcotics, National Institute of Health Sciences (NIHS) successively has surveyed illegal constituents in health food products implicitly advertizing tonic or slimming effect since the fiscal year of 2002 (slimming type) or 2003 (tonic type). The average numbers of the analyzed products per year are about 100 (slimming type) and 150 (tonic type), respectively. We also continuously distribute standards of authentic samples of several illegal components such as N-nitrosofenfluramine (NFF) and sildenafil (SIL) to prefectural institutes and the average gross number per year is about 140. In the case of slimming type, the fact that the products containing NFF were widely sold in Japanese markets in 2002 is well known. In addition, phenolphthalein, fenfluramine, sibtramine, desdimethylsibtramine, orlistat, mazindol, Rhubarb, Senna Leaf, etc. have been found as illegal constituents. In the tonic type products, we have identified more than 20 synthetic compounds relating to the erectile dysfunction (ED) treatment drugs, SIL, vardenafil and tadalafil (TDF). Since 2005, their synthetic intermediates and the patented but non-approved PDE5 inhibitors also have been found. It should be noted that TDF was found in the shells of capsule in 2009 and that mutaprodenafil was found as pro-drug type illegal component in 2010. In this report identification method of these illegal constituents is briefly described and then analytical trend in this decade is reviewed.

Discovery of a Phosphodiesterase 9A Inhibitor as a Potential Hypoglycemic Agent

PubMed Central

2015-01-01

Phosphodiesterase 9 (PDE9) inhibitors have been studied as potential therapeutics for treatment of diabetes and Alzheimer’s disease. Here we report a potent PDE9 inhibitor 3r that has an IC50 of 0.6 nM and >150-fold selectivity over other PDEs. The HepG2 cell-based assay shows that 3r inhibits the mRNA expression of phosphoenolpyruvate carboxykinase and glucose 6-phosphatase. These activities of 3r, together with the reasonable pharmacokinetic properties and no acute toxicity at 1200 mg/kg dosage, suggest its potential as a hypoglycemic agent. The crystal structure of PDE9-3r reveals significantly different conformation and hydrogen bonding pattern of 3r from those of previously published 28s. Both 3r and 28s form a hydrogen bond with Tyr424, a unique PDE9 residue (except for PDE8), but 3r shows an additional hydrogen bond with Ala452. This structure information might be useful for design of PDE9 inhibitors. PMID:25432025

Multiscale Modeling of Angiogenesis and Predictive Capacity

NASA Astrophysics Data System (ADS)

Pillay, Samara; Byrne, Helen; Maini, Philip

Tumors induce the growth of new blood vessels from existing vasculature through angiogenesis. Using an agent-based approach, we model the behavior of individual endothelial cells during angiogenesis. We incorporate crowding effects through volume exclusion, motility of cells through biased random walks, and include birth and death-like processes. We use the transition probabilities associated with the discrete model and a discrete conservation equation for cell occupancy to determine collective cell behavior, in terms of partial differential equations (PDEs). We derive three PDE models incorporating single, multi-species and no volume exclusion. By fitting the parameters in our PDE models and other well-established continuum models to agent-based simulations during a specific time period, and then comparing the outputs from the PDE models and agent-based model at later times, we aim to determine how well the PDE models predict the future behavior of the agent-based model. We also determine whether predictions differ across PDE models and the significance of those differences. This may impact drug development strategies based on PDE models.

Phosphodiesterases regulate airway smooth muscle function in health and disease.

PubMed

Krymskaya, Vera P; Panettieri, Reynold A

2007-01-01

On the basis of structure, regulation, and kinetic properties, phosphodiesterases (PDEs) represent a superfamily of enzymes divided into 11 subfamilies that catalyze cytosolic levels of 3',5'-cyclic adenosine monophosphate (cAMP) or 3',5'-cyclic guanosine monophosphate (cGMP) to 5'-AMP or 5'-GMP, respectively. PDE4 represents the major PDE expressed in inflammatory cells as well as airway smooth muscle (ASM), and selective PDE4 inhibitors provide a broad spectrum of anti-inflammatory effects such as abrogating cytokine and chemokine release from inflammatory cells and inhibiting inflammatory cell trafficking. Due to cell- and tissue-specific gene expression and regulation, PDEs modulate unique organ-based functions. New tools or compounds that selectively inhibit PDE subfamilies and genetically engineered mice deficient in selective isoforms have greatly enhanced our understanding of PDE function in airway inflammation and resident cell function. This chapter will focus on recent advances in our understanding of the role of PDE in regulating ASM function.

A short review on structure and role of cyclic-3',5'-adenosine monophosphate-specific phosphodiesterase 4 as a treatment tool.

PubMed

Eskandari, Nahid; Mirmosayyeb, Omid; Bordbari, Gazaleh; Bastan, Reza; Yousefi, Zahra; Andalib, Alireza

2015-01-01

Cyclic nucleotide phosphodiesterases (PDEs) are known as a super-family of enzymes which catalyze the metabolism of the intracellular cyclic nucleotides, cyclic-3',5'-adenosine monophosphate (cAMP), and cyclic-3',5'-guanosine monophosphate that are expressed in a variety of cell types that can exert various functions based on their cells distribution. The PDE4 family has been the focus of vast research efforts over recent years because this family is considered as a prime target for therapeutic intervention in a number of inflammatory diseases such as asthma, chronic obstructive pulmonary disease, and rheumatoid arthritis, and it should be used and researched by pharmacists. This is because the major isoform of PDE that regulates inflammatory cell activity is the cAMP-specific PDE, PDE4. This review discusses the relationship between PDE4 and its inhibitor drugs based on structures, cells distribution, and pharmacological properties of PDE4 which can be informative for all pharmacy specialists.

Superoxide from NADPH oxidase upregulates type 5 phosphodiesterase in human vascular smooth muscle cells: inhibition with iloprost and NONOate

PubMed Central

Muzaffar, S; Shukla, N; Bond, M; Sala-Newby, G B; Newby, A C; Angelini, G D; Jeremy, J Y

2008-01-01

Background and purpose: To determine whether there is an association between vascular NADPH oxidase (NOX), superoxide, the small GTPase Rac1 and PDE type 5 (PDE5) in human vascular smooth muscle cell (hVSMCs). Experimental approach: hVSMCs were incubated with xanthine–xanthine oxidase (X-XO; a superoxide generating system) or the thromboxane A2 analogue, U46619 (±superoxide dismutase (SOD) or apocynin) for 16 h. The expression of PDE5 and NOX-1 was assessed using Western blotting and superoxide measured. The role of Rac1 in superoxide generation was assessed by overexpressing either the dominant-negative or constitutively active Rac isoforms. The effects of iloprost, DETA-NONOate and the Rho-kinase inhibitor, Y27632, on PDE5 and NOX-1 expression were also studied. Key results: Following 16 h incubation, U46619 and X-XO promoted the expression of PDE5 and NOX-1, an effect blocked by SOD or apocynin when co-incubated over the same time course. X-XO and U46619 both promoted the formation of superoxide. Overexpression of dominant-negative Rac1 or addition of iloprost, DETA-NONOate or Y27632 completely blocked both superoxide release and PDE5 protein expression and activity. Conclusions and implications: These data demonstrate that superoxide derived from NOX upregulates the expression of PDE5 in human VSMCs. As PDE5 hydrolyses cyclic GMP, this effect may blunt the vasculoprotective actions of NO. PMID:18660830

An insight into the pharmacophores of phosphodiesterase-5 inhibitors from synthetic and crystal structural studies

PubMed Central

Chen, Gong; Wang, Huanchen; Robinson, Howard; Cai, Jiwen; Wan, Yiqian; Ke, Hengming

2008-01-01

Selective inhibitors of cyclic nucleotide phosphodiesterase-5 (PDE5) have been used as drugs for treatment of male erectile dysfunction and pulmonary hypertension. An insight into the pharmacophores of PDE5 inhibitors is essential for development of second generation of PDE5 inhibitors, but has not been completely illustrated. Here we report the synthesis of a new class of the sildenafil derivatives and a crystal structure of the PDE5 catalytic domain in complex with 5-(2-ethoxy-5-(sulfamoyl)-3-thienyl)-1-methyl-3-propyl-1,6-dihydro-7H-pyrazolo[4,3-d] pyrimidin-7-one (12). Inhibitor 12 induces conformational change of the H-loop (residues 660–683), which is different from any of the known PDE5 structures. The pyrazolopyrimidinone groups of 12 and sildenafil are well superimposed, but their sulfonamide groups show a positional difference of as much as 1.5 Å. The structure-activity analysis suggests that a small hydrophobic pocket and the H-loop of PDE5 are important for the inhibitor affinity, in addition to two common elements for binding of almost all the PDE inhibitors: the stack against the phenylalanine and the hydrogen bond with the invariant glutamine. However, the PDE5-12 structure does not provide a full explanation to affinity changes of the inhibitors. Thus alternatives such as conformational change of the M-loop are open and further structural study is required. PMID:18346713

PDE and cognitive processing: beyond the memory domain.

PubMed

Heckman, P R A; Blokland, A; Ramaekers, J; Prickaerts, J

2015-03-01

Phosphodiesterase inhibitors (PDE-Is) enhance cAMP and/or cGMP signaling via reducing the degradation of these cyclic nucleotides. Both cAMP and cGMP signaling are essential for a variety of cellular functions and exert their effects both pre- and post-synaptically. Either of these second messengers relays and amplifies incoming signals at receptors on the cell surface making them important elements in signal transduction cascades and essential in cellular signaling in a variety of cell functions including neurotransmitter release and neuroprotection. Consequently, these processes can be influenced by PDE-Is as they increase cAMP and/or cGMP concentrations. PDE-Is have been considered as possible therapeutic agents to treat impaired memory function linked to several brain disorders, including depression, schizophrenia and Alzheimer's disease (AD). This review will, however, focus on the possible role of phosphodiesterases (PDEs) in cognitive decline beyond the memory domain. Here we will discuss the involvement of PDEs on three related domains: attention, information filtering (sensory- and sensorimotor gating) and response inhibition (drug-induced hyperlocomotion). Currently, these are emerging cognitive domains in the field of PDE research. Here we discuss experimental studies and the potential beneficial effects of PDE-I drugs on these cognitive domains, as effects of PDE-Is on these domains could potentially influence effects on memory performance. Overall, PDE4 seems to be the most promising target for all domains discussed in this review. Copyright © 2014 Elsevier Inc. All rights reserved.

Dialysate bacterial endotoxin as a prognostic indicator of peritoneal dialysis related peritonitis.

PubMed

Szeto, Cheuk-Chun; Lai, Ka-Bik; Chow, Kai-Ming; Kwan, Bonnie Ching-Ha; Law, Man-Ching; Pang, Wing-Fai; Ma, Terry King-Wing; Leung, Chi-Bon; Li, Philip Kam-Tao

2016-12-01

Peritonitis is the major complication of peritoneal dialysis (PD). The aim of our present study is to explore the prognostic value of endotoxin level in PD effluent for the prediction of treatment failure in PD-related peritonitis. We studied 325 peritonitis episodes in 223 patients. PD effluent (PDE) was collected every 5 days for endotoxin level and leukocyte count. Patients were followed for relapsing or recurrent peritonitis. We found 20 episodes (6.2%) had primary treatment failure; 41 (12.6%) developed relapsing, 19 (5.8%) had recurrent, and 22 (6.8%) had repeat episodes. Endotoxin was detectable in the PDE of 19 episodes (24.4%) caused by Gram negative organisms, 4 episodes (6.8%) of mixed bacterial growth, and none of the culture negative episodes or those by Gram positive organisms. For episodes caused by Gram negative bacteria, a detectable endotoxin level in PDE on day 5 had a sensitivity and specificity of 66.7% and 83.3%, respectively, for predicting primary treatment failure. In contrast, PDE leukocyte count > 1000 per mm3 on day 5 had a sensitivity and specificity of 88.9% and 89.1%, respectively; the addition of PDE endotoxin assay did not improve the sensitivity or specificity. We conclude that detectable endotoxin in PDE 5 days after antibiotic therapy might predict primary treatment failure in peritonitis episodes caused by Gram negative organisms. However, the sensitivity and specificity of PDE endotoxin assay was inferior to PDE leukocyte count. © 2016 Asian Pacific Society of Nephrology.

Implementation of the chemistry module MECCA (v2.5) in the modal aerosol version of the Community Atmosphere Model component (v3.6.33) of the Community Earth System Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Long, M. S.; Keene, W. C.; Easter, Richard C.

2013-02-22

A coupled atmospheric chemistry and climate system model was developed using the modal aerosol version of the National Center for Atmospheric Research Community Atmosphere Model (modal-CAM; v3.6.33) and the Max Planck Institute for Chemistry’s Module Efficiently Calculating the Chemistry of the Atmosphere (MECCA; v2.5) to provide enhanced resolution of multiphase processes, particularly those involving inorganic halogens, and associated impacts on atmospheric composition and climate. Three Rosenbrock solvers (Ros-2, Ros-3, RODAS-3) were tested in conjunction with the basic load-balancing options available to modal-CAM (1) to establish an optimal configuration of the implicitly-solved multiphase chemistry module that maximizes both computational speed andmore » repeatability of Ros- 2 and RODAS-3 results versus Ros-3, and (2) to identify potential implementation strategies for future versions of this and similar coupled systems. RODAS-3 was faster than Ros-2 and Ros-3 with good reproduction of Ros-3 results, while Ros-2 was both slower and substantially less reproducible relative to Ros-3 results. Modal-CAM with MECCA chemistry was a factor of 15 slower than modal-CAM using standard chemistry. MECCA chemistry integration times demonstrated a systematic frequency distribution for all three solvers, and revealed that the change in run-time performance was due to a change in the frequency distribution of chemical integration times; the peak frequency was similar for all solvers. This suggests that efficient chemistry-focused load-balancing schemes can be developed that rely on the parameters of this frequency distribution.« less

Photoaffinity labelling of cyclic GMP-inhibited phosphodiesterase (PDE III) in human and rat platelets and rat tissues: effects of phosphodiesterase inhibitors.

PubMed

Tang, K M; Jang, E K; Haslam, R J

1994-06-15

Ultraviolet irradiation of human platelet cytosol in the presence of 32P-labelled cyclic GMP (cGMP) can specifically label 110, 80, 55, 49 and 38 kDa proteins; the 110 kDa species is the subunit of cGMP-inhibited phosphodiesterase (PDE III) and the 80 kDa species that of cGMP-dependent protein kinase (Tang et al., 1993, Biochem. J. 294, 329). We have now shown that although photolabelling of platelet PDE III was inhibited by unlabelled cGMP, 8-bromo-cGMP and cyclic AMP (cAMP), it was not affected by phosphorothioate analogues of these cyclic nucleotides. Specific concentration-dependent inhibitions of the photolabelling of PDE III were observed with the following PDE inhibitors: trequinsin (IC50 = 13 +/- 2 nM), lixazinone (IC50 = 22 +/- 4 nM), milrinone (IC50 = 56 +/- 12 nM), cilostamide (IC50 = 70 +/- 9 nM), siguazodan (IC50 = 117 +/- 29 nM) and 3-isobutyl 1-methylxanthine (IBMX) (IC50 = 3950 +/- 22 nM). Thus, measurements of the inhibitory effects of compounds on the photolabelling of platelet PDE III provide a simple quantitative means of investigating their actions at a molecular level that avoids the need to purify the enzyme. Photolabelling of rat platelet lysate or rat heart homogenate by [32P]cGMP showed that the 110 kDa PDE III present in human material was replaced by a 115 kDa protein, labelling of which was also blocked by PDE III inhibitors. Heart and other rat tissues contained much less of this putative 115 kDa PDE III than rat platelets. In contrast, the 80 kDa protein was labelled much less in platelets than in many other rat tissue homogenates (e.g., heart, aorta, uterus and lung). Thus, comparison of the relative amounts of specific photolabelled proteins in different cells may provide an indication of different patterns of cyclic nucleotide action. We compared the abilities of phosphodiesterase inhibitors to block the photolabelling of PDE III in human platelet cytosol and to increase the iloprost-stimulated accumulation of cAMP in intact platelets. Whereas trequinsin (EC50 = 19 +/- 3 nM), lixazinone (EC50 = 122 +/- 8 nM), milrinone (EC50 = 5320 +/- 970 nM) and siguazodan (EC50 = 18880 +/- 3110 nM) all increased platelet cAMP to the same maximum extent, cilostamide and IBMX increased cAMP further, indicating that they inhibited a PDE isozyme in addition to PDE III.

Progress in development of HEDP capabilities in FLASH's Unsplit Staggered Mesh MHD solver

NASA Astrophysics Data System (ADS)

Lee, D.; Xia, G.; Daley, C.; Dubey, A.; Gopal, S.; Graziani, C.; Lamb, D.; Weide, K.

2011-11-01

FLASH is a publicly available astrophysical community code designed to solve highly compressible multi-physics reactive flows. We are adding capabilities to FLASH that will make it an open science code for the academic HEDP community. Among many important numerical requirements, we consider the following features to be important components necessary to meet our goals for FLASH as an HEDP open toolset. First, we are developing computationally efficient time-stepping integration methods that overcome the stiffness that arises in the equations describing a physical problem when there are disparate time scales. To this end, we are adding two different time-stepping schemes to FLASH that relax the time step limit when diffusive effects are present: an explicit super-time-stepping algorithm (Alexiades et al. in Com. Num. Mech. Eng. 12:31-42, 1996) and a Jacobian-Free Newton-Krylov implicit formulation. These two methods will be integrated into a robust, efficient, and high-order accurate Unsplit Staggered Mesh MHD (USM) solver (Lee and Deane in J. Comput. Phys. 227, 2009). Second, we have implemented an anisotropic Spitzer-Braginskii conductivity model to treat thermal heat conduction along magnetic field lines. Finally, we are implementing the Biermann Battery term to account for spontaneous generation of magnetic fields in the presence of non-parallel temperature and density gradients.

ALPS: A Linear Program Solver

NASA Technical Reports Server (NTRS)

Ferencz, Donald C.; Viterna, Larry A.

1991-01-01

ALPS is a computer program which can be used to solve general linear program (optimization) problems. ALPS was designed for those who have minimal linear programming (LP) knowledge and features a menu-driven scheme to guide the user through the process of creating and solving LP formulations. Once created, the problems can be edited and stored in standard DOS ASCII files to provide portability to various word processors or even other linear programming packages. Unlike many math-oriented LP solvers, ALPS contains an LP parser that reads through the LP formulation and reports several types of errors to the user. ALPS provides a large amount of solution data which is often useful in problem solving. In addition to pure linear programs, ALPS can solve for integer, mixed integer, and binary type problems. Pure linear programs are solved with the revised simplex method. Integer or mixed integer programs are solved initially with the revised simplex, and the completed using the branch-and-bound technique. Binary programs are solved with the method of implicit enumeration. This manual describes how to use ALPS to create, edit, and solve linear programming problems. Instructions for installing ALPS on a PC compatible computer are included in the appendices along with a general introduction to linear programming. A programmers guide is also included for assistance in modifying and maintaining the program.

Performance of a parallel algebraic multilevel preconditioner for stabilized finite element semiconductor device modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Paul T.; Shadid, John N.; Sala, Marzio

In this study results are presented for the large-scale parallel performance of an algebraic multilevel preconditioner for solution of the drift-diffusion model for semiconductor devices. The preconditioner is the key numerical procedure determining the robustness, efficiency and scalability of the fully-coupled Newton-Krylov based, nonlinear solution method that is employed for this system of equations. The coupled system is comprised of a source term dominated Poisson equation for the electric potential, and two convection-diffusion-reaction type equations for the electron and hole concentration. The governing PDEs are discretized in space by a stabilized finite element method. Solution of the discrete system ismore » obtained through a fully-implicit time integrator, a fully-coupled Newton-based nonlinear solver, and a restarted GMRES Krylov linear system solver. The algebraic multilevel preconditioner is based on an aggressive coarsening graph partitioning of the nonzero block structure of the Jacobian matrix. Representative performance results are presented for various choices of multigrid V-cycles and W-cycles and parameter variations for smoothers based on incomplete factorizations. Parallel scalability results are presented for solution of up to 10{sup 8} unknowns on 4096 processors of a Cray XT3/4 and an IBM POWER eServer system.« less

PDE1 Encodes a P-Type ATPase Involved in Appressorium-Mediated Plant Infection by the Rice Blast Fungus Magnaporthe grisea

PubMed Central

Balhadère, Pascale V.; Talbot, Nicholas J.

2001-01-01

Plant infection by the rice blast fungus Magnaporthe grisea is brought about by the action of specialized infection cells called appressoria. These infection cells generate enormous turgor pressure, which is translated into an invasive force that allows a narrow penetration hypha to breach the plant cuticle. The Magnaporthe pde1 mutant was identified previously by restriction enzyme–mediated DNA integration mutagenesis and is impaired in its ability to elaborate penetration hyphae. Here we report that the pde1 mutation is the result of an insertion into the promoter of a P-type ATPase-encoding gene. Targeted gene disruption confirmed the role of PDE1 in penetration hypha development and pathogenicity but highlighted potential differences in PDE1 regulation in different Magnaporthe strains. The predicted PDE1 gene product was most similar to members of the aminophospholipid translocase group of P-type ATPases and was shown to be a functional homolog of the yeast ATPase gene ATC8. Spatial expression studies showed that PDE1 is expressed in germinating conidia and developing appressoria. These findings implicate the action of aminophospholipid translocases in the development of penetration hyphae and the proliferation of the fungus beyond colonization of the first epidermal cell. PMID:11549759

UCR1C is a novel activator of phosphodiesterase 4 (PDE4) long isoforms and attenuates cardiomyocyte hypertrophy.

PubMed

Wang, Li; Burmeister, Brian T; Johnson, Keven R; Baillie, George S; Karginov, Andrei V; Skidgel, Randal A; O'Bryan, John P; Carnegie, Graeme K

2015-05-01

Hypertrophy increases the risk of heart failure and arrhythmia. Prevention or reversal of the maladaptive hypertrophic phenotype has thus been proposed to treat heart failure. Chronic β-adrenergic receptor (β-AR) stimulation induces cardiomyocyte hypertrophy by elevating 3',5'-cyclic adenosine monophosphate (cAMP) levels and activating downstream effectors such protein kinase A (PKA). Conversely, hydrolysis of cAMP by phosphodiesterases (PDEs) spatiotemporally restricts cAMP signaling. Here, we demonstrate that PDE4, but not PDE3, is critical in regulating cardiomyocyte hypertrophy, and may represent a potential target for preventing maladaptive hypertrophy. We identify a sequence within the upstream conserved region 1 of PDE4D, termed UCR1C, as a novel activator of PDE4 long isoforms. UCR1C activates PDE4 in complex with A-kinase anchoring protein (AKAP)-Lbc resulting in decreased PKA signaling facilitated by AKAP-Lbc. Expression of UCR1C in cardiomyocytes inhibits hypertrophy in response to chronic β-AR stimulation. This effect is partially due to inhibition of nuclear PKA activity, which decreases phosphorylation of the transcription factor cAMP response element-binding protein (CREB). In conclusion, PDE4 activation by UCR1C attenuates cardiomyocyte hypertrophy by specifically inhibiting nuclear PKA activity. Published by Elsevier Inc.

PDE3, but not PDE4, reduces β1- and β2-adrenoceptor-mediated inotropic and lusitropic effects in failing ventricle from metoprolol-treated patients

PubMed Central

Molenaar, Peter; Christ, Torsten; Hussain, Rizwan I; Engel, Andreas; Berk, Emanuel; Gillette, Katherine T; Chen, Lu; Galindo-Tovar, Alejandro; Krobert, Kurt A; Ravens, Ursula; Levy, Finn Olav; Kaumann, Alberto J

2013-01-01

Background and Purpose PDE3 and/or PDE4 control ventricular effects of catecholamines in several species but their relative effects in failing human ventricle are unknown. We investigated whether the PDE3-selective inhibitor cilostamide (0.3–1 μM) or PDE4 inhibitor rolipram (1–10 μM) modified the positive inotropic and lusitropic effects of catecholamines in human failing myocardium. Experimental Approach Right and left ventricular trabeculae from freshly explanted hearts of 5 non-β-blocker-treated and 15 metoprolol-treated patients with terminal heart failure were paced to contract at 1 Hz. The effects of (-)-noradrenaline, mediated through β1 adrenoceptors (β2 adrenoceptors blocked with ICI118551), and (-)-adrenaline, mediated through β2 adrenoceptors (β1 adrenoceptors blocked with CGP20712A), were assessed in the absence and presence of PDE inhibitors. Catecholamine potencies were estimated from –logEC50s. Key Results Cilostamide did not significantly potentiate the inotropic effects of the catecholamines in non-β-blocker-treated patients. Cilostamide caused greater potentiation (P = 0.037) of the positive inotropic effects of (-)-adrenaline (0.78 ± 0.12 log units) than (-)-noradrenaline (0.47 ± 0.12 log units) in metoprolol-treated patients. Lusitropic effects of the catecholamines were also potentiated by cilostamide. Rolipram did not affect the inotropic and lusitropic potencies of (-)-noradrenaline or (-)-adrenaline on right and left ventricular trabeculae from metoprolol-treated patients. Conclusions and Implications Metoprolol induces a control by PDE3 of ventricular effects mediated through both β1 and β2 adrenoceptors, thereby further reducing sympathetic cardiostimulation in patients with terminal heart failure. Concurrent therapy with a PDE3 blocker and metoprolol could conceivably facilitate cardiostimulation evoked by adrenaline through β2 adrenoceptors. PDE4 does not appear to reduce inotropic and lusitropic effects of catecholamines in failing human ventricle. Linked Article This article is commented on by Eschenhagen, pp 524–527 of this issue. To view this commentary visit http://dx.doi.org/10.1111/bph.12168 PMID:23489141

CHBPR: Decreased cGMP level contributes to increased contraction in arteries from hypertensive rats: role of PDE1

PubMed Central

Giachini, Fernanda R.; Lima, Victor V.; Carneiro, Fernando S.; Tostes, Rita C.; Webb, R. Clinton

2011-01-01

Recent evidence suggests that angiotensin II (Ang II) upregulates phosphodiesterase (PDE)-1A expression. We hypothesized that Ang II augmented PDE1 activation, decreasing the bioavailability of cyclic cyclic guanosine 3', 5'-monophosphate (cGMP), contributing to increased vascular contractility. Male Sprague-Dawley rats received mini-osmotic pumps with Ang II (60 ng.min−1) or saline for 14 days. PE-induced contractions were increased in aorta (Emax168±8 vs. 136±4%) and small-mesenteric arteries [(SMA), Emax170±6 vs. 143±3%] from Ang II infused rats compared to control. PDE1 inhibition with vinpocetine (10µM) reduced PE-induced contraction in aortas from Ang II rats (Emax94±12%) but not in control (154±7%). Vinpocetine decreased the sensitivity to PE in SMA from Ang II rats compared to vehicle (pD2 5.1±0.1 vs. 5.9±0.06), but not in control (6.0±0.03 vs. 6.1±0.04). Sildenafil (10µM), a PDE5 inhibitor reduced PE-induced maximal contraction similarly in Ang II and control rats. Arteries were contracted with PE (1µM) and concentration-dependent relaxation to vinpocetine and sildenafil was evaluated. Aortas from Ang II rats displayed increased relaxation to vinpocetine compared to control (Emax82±12 vs. 44±5%). SMA from Ang II rats showed greater sensitivity during vinpocetine-induced relaxation, compared to control (pD2 6.1±0.3 vs. 5.3±0.1). No differences in sildenafil-induced relaxation were observed. PDE1A and PDE1C expressions in aorta and PDE1A expression in SMA were increased in Ang II rats. cGMP production, which is decreased in arteries from Ang II rats, was restored after PDE1 blockade. We conclude that PDE1 activation reduces cGMP bioavailability in arteries from ANG II, contributing to increased contractile responsiveness. PMID:21282562

Cyanidin-3-glucoside suppresses B[a]PDE-induced cyclooxygenase-2 expression by directly inhibiting Fyn kinase activity.

PubMed

Lim, Tae-Gyu; Kwon, Jung Yeon; Kim, Jiyoung; Song, Nu Ry; Lee, Kyung Mi; Heo, Yong-Seok; Lee, Hyong Joo; Lee, Ki Won

2011-07-15

Benzo[a]pyrene-7,8-diol-9,10-epoxide (B[a]PDE) is a well-known carcinogen that is associated with skin cancer. Abnormal expression of cyclooxygenase-2 (COX-2) is an important mediator in inflammation and tumor promotion. We investigated the inhibitory effect of cyanidin-3-glucoside (C3G), an anthocyanin present in fruits, on B[a]PDE-induced COX-2 expression in mouse epidermal JB6 P+ cells. Pretreatment with C3G resulted in the reduction of B[a]PDE-induced expression of COX-2 and COX-2 promoter activity. The activation of activator protein-1 (AP-1) and nuclear factor-κB (NF-κB) induced by B[a]PDE was also attenuated by C3G. C3G attenuated the B[a]PDE-induced phosphorylation of MEK, MKK4, Akt, and mitogen-activated protein kinases (MAPKs), but no effect on the phosphorylation of the upstream MAPK regulator Fyn. However, kinase assays demonstrated that C3G suppressed Fyn kinase activity and C3G directly binds Fyn kinase noncompetitively with ATP. By using PP2, a pharmacological inhibitor for SFKs, we showed that Fyn kinase regulates B[a]PDE-induced COX-2 expression by activating MAPKs, AP-1 and NF-κB. These results suggest that C3G suppresses B[a]PDE-induced COX-2 expression mainly by blocking the activation of the Fyn signaling pathway, which may contribute to its chemopreventive potential. Copyright © 2011 Elsevier Inc. All rights reserved.

Regulation of Phosphodiesterase 3 in the Pulmonary Arteries During the Perinatal Period in Sheep

PubMed Central

Chen, Bernadette; Lakshminrusimha, Satyan; Czech, Lyubov; Groh, Beezly S.; Gugino, Sylvia F.; Russell, James A.; Farrow, Kathryn N.; Steinhorn, Robin H.

2009-01-01

The role of cAMP in the pulmonary vasculature during the transition from intrauterine to extrauterine life is poorly understood. We hypothesized that cAMP levels are regulated by alterations in phosphodiesterase 3 (PDE3), which hydrolyzes cAMP. PDE3 protein expression and hydrolytic activity were increased in resistance pulmonary arteries (PA) from spontaneously breathing one-day-old (1dSB) lambs relative to equivalent-gestation fetuses. This was accompanied by a decrease in steady-state cAMP. Ventilation with 21% O2 and 100% O2 for 24h disrupted the normal transition, whereas ventilation with 100% O2+inhaled NO (iNO) for 24h restored both PDE3 activity and cAMP to 1dSB levels. Consistent with these findings, relaxation to milrinone, a PDE3 inhibitor, was greater in PA isolated from 1dSB and 100% O2+iNO lambs, relative to fetal, 21% O2, and 100% O2 lambs. In conclusion, PDE3 expression and activity in PA dramatically increase after birth, with a concomitant decrease in steady-state cAMP. Ventilation with either 21% O2 or 100% O2 blunts this PDE3 increase, whereas iNO restores PDE3 activity to levels equivalent to 1dSB lambs. The vasodilatory effects of milrinone were most pronounced in vessels from lambs with the highest PDE3 activity, i.e. 1dSB and 100% O2+iNO lambs. Thus, milrinone may be most beneficial when used in conjunction with iNO. PMID:19707176

Inhibition of Cyclic Adenosine Monophosphate-Specific Phosphodiesterase by Various Food Plant-Derived Phytotherapeutic Agents

PubMed Central

Pacjuk, Olga; Hernández-Huguet, Silvia; Körner, Johanna; Scherer, Katharina; Richling, Elke

2017-01-01

Background: Phosphodiesterases (PDEs) play a major role in the regulation of cyclic adenosine monophosphate (cAMP)- and cyclic guanosine monophosphate (cGMP)-mediated pathways. Their inhibitors exhibit anti-inflammatory, vasodilatory and antithrombotic effects. Therefore, consumption of foods with PDE-inhibiting potential may possess beneficial influence on the risk of cardiovascular diseases. Methods: Four plant extracts (Arbutus unedo, Camellia sinensis, Cynara scolymus, Zingiber officinale) with promising ingredient profiles and physiological effects were tested for their ability to inhibit cAMP-specific PDE in vitro in a radioactive assay. Results: Strawberry tree fruit (Arbutus unedo) and tea (Camellia sinensis) extracts did not inhibit PDE markedly. Alternatively, artichoke (Cynara scolymus) extract had a significant inhibitory influence on PDE activity (IC50 = 0.9 ± 0.1 mg/mL) as well as its flavone luteolin (IC50 = 41 ± 10 μM) and 3,4-dicaffeoylquinic acid (IC50 > 1.0 mM). Additionally, the ginger (Zingiber officinale) extract and one of its constituents, [6]-gingerol, significantly inhibited PDE (IC50 = 1.7 ± 0.2 mg/mL and IC50 > 1.7 mM, respectively). Crude fractionation of ginger extract showed that substances responsible for PDE inhibition were in the lipoid fraction (IC50 = 455 ± 19 μg/mL). Conclusions: A PDE-inhibitory effect was shown for artichoke and ginger extract. Whether PDE inhibition in vivo can be achieved through ingestion of artichoke or ginger extracts leading to physiological effects concerning cardiovascular health should be addressed in future research. PMID:29113064

PDE5 inhibitors as therapeutics for heart disease, diabetes and cancer.

PubMed

Das, Anindita; Durrant, David; Salloum, Fadi N; Xi, Lei; Kukreja, Rakesh C

2015-03-01

The phosphodiesterase 5 (PDE5) inhibitors, including sildenafil (Viagra™), vardenafil (Levitra™), and tadalafil (Cialis™) have been developed for treatment of erectile dysfunction. Moreover, sildenafil and tadalafil are used for the management of pulmonary arterial hypertension in patients. Since our first report showing the cardioprotective effect of sildenafil in 2002, there has been tremendous growth of preclinical and clinical studies on the use of PDE5 inhibitors for cardiovascular diseases and cancer. Numerous animal studies have demonstrated that PDE5 inhibitors have powerful protective effect against myocardial ischemia/reperfusion (I/R) injury, doxorubicin cardiotoxicity, ischemic and diabetic cardiomyopathy, cardiac hypertrophy, Duchenne muscular dystrophy and the improvement of stem cell efficacy for myocardial repair. Mechanistically, PDE5 inhibitors protect the heart against I/R injury through increased expression of nitric oxide synthases, activation of protein kinase G (PKG), PKG-dependent hydrogen sulfide generation, and phosphorylation of glycogen synthase kinase-3β - a master switch immediately proximal to mitochondrial permeability transition pore and the end effector of cardioprotection. In addition, PDE5 inhibitors enhance the sensitivity of certain types of cancer to standard chemotherapeutic drugs, including doxorubicin. Many clinical trials with PDE5 inhibitors have focused on the potential cardiovascular and anti-cancer benefits. Despite mixed results of these clinical trials, there is a continuing strong interest by basic scientists and clinical investigators in exploring their new clinical uses. It is our hope that future new mechanistic investigations and carefully designed clinical trials would help in reaping additional benefits of PDE5 inhibitors for cardiovascular disease and cancer in patients. Copyright © 2014 Elsevier Inc. All rights reserved.

Airbreathing Pulse Detonation Engine Performance

NASA Technical Reports Server (NTRS)

Povinelli, Louis A.; Yungster, Shaye

2002-01-01

This paper presents performance results for pulse detonation engines (PDE) taking into account the effects of dissociation and recombination. The amount of sensible heat recovered through recombination in the PDE chamber and exhaust process was found to be significant. These results have an impact on the specific thrust, impulse and fuel consumption of the PDE.

The safety of phosphodiesterase type 5 inhibitors for erectile dysfunction.

PubMed

Ventimiglia, Eugenio; Capogrosso, Paolo; Montorsi, Francesco; Salonia, Andrea

2016-01-01

Phosphodiesterase type 5 inhibitors (PDE5Is) are the leading drugs for the treatment of erectile dysfunction (ED), being recommended as a first line treatment by both the European and US urological guidelines. PDE5Is are highly effective as compared to placebo, well tolerated and have a very low, though not negligible, rate of severe treatment-related adverse events. This paper reviews the safety profile of currently available PDE5Is, comparing them in a broad spectrum ED population and outlining a number of real-life aspects of importance in the real-life everyday clinical setting. Guidelines unanimously agree in considering PDE5Is as first line treatments for ED when well-tolerated and not contraindicated. Despite the fact that no high-grade evidence comparing the efficacy and the safety for PDE5Is is currently available, published data seem to suggest that there are no major differences in their safety profiles. Moreover, although oral PDE5Is were shown to cause more AEs than placebo, they were generally mild and well tolerated.

A substrate selectivity and inhibitor design lesson from the PDE10-cAMP crystal structure: a computational study.

PubMed

Lau, Justin Kai-Chi; Li, Xiao-Bo; Cheng, Yuen-Kit

2010-04-22

Phosphodiesterases (PDEs) catalyze the hydrolysis of second messengers cAMP and cGMP in regulating many important cellular signals and have been recognized as important drug targets. Experimentally, a range of specificity/selectivity toward cAMP and cGMP is well-known for the individual PDE families. The study reported here reveals that PDEs might also exhibit selectivity toward conformations of the endogenous substrates cAMP and cGMP. Molecular dynamics simulations and free energy study have been applied to study the binding of the cAMP torsional conformers about the glycosyl bond in PDE10A2. The computational results elucidated that PDE10A2 is energetically more favorable in complex with the syn cAMP conformer (as reported in the crystal structure) and the binding of anti cAMP to PDE10A2 would lead to either a nonreactive configuration or significant perturbation on the catalytic pocket of the enzyme. This experimentally inaccessible information provides important molecular insights for the development of effective PDE10 ligands.

East Indian Sandalwood Oil Is a Phosphodiesterase Inhibitor: A New Therapeutic Option in the Treatment of Inflammatory Skin Disease.

PubMed

Sharma, Manju; Levenson, Corey; Browning, John C; Becker, Emily M; Clements, Ian; Castella, Paul; Cox, Michael E

2018-01-01

Cyclic adenosine monophosphate phosphodiesterases (PDEs) regulate pro-inflammatory cytokine production. One isoform, PDE4, is overactive in chronic relapsing inflammatory skin diseases: psoriasis and eczema/atopic dermatitis, and in several cancers. East Indian sandalwood oil (EISO) has significant anti-inflammatory properties. Here, we report that 75% of pediatric eczema/atopic dermatitis patients treated with topical EISO formulations achieved a >50% reduction in their Eczema Area and Severity Index score. EISO treatment of a psoriasis model reduced PDE4 expression and reversed histopathology. EISO directly inhibited PDE enzymatic activity in vitro . In lipopolysaccharide-stimulated human dermal fibroblast, BEAS-2B, A549, and THP-1 cells, EISO suppressed total cellular PDE activity, PDE4, and 7 transcript levels, nuclear factor kappa B (NF-κB) activation, and pro-inflammatory cytokines/chemokine production. These results suggest that EISO anti-inflammatory activity is mediated through suppressing PDE activity, thus facilitating cAMP-regulated inhibition of NF-κB and indicate EISO as an attractive natural therapeutic for chronic and acute inflammatory disorders.

Inhibitors of cyclic nucleotide phosphodiesterase 3 and 5 as therapeutic agents in heart failure.

PubMed

Stehlik, Josef; Movsesian, Matthew A

2006-07-01

Cyclic nucleotide phosphodiesterases (PDE) 3 and 5 regulate cAMP and cGMP signalling in cardiac and smooth muscle myocytes. Important advances in the understanding of the roles of these enzymes have recently been made. PDE3 inhibitors have inotropic and vasodilatory properties, and although they acutely improve haemodynamics in patients with heart failure, they do not improve long-term morbidity and mortality. Although combination therapy with beta-adrenergic receptor antagonists or selective inhibition of specific PDE3 isoforms might result in a more favourable long-term outcome, more clinical data are needed to test this proposition. The role of PDE5 inhibitors in the treatment of cardiac disease is evolving. PDE5 inhibitors cause pulmonary and systemic vasodilation. How these drugs will compare with other vasodilators in terms of long-term outcomes in patients with heart failure is unknown. Recent studies also suggest that PDE5 inhibitors may have antihypertropic effects, exerted through increased myocardial cGMP signalling, that could be of additional benefit in patients with heart failure.

East Indian Sandalwood Oil Is a Phosphodiesterase Inhibitor: A New Therapeutic Option in the Treatment of Inflammatory Skin Disease

PubMed Central

Sharma, Manju; Levenson, Corey; Browning, John C.; Becker, Emily M.; Clements, Ian; Castella, Paul; Cox, Michael E.

2018-01-01

Cyclic adenosine monophosphate phosphodiesterases (PDEs) regulate pro-inflammatory cytokine production. One isoform, PDE4, is overactive in chronic relapsing inflammatory skin diseases: psoriasis and eczema/atopic dermatitis, and in several cancers. East Indian sandalwood oil (EISO) has significant anti-inflammatory properties. Here, we report that 75% of pediatric eczema/atopic dermatitis patients treated with topical EISO formulations achieved a >50% reduction in their Eczema Area and Severity Index score. EISO treatment of a psoriasis model reduced PDE4 expression and reversed histopathology. EISO directly inhibited PDE enzymatic activity in vitro. In lipopolysaccharide-stimulated human dermal fibroblast, BEAS-2B, A549, and THP-1 cells, EISO suppressed total cellular PDE activity, PDE4, and 7 transcript levels, nuclear factor kappa B (NF-κB) activation, and pro-inflammatory cytokines/chemokine production. These results suggest that EISO anti-inflammatory activity is mediated through suppressing PDE activity, thus facilitating cAMP-regulated inhibition of NF-κB and indicate EISO as an attractive natural therapeutic for chronic and acute inflammatory disorders. PMID:29593534

Topical otic drugs in a multi-purpose manufacturing facility: a guide on determination and application of permitted daily exposure (PDE).

PubMed

Wiesner, Lisa; Prause, Maarten; Lovsin Barle, Ester

2018-03-01

Due to newly introduced EU GMP (Good Manufacturing Practice) guideline for Medicinal Products for Human and Veterinary use, product specific permitted daily exposure (PDE) for toxicological evaluation in multi-purpose facilities are required within a documented process for risk assessment. European Medicines Agency (EMA) guidance on setting PDE limits so far focused on systemic administration routes such as intravenous (IV), oral or inhalation. This article provides guidance on setting PDE values for risk management purposes in multi-purpose facilities for active pharmaceutical ingredients (APIs) applied as topical otic drugs to the outer ear canal. The therewith determined PDE otic, is used for the calculation of maximum safe carry-over (MSC) in manufacturing scenarios where a topical otic product is manufactured followed by another topical otic product.

Parallel 3D Multi-Stage Simulation of a Turbofan Engine

NASA Technical Reports Server (NTRS)

Turner, Mark G.; Topp, David A.

1998-01-01

A 3D multistage simulation of each component of a modern GE Turbofan engine has been made. An axisymmetric view of this engine is presented in the document. This includes a fan, booster rig, high pressure compressor rig, high pressure turbine rig and a low pressure turbine rig. In the near future, all components will be run in a single calculation for a solution of 49 blade rows. The simulation exploits the use of parallel computations by using two levels of parallelism. Each blade row is run in parallel and each blade row grid is decomposed into several domains and run in parallel. 20 processors are used for the 4 blade row analysis. The average passage approach developed by John Adamczyk at NASA Lewis Research Center has been further developed and parallelized. This is APNASA Version A. It is a Navier-Stokes solver using a 4-stage explicit Runge-Kutta time marching scheme with variable time steps and residual smoothing for convergence acceleration. It has an implicit K-E turbulence model which uses an ADI solver to factor the matrix. Between 50 and 100 explicit time steps are solved before a blade row body force is calculated and exchanged with the other blade rows. This outer iteration has been coined a "flip." Efforts have been made to make the solver linearly scaleable with the number of blade rows. Enough flips are run (between 50 and 200) so the solution in the entire machine is not changing. The K-E equations are generally solved every other explicit time step. One of the key requirements in the development of the parallel code was to make the parallel solution exactly (bit for bit) match the serial solution. This has helped isolate many small parallel bugs and guarantee the parallelization was done correctly. The domain decomposition is done only in the axial direction since the number of points axially is much larger than the other two directions. This code uses MPI for message passing. The parallel speed up of the solver portion (no 1/0 or body force calculation) for a grid which has 227 points axially.

Rip3 knockdown rescues photoreceptor cell death in blind pde6c zebrafish.

PubMed

Viringipurampeer, I A; Shan, X; Gregory-Evans, K; Zhang, J P; Mohammadi, Z; Gregory-Evans, C Y

2014-05-01

Achromatopsia is a progressive autosomal recessive retinal disease characterized by early loss of cone photoreceptors and later rod photoreceptor loss. In most cases, mutations have been identified in CNGA3, CNGB3, GNAT2, PDE6C or PDE6H genes. Owing to this genetic heterogeneity, mutation-independent therapeutic schemes aimed at preventing cone cell death are very attractive treatment strategies. In pde6c(w59) mutant zebrafish, cone photoreceptors expressed high levels of receptor-interacting protein kinase 1 (RIP1) and receptor-interacting protein kinase 3 (RIP3) kinases, key regulators of necroptotic cell death. In contrast, rod photoreceptor cells were alternatively immunopositive for caspase-3 indicating activation of caspase-dependent apoptosis in these cells. Morpholino gene knockdown of rip3 in pde6c(w59) embryos rescued the dying cone photoreceptors by inhibiting the formation of reactive oxygen species and by inhibiting second-order neuron remodelling in the inner retina. In rip3 morphant larvae, visual function was restored in the cones by upregulation of the rod phosphodiesterase genes (pde6a and pde6b), compensating for the lack of cone pde6c suggesting that cones are able to adapt to their local environment. Furthermore, we demonstrated through pharmacological inhibition of RIP1 and RIP3 activity that cone cell death was also delayed. Collectively, these results demonstrate that the underlying mechanism of cone cell death in the pde6c(w59) mutant retina is through necroptosis, whereas rod photoreceptor bystander death occurs through a caspase-dependent mechanism. This suggests that targeting the RIP kinase signalling pathway could be an effective therapeutic intervention in retinal degeneration patients. As bystander cell death is an important feature of many retinal diseases, combinatorial approaches targeting different cell death pathways may evolve as an important general principle in treatment.

Nebivolol potentiates the efficacy of PDE5 inhibitors to relax corpus cavernosum and penile arteries from diabetic patients by enhancing the NO/cGMP pathway.

PubMed

Martínez-Salamanca, Juan I; La Fuente, José M; Cardoso, José; Fernández, Argentina; Cuevas, Pedro; Wright, Harold M; Angulo, Javier

2014-05-01

The efficacy of oral pharmacotherapy for erectile dysfunction (ED) (i.e., type 5 phosphodiesterase[PDE5] inhibitors) is significantly reduced in diabetic patients. Nebivolol is a selective β1-blocker used for treatinghy pertension that has been shown to increase the efficacy of sildenafil to reverse ED in diabetic rats. To evaluate the effects of nebivolol on the efficacy of the PDE5 inhibitors, sildenafil, tadalafil, and vardenafil to relax human corpus cavernosum (HCC) and vasodilate human penile resistance arteries (HPRA) from diabetic patients with ED (DMED). The influence of nebivolol on the capacity of these three PDE5 inhibitors to stimulate cyclic guanosine monophosphate (cGMP) production in HCC was also evaluated. HCC and HPRA were obtained from organ donors without ED (NEND; n = 18) or patients with diabetes undergoing penile prosthesis implantation (DMED; n = 19). Relaxations of HCC strips and HPRA to sildenafil,tadalafil, and vardenafil were evaluated in organ chambers and wire myographs. cGMP content in HCC was determined by ether extraction and quantification by ELISA. Effects of nebivolol on PDE5 inhibitor-induced relaxation of HCC, vasodilation ofHPRA and cGMP accumulation in HCC. Treatment with nebivolol (1 μM) significantly potentiated sildenafil-, tadalafil- and vardenafil-induced relaxations of HCC and vasodilations of HPRA from both NEND and DMED. Enhancement of relaxant capacity by nebivolol resulted in reversion of the impairment of PDE5 inhibition-induced responses in DMED and it was accompanied by enhancing the ability of PDE5 inhibitors to increase cGMP in HCC restoring reduced cGMP levelsin HCC from DMED. Nebivolol potentiated the capacity of PDE5 inhibitors to relax vascular structures of erectile tissue from diabetic patients by enhancing the nitric oxide (NO)/cGMP pathway in these tissues. These effects suggest a potential therapeutic utility of nebivolol as an adjunct to PDE5 inhibitors for the treatment of ED associated with diabetes.

Characterization of particulate cyclic nucleotide phosphodiesterases from bovine brain: Purification of a distinct cGMP-stimulated isoenzyme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Murashima, Seiko; Tanaka, Takayuki; Hockman, S.

1990-06-05

In the absence of detergent, {approx}80-85% of the total cGMP-stimulated phosphodiesterase (PDE) activity in bovine brain was associated with washed particulate fractions; {approx}85-90% of the calmodulin-sensitive PDE was soluble. Particulate cGMP-stimulated PDE was higher in cerebral cortical gray matter than in other regions. Homogenization of the brain particulate fraction in 1% Lubrol increased cGMP-stimulated activity {approx}100% and calmodulin-stimulated {approx}400-500%. Although 1% Lubrol readily solubilized these PDE activities, {approx}75% of the cAMP PDE activity (0.5 {mu}M ({sup 3}H)cAMP) that was not affected by cGMP was not solubilized. This cAMP PDE activity was very sensitive to inhibition by Rolipram but not cilostamide.more » Thus, three different PDE types, i.e., cGMP stimulated, calmodulin sensitive, and Rolipram inhibited, are associated in different ways with crude bovine brain particulate fractions. The brain enzyme exhibited a slightly greater subunit M{sub r} than did soluble forms from calf liver or bovine brain, as evidenced by protein staining or immunoblotting after polyacrylamide gel electrophoresis under denaturing conditions. Incubation of brain particulate and liver soluble cGMP-stimulated PDEs with V{sub 8} protease produced several peptides of similar size, as well as at least two distinct fragments of {approx}27 kDa from the brain and {approx}23 kDa from the liver enzyme. After photolabeling in the presence of ({sup 32}P)cGMP and digestion with V{sub 8} protease, ({sup 32}P)cGMP in each PDE was predominantly recovered with a peptide of {approx}14 kDa. All of these observations are consistent with the existence of at least two discrete forms (isoenzymes) of cGMP-stimulated PDE.« less