Ablation, Thermal Response, and Chemistry Program for Analysis of Thermal Protection Systems

NASA Technical Reports Server (NTRS)

Milos, Frank S.; Chen, Yih-Kanq

2010-01-01

In previous work, the authors documented the Multicomponent Ablation Thermochemistry (MAT) and Fully Implicit Ablation and Thermal response (FIAT) programs. In this work, key features from MAT and FIAT were combined to create the new Fully Implicit Ablation, Thermal response, and Chemistry (FIATC) program. FIATC is fully compatible with FIAT (version 2.5) but has expanded capabilities to compute the multispecies surface chemistry and ablation rate as part of the surface energy balance. This new methodology eliminates B' tables, provides blown species fractions as a function of time, and enables calculations that would otherwise be impractical (e.g. 4+ dimensional tables) such as pyrolysis and ablation with kinetic rates or unequal diffusion coefficients. Equations and solution procedures are presented, then representative calculations of equilibrium and finite-rate ablation in flight and ground-test environments are discussed.

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G., E-mail: maginot1@llnl.gov; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim E., E-mail: morel@tamu.edu

This work presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

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

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

High-order solution methods for grey discrete ordinates thermal radiative transfer

DOE PAGES

Maginot, Peter G.; Ragusa, Jean C.; Morel, Jim E.

2016-09-29

This paper presents a solution methodology for solving the grey radiative transfer equations that is both spatially and temporally more accurate than the canonical radiative transfer solution technique of linear discontinuous finite element discretization in space with implicit Euler integration in time. We solve the grey radiative transfer equations by fully converging the nonlinear temperature dependence of the material specific heat, material opacities, and Planck function. The grey radiative transfer equations are discretized in space using arbitrary-order self-lumping discontinuous finite elements and integrated in time with arbitrary-order diagonally implicit Runge–Kutta time integration techniques. Iterative convergence of the radiation equation ismore » accelerated using a modified interior penalty diffusion operator to precondition the full discrete ordinates transport operator.« less

Fully Implict Magneto-hydrodynamics Simulations of Coaxial Plasma Accelerators

DOE PAGES

Subramaniam, Vivek; Raja, Laxminarayan L.

2017-01-05

The resistive Magneto-Hydrodynamic (MHD) model describes the behavior of a strongly ionized plasma in the presence of external electric and magnetic fields. We developed a fully implicit MHD simulation tool to solve the resistive MHD governing equations in the context of a cell-centered finite-volume scheme. The primary objective of this study is to use the fully-implicit algorithm to obtain insights into the plasma acceleration and jet formation processes in Coaxial Plasma accelerators; electromagnetic acceleration devices that utilize self-induced magnetic fields to accelerate thermal plasmas to large velocities. We also carry out plasma-surface simulations in order to study the impact interactionsmore » when these high velocity plasma jets impinge on target material surfaces. Scaling studies are carried out to establish some basic functional relationships between the target-stagnation conditions and the current discharged between the coaxial electrodes.« less

SMAUMAT_ITI

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

Jannetti, C.; Becker, R.

The software is an ABAQUS/Standard UMAT (user defined material behavior subroutine) that implements the constitutive model for shape-memory alloy materials developed by Jannetti et. al. (2003a) using a fully implicit time integration scheme to integrate the constitutive equations. The UMAT is used in conjunction with ABAQUS/Standard to perform a finite-element analysis of SMA materials.

Fully-Implicit Navier-Stokes (FIN-S)

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.

2010-01-01

FIN-S is a SUPG finite element code for flow problems under active development at NASA Lyndon B. Johnson Space Center and within PECOS: a) The code is built on top of the libMesh parallel, adaptive finite element library. b) The initial implementation of the code targeted supersonic/hypersonic laminar calorically perfect gas flows & conjugate heat transfer. c) Initial extension to thermochemical nonequilibrium about 9 months ago. d) The technologies in FIN-S have been enhanced through a strongly collaborative research effort with Sandia National Labs.

A fully implicit finite element method for bidomain models of cardiac electromechanics

PubMed Central

Dal, Hüsnü; Göktepe, Serdar; Kaliske, Michael; Kuhl, Ellen

2012-01-01

We propose a novel, monolithic, and unconditionally stable finite element algorithm for the bidomain-based approach to cardiac electromechanics. We introduce the transmembrane potential, the extracellular potential, and the displacement field as independent variables, and extend the common two-field bidomain formulation of electrophysiology to a three-field formulation of electromechanics. The intrinsic coupling arises from both excitation-induced contraction of cardiac cells and the deformation-induced generation of intra-cellular currents. The coupled reaction-diffusion equations of the electrical problem and the momentum balance of the mechanical problem are recast into their weak forms through a conventional isoparametric Galerkin approach. As a novel aspect, we propose a monolithic approach to solve the governing equations of excitation-contraction coupling in a fully coupled, implicit sense. We demonstrate the consistent linearization of the resulting set of non-linear residual equations. To assess the algorithmic performance, we illustrate characteristic features by means of representative three-dimensional initial-boundary value problems. The proposed algorithm may open new avenues to patient specific therapy design by circumventing stability and convergence issues inherent to conventional staggered solution schemes. PMID:23175588

Towards full-Braginskii implicit extended MHD

NASA Astrophysics Data System (ADS)

Chacon, Luis

2009-05-01

Recently, viable algorithms have been proposed for the scalable, fully-implicit temporal integration of 3D resistive MHD and cold-ion extended MHD models. While significant, these achievements must be tempered by the fact that such models lack predictive capabilities in regimes of interest for magnetic fusion. Short of including kinetic closures, a natural evolution path towards predictability starts by considering additional terms as described in Braginskii's fluid closures in the collisional regime. Here, we focus on the inclusion of two fundamental elements of relevance for fusion plasmas: anisotropic parallel electron transport, and warm-ion physics (i.e., ion finite Larmor radius effects, included via gyroviscosity). Both these elements introduce significant numerical difficulties, due to the strong anisotropy in the former, and the presence of dispersive waves in the latter. In this presentation, we will discuss progress in our fully implicit algorithmic formulation towards the inclusion of both these elements. L. Chac'on, Phys. Plasmas, 15, 056103 (2008) L. Chac'on, J. Physics: Conf. Series, 125, 012041 (2008)

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.

TRIM—3D: a three-dimensional model for accurate simulation of shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Bertolazzi, Enrico; Cheng, Ralph T.

1993-01-01

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is discussed. The governing equations are the three-dimensional Reynolds equations in which the pressure is assumed to be hydrostatic. A minimal degree of implicitness has been introduced in the finite difference formula so that the resulting algorithm permits the use of large time steps at a minimal computational cost. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers. The high computational efficiency of this method has made it possible to provide the fine details of circulation structure in complex regions that previous studies were unable to obtain. For proper interpretation of the model results suitable interactive graphics is also an essential tool.

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code.

NASA Astrophysics Data System (ADS)

Chacon, L.; Knoll, D. A.

2004-11-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended primitive-variable MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field, non-dissipative, and stable in the absence of physical dissipation.(L. Chacón , phComput. Phys. Comm.) submitted (2004) PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, first and second-order implicit schemes are available, although higher-order temporal implicit schemes can be effortlessly implemented within the Newton-Krylov framework. A successful, scalable, MG physics-based preconditioning strategy, similar in concept to previous 2D MHD efforts,(L. Chacón et al., phJ. Comput. Phys). 178 (1), 15- 36 (2002); phJ. Comput. Phys., 188 (2), 573-592 (2003) has been developed. We are currently in the process of parallelizing the code using the PETSc library, and a Newton-Krylov-Schwarz approach for the parallel treatment of the preconditioner. In this poster, we will report on both the serial and parallel performance of PIXIE3D, focusing primarily on scalability and CPU speedup vs. an explicit approach.

PIXIE3D: A Parallel, Implicit, eXtended MHD 3D Code

NASA Astrophysics Data System (ADS)

Chacon, Luis

2006-10-01

We report on the development of PIXIE3D, a 3D parallel, fully implicit Newton-Krylov extended MHD code in general curvilinear geometry. PIXIE3D employs a second-order, finite-volume-based spatial discretization that satisfies remarkable properties such as being conservative, solenoidal in the magnetic field to machine precision, non-dissipative, and linearly and nonlinearly stable in the absence of physical dissipation. PIXIE3D employs fully-implicit Newton-Krylov methods for the time advance. Currently, second-order implicit schemes such as Crank-Nicolson and BDF2 (2^nd order backward differentiation formula) are available. PIXIE3D is fully parallel (employs PETSc for parallelism), and exhibits excellent parallel scalability. A parallel, scalable, MG preconditioning strategy, based on physics-based preconditioning ideas, has been developed for resistive MHD, and is currently being extended to Hall MHD. In this poster, we will report on progress in the algorithmic formulation for extended MHD, as well as the the serial and parallel performance of PIXIE3D in a variety of problems and geometries. L. Chac'on, Comput. Phys. Comm., 163 (3), 143-171 (2004) L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002); J. Comput. Phys., 188 (2), 573-592 (2003) L. Chac'on, 32nd EPS Conf. Plasma Physics, Tarragona, Spain, 2005 L. Chac'on et al., 33rd EPS Conf. Plasma Physics, Rome, Italy, 2006

An interacting boundary layer model for cascades

NASA Technical Reports Server (NTRS)

Davis, R. T.; Rothmayer, A. P.

1983-01-01

A laminar, incompressible interacting boundary layer model is developed for two-dimensional cascades. In the limit of large cascade spacing these equations reduce to the interacting boundary layer equations for a single body immersed in an infinite stream. A fully implicit numerical method is used to solve the governing equations, and is found to be at least as efficient as the same technique applied to the single body problem. Solutions are then presented for a cascade of finite flat plates and a cascade of finite sine-waves, with cusped leading and trailing edges.

A multi-dimensional nonlinearly implicit, electromagnetic Vlasov-Darwin particle-in-cell (PIC) algorithm

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacón, Luis; CoCoMans Team

2014-10-01

For decades, the Vlasov-Darwin model has been recognized to be attractive for PIC simulations (to avoid radiative noise issues) in non-radiative electromagnetic regimes. However, the Darwin model results in elliptic field equations that renders explicit time integration unconditionally unstable. Improving on linearly implicit schemes, fully implicit PIC algorithms for both electrostatic and electromagnetic regimes, with exact discrete energy and charge conservation properties, have been recently developed in 1D. This study builds on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the particle-field equations in multiple dimensions. The algorithm conserves energy, charge, and canonical-momentum exactly, even with grid packing. A simple fluid preconditioner allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. We demonstrate the accuracy and efficiency properties of the of the algorithm with various numerical experiments in 2D3V.

Development of cost-effective surfactant flooding technology. Final report

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

Pope, G.A.; Sepehrnoori, K.

1996-11-01

Task 1 of this research was the development of a high-resolution, fully implicit, finite-difference, multiphase, multicomponent, compositional simulator for chemical flooding. The major physical phenomena modeled in this simulator are dispersion, heterogeneous permeability and porosity, adsorption, interfacial tension, relative permeability and capillary desaturation, compositional phase viscosity, compositional phase density and gravity effects, capillary pressure, and aqueous-oleic-microemulsion phase behavior. Polymer and its non-Newtonian rheology properties include shear-thinning viscosity, permeability reduction, inaccessible pore volume, and adsorption. Options of constant or variable space grids and time steps, constant-pressure or constant-rate well conditions, horizontal and vertical wells, and multiple slug injections are also availablemore » in the simulator. The solution scheme used in this simulator is fully implicit. The pressure equation and the mass-conservation equations are solved simultaneously for the aqueous-phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used that greatly reduce numerical dispersion effects. Task 2 was the optimization of surfactant flooding. The code UTCHEM was used to simulate surfactant polymer flooding.« less

Semi-implicit finite difference methods for three-dimensional shallow water flow

USGS Publications Warehouse

Casulli, Vincenzo; Cheng, Ralph T.

1992-01-01

A semi-implicit finite difference method for the numerical solution of three-dimensional shallow water flows is presented and discussed. The governing equations are the primitive three-dimensional turbulent mean flow equations where the pressure distribution in the vertical has been assumed to be hydrostatic. In the method of solution a minimal degree of implicitness has been adopted in such a fashion that the resulting algorithm is stable and gives a maximal computational efficiency at a minimal computational cost. At each time step the numerical method requires the solution of one large linear system which can be formally decomposed into a set of small three-diagonal systems coupled with one five-diagonal system. All these linear systems are symmetric and positive definite. Thus the existence and uniquencess of the numerical solution are assured. When only one vertical layer is specified, this method reduces as a special case to a semi-implicit scheme for solving the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm has been shown to be fast, accurate and mass-conservative and can also be applied to simulate flooding and drying of tidal mud-flats in conjunction with three-dimensional flows. Furthermore, the resulting algorithm is fully vectorizable for an efficient implementation on modern vector computers.

An in-depth stability analysis of nonuniform FDTD combined with novel local implicitization techniques

NASA Astrophysics Data System (ADS)

Van Londersele, Arne; De Zutter, Daniël; Vande Ginste, Dries

2017-08-01

This work focuses on efficient full-wave solutions of multiscale electromagnetic problems in the time domain. Three local implicitization techniques are proposed and carefully analyzed in order to relax the traditional time step limit of the Finite-Difference Time-Domain (FDTD) method on a nonuniform, staggered, tensor product grid: Newmark, Crank-Nicolson (CN) and Alternating-Direction-Implicit (ADI) implicitization. All of them are applied in preferable directions, alike Hybrid Implicit-Explicit (HIE) methods, as to limit the rank of the sparse linear systems. Both exponential and linear stability are rigorously investigated for arbitrary grid spacings and arbitrary inhomogeneous, possibly lossy, isotropic media. Numerical examples confirm the conservation of energy inside a cavity for a million iterations if the time step is chosen below the proposed, relaxed limit. Apart from the theoretical contributions, new accomplishments such as the development of the leapfrog Alternating-Direction-Hybrid-Implicit-Explicit (ADHIE) FDTD method and a less stringent Courant-like time step limit for the conventional, fully explicit FDTD method on a nonuniform grid, have immediate practical applications.

Numerical Simulation of Combustion and Rotor-Stator Interaction in a Turbine Combustor

DOE PAGES

Isvoranu, Dragos D.; Cizmas, Paul G. A.

2003-01-01

This article presents the development of a numerical algorithm for the computation of flow and combustion in a turbine combustor. The flow and combustion are modeled by the Reynolds-averaged Navier-Stokes equations coupled with the species-conservation equations. The chemistry model used herein is a two-step, global, finite-rate combustion model for methane and combustion gases. The governing equations are written in the strong conservation form and solved using a fully implicit, finite-difference approximation. The gas dynamics and chemistry equations are fully decoupled. A correction technique has been developed to enforce the conservation of mass fractions. The numerical algorithm developed herein has beenmore » used to investigate the flow and combustion in a one-stage turbine combustor.« less

An implicit finite-difference solution to the viscous shock layer, including the effects of radiation and strong blowing

NASA Technical Reports Server (NTRS)

Garrett, L. B.; Smith, G. L.; Perkins, J. N.

1972-01-01

An implicit finite-difference scheme is developed for the fully coupled solution of the viscous, radiating stagnation-streamline equations, including strong blowing. Solutions are presented for both air injection and injection of carbon-phenolic ablation products into air at conditions near the peak radiative heating point in an earth entry trajectory from interplanetary return missions. A detailed radiative-transport code that accounts for the important radiative exchange processes for gaseous mixtures in local thermodynamic and chemical equilibrium is utilized in the study. With minimum number of assumptions for the initially unknown parameters and profile distributions, convergent solutions to the full stagnation-line equations are rapidly obtained by a method of successive approximations. Damping of selected profiles is required to aid convergence of the solutions for massive blowing. It is shown that certain finite-difference approximations to the governing differential equations stabilize and improve the solutions. Detailed comparisons are made with the numerical results of previous investigations. Results of the present study indicate lower radiative heat fluxes at the wall for carbonphenolic ablation than previously predicted.

Hamiltonian approaches to spatial and temporal discretization of fully compressible equations

NASA Astrophysics Data System (ADS)

Dubos, Thomas; Dubey, Sarvesh

2017-04-01

The fully compressible Euler (FCE) equations are the most accurate for representing atmospheric motion, compared to approximate systems like the hydrostatic, anelastic or pseudo-incompressible systems. The price to pay for this accuracy is the presence of additional degrees of freedom and high-frequency acoustic waves that must be treated implicitly. In this work we explore a Hamiltonian approach to the issue of stable spatial and temporal discretization of the FCE using a non-Eulerian vertical coordinate. For scalability, a horizontally-explicit, vertically-implicit (HEVI) time discretization is adopted. The Hamiltonian structure of the equations is used to obtain the spatial finite-difference discretization and also in order to identify those terms of the equations of motion that need to be treated implicitly. A novel treatment of the lower boundary condition in the presence of orography is introduced: rather than enforcing a no-normal-flow boundary condition, which couples the horizontal and vertical velocity components and interferes with the HEVI structure, the ground is treated as a flexible surface with arbitrarily large stiffness, resulting in a decoupling of the horizontal and vertical dynamics and yielding a simple implicit problem which can be solved efficiently. Standard test cases performed in a vertical slice configuration suggest that an effective horizontal acoustic Courant number close to 1 can be achieved.

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

Weak Galerkin method for the Biot’s consolidation model

DOE PAGES

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

2017-08-23

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« less

Weak Galerkin method for the Biot’s consolidation model

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

Hu, Xiaozhe; Mu, Lin; Ye, Xiu

In this study, we develop a weak Galerkin (WG) finite element method for the Biot’s consolidation model in the classical displacement–pressure two-field formulation. Weak Galerkin linear finite elements are used for both displacement and pressure approximations in spatial discretizations. Backward Euler scheme is used for temporal discretization in order to obtain an implicit fully discretized scheme. We study the well-posedness of the linear system at each time step and also derive the overall optimal-order convergence of the WG formulation. Such WG scheme is designed on general shape regular polytopal meshes and provides stable and oscillation-free approximation for the pressure withoutmore » special treatment. Lastlyl, numerical experiments are presented to demonstrate the efficiency and accuracy of the proposed weak Galerkin finite element method.« 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

Characteristic-based algorithms for flows in thermo-chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Walters, Robert W.; Cinnella, Pasquale; Slack, David C.; Halt, David

1990-01-01

A generalized finite-rate chemistry algorithm with Steger-Warming, Van Leer, and Roe characteristic-based flux splittings is presented in three-dimensional generalized coordinates for the Navier-Stokes equations. Attention is placed on convergence to steady-state solutions with fully coupled chemistry. Time integration schemes including explicit m-stage Runge-Kutta, implicit approximate-factorization, relaxation and LU decomposition are investigated and compared in terms of residual reduction per unit of CPU time. Practical issues such as code vectorization and memory usage on modern supercomputers are discussed.

An Implicit Algorithm for the Numerical Simulation of Shape-Memory Alloys

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

Becker, R; Stolken, J; Jannetti, C

Shape-memory alloys (SMA) have the potential to be used in a variety of interesting applications due to their unique properties of pseudoelasticity and the shape-memory effect. However, in order to design SMA devices efficiently, a physics-based constitutive model is required to accurately simulate the behavior of shape-memory alloys. The scope of this work is to extend the numerical capabilities of the SMA constitutive model developed by Jannetti et. al. (2003), to handle large-scale polycrystalline simulations. The constitutive model is implemented within the finite-element software ABAQUS/Standard using a user defined material subroutine, or UMAT. To improve the efficiency of the numericalmore » simulations, so that polycrystalline specimens of shape-memory alloys can be modeled, a fully implicit algorithm has been implemented to integrate the constitutive equations. Using an implicit integration scheme increases the efficiency of the UMAT over the previously implemented explicit integration method by a factor of more than 100 for single crystal simulations.« less

User`s guide for UTCHEM implicit (1.0) a three dimensional chemical flood simulator. Final report, September 30, 1992--December 31, 1995

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

NONE

1996-07-01

UTCHEM IMPLICIT is a three-dimensional chemical flooding simulator. The solution scheme is fully implicit. The pressure equation and the mass conservation equations are solved simultaneously for the aqueous phase pressure and the total concentrations of each component. A third-order-in-space, second-order-in-time finite-difference method and a new total-variation-diminishing (TVD) third-order flux limiter are used to reduce numerical dispersion effects. Saturations and phase concentrations are solved in a flash routine. The major physical phenomena modeled in the simulator are: dispersion, adsorption, aqueous-oleic-microemulsion phase behavior, interfacial tension, relative permeability, capillary trapping, compositional phase viscosity, capillary pressure, phase density, polymer properties: shear thinning viscosity, inaccessiblemore » pore volume, permeability reduction, and adsorption. The following options are available in the simulator: constant or variable time-step sizes, uniform or nonuniform grid, pressure or rate constrained wells, horizontal and vertical wells.« less

A finite-volume module for all-scale Earth-system modelling at ECMWF

NASA Astrophysics Data System (ADS)

Kühnlein, Christian; Malardel, Sylvie; Smolarkiewicz, Piotr

2017-04-01

We highlight recent advancements in the development of the finite-volume module (FVM) (Smolarkiewicz et al., 2016) for the IFS at ECMWF. FVM represents an alternative dynamical core that complements the operational spectral dynamical core of the IFS with new capabilities. Most notably, these include a compact-stencil finite-volume discretisation, flexible meshes, conservative non-oscillatory transport and all-scale governing equations. As a default, FVM solves the compressible Euler equations in a geospherical framework (Szmelter and Smolarkiewicz, 2010). The formulation incorporates a generalised terrain-following vertical coordinate. A hybrid computational mesh, fully unstructured in the horizontal and structured in the vertical, enables efficient global atmospheric modelling. Moreover, a centred two-time-level semi-implicit integration scheme is employed with 3D implicit treatment of acoustic, buoyant, and rotational modes. The associated 3D elliptic Helmholtz problem is solved using a preconditioned Generalised Conjugate Residual approach. The solution procedure employs the non-oscillatory finite-volume MPDATA advection scheme that is bespoke for the compressible dynamics on the hybrid mesh (Kühnlein and Smolarkiewicz, 2017). The recent progress of FVM is illustrated with results of benchmark simulations of intermediate complexity, and comparison to the operational spectral dynamical core of the IFS. C. Kühnlein, P.K. Smolarkiewicz: An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics, J. Comput. Phys. (2017), in press. P.K. Smolarkiewicz, W. Deconinck, M. Hamrud, C. Kühnlein, G. Mozdzynski, J. Szmelter, N.P. Wedi: A finite-volume module for simulating global all-scale atmospheric flows, J. Comput. Phys. 314 (2016) 287-304. J. Szmelter, P.K. Smolarkiewicz: An edge-based unstructured mesh discretisation in geospherical framework, J. Comput. Phys. 229 (2010) 4980-4995.

Nonuniform grid implicit spatial finite difference method for acoustic wave modeling in tilted transversely isotropic media

NASA Astrophysics Data System (ADS)

Chu, Chunlei; Stoffa, Paul L.

2012-01-01

Discrete earth models are commonly represented by uniform structured grids. In order to ensure accurate numerical description of all wave components propagating through these uniform grids, the grid size must be determined by the slowest velocity of the entire model. Consequently, high velocity areas are always oversampled, which inevitably increases the computational cost. A practical solution to this problem is to use nonuniform grids. We propose a nonuniform grid implicit spatial finite difference method which utilizes nonuniform grids to obtain high efficiency and relies on implicit operators to achieve high accuracy. We present a simple way of deriving implicit finite difference operators of arbitrary stencil widths on general nonuniform grids for the first and second derivatives and, as a demonstration example, apply these operators to the pseudo-acoustic wave equation in tilted transversely isotropic (TTI) media. We propose an efficient gridding algorithm that can be used to convert uniformly sampled models onto vertically nonuniform grids. We use a 2D TTI salt model to demonstrate its effectiveness and show that the nonuniform grid implicit spatial finite difference method can produce highly accurate seismic modeling results with enhanced efficiency, compared to uniform grid explicit finite difference implementations.

Discontinuous dual-primal mixed finite elements for elliptic problems

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo

2000-01-01

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

Numerical simulation of the control of the three-dimensional transition process in boundary layers

NASA Technical Reports Server (NTRS)

Kral, L. D.; Fasel, H. F.

1990-01-01

Surface heating techniques to control the three-dimensional laminar-turbulent transition process are numerically investigated for a water boundary layer. The Navier-Stokes and energy equations are solved using a fully implicit finite difference/spectral method. The spatially evolving boundary layer is simulated. Results of both passive and active methods of control are shown for small amplitude two-dimensional and three-dimensional disturbance waves. Control is also applied to the early stages of the secondary instability process using passive or active control techniques.

Gradient-Based Aerodynamic Shape Optimization Using ADI Method for Large-Scale Problems

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Baysal, Oktay

1997-01-01

A gradient-based shape optimization methodology, that is intended for practical three-dimensional aerodynamic applications, has been developed. It is based on the quasi-analytical sensitivities. The flow analysis is rendered by a fully implicit, finite volume formulation of the Euler equations.The aerodynamic sensitivity equation is solved using the alternating-direction-implicit (ADI) algorithm for memory efficiency. A flexible wing geometry model, that is based on surface parameterization and platform schedules, is utilized. The present methodology and its components have been tested via several comparisons. Initially, the flow analysis for for a wing is compared with those obtained using an unfactored, preconditioned conjugate gradient approach (PCG), and an extensively validated CFD code. Then, the sensitivities computed with the present method have been compared with those obtained using the finite-difference and the PCG approaches. Effects of grid refinement and convergence tolerance on the analysis and shape optimization have been explored. Finally the new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4. Despite the expected increase in the computational time, the results indicate that shape optimization, which require large numbers of grid points can be resolved with a gradient-based approach.

Nonlinear 3D visco-resistive MHD modeling of fusion plasmas: a comparison between numerical codes

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Chacon, L.; Cappello, S.

2008-11-01

Fluid plasma models (and, in particular, the MHD model) are extensively used in the theoretical description of laboratory and astrophysical plasmas. We present here a successful benchmark between two nonlinear, three-dimensional, compressible visco-resistive MHD codes. One is the fully implicit, finite volume code PIXIE3D [1,2], which is characterized by many attractive features, notably the generalized curvilinear formulation (which makes the code applicable to different geometries) and the possibility to include in the computation the energy transport equation and the extended MHD version of Ohm's law. In addition, the parallel version of the code features excellent scalability properties. Results from this code, obtained in cylindrical geometry, are compared with those produced by the semi-implicit cylindrical code SpeCyl, which uses finite differences radially, and spectral formulation in the other coordinates [3]. Both single and multi-mode simulations are benchmarked, regarding both reversed field pinch (RFP) and ohmic tokamak magnetic configurations. [1] L. Chacon, Computer Physics Communications 163, 143 (2004). [2] L. Chacon, Phys. Plasmas 15, 056103 (2008). [3] S. Cappello, Plasma Phys. Control. Fusion 46, B313 (2004) & references therein.

A three-dimensional multiphase flow model for assesing NAPL contamination in porous and fractured media, 1. Formulation

NASA Astrophysics Data System (ADS)

Huyakorn, P. S.; Panday, S.; Wu, Y. S.

1994-06-01

A three-dimensional, three-phase numerical model is presented for stimulating the movement on non-aqueous-phase liquids (NAPL's) through porous and fractured media. The model is designed for practical application to a wide variety of contamination and remediation scenarios involving light or dense NAPL's in heterogeneous subsurface systems. The model formulation is first derived for three-phase flow of water, NAPL and air (or vapor) in porous media. The formulation is then extended to handle fractured systems using the dual-porosity and discrete-fracture modeling approaches The model accommodates a wide variety of boundary conditions, including withdrawal and injection well conditions which are treated rigorously using fully implicit schemes. The three-phase of formulation collapses to its simpler forms when air-phase dynamics are neglected, capillary effects are neglected, or two-phase-air-liquid, liquid-liquid systems with one or two active phases are considered. A Galerkin procedure with upstream weighting of fluid mobilities, storage matrix lumping, and fully implicit treatment of nonlinear coefficients and well conditions is used. A variety of nodal connectivity schemes leading to finite-difference, finite-element and hybrid spatial approximations in three dimensions are incorporated in the formulation. Selection of primary variables and evaluation of the terms of the Jacobian matrix for the Newton-Raphson linearized equations is discussed. The various nodal lattice options, and their significance to the computational time and memory requirements with regards to the block-Orthomin solution scheme are noted. Aggressive time-stepping schemes and under-relaxation formulas implemented in the code further alleviate the computational burden.

A compatible high-order meshless method for the Stokes equations with applications to suspension flows

NASA Astrophysics Data System (ADS)

Trask, Nathaniel; Maxey, Martin; Hu, Xiaozhe

2018-02-01

A stable numerical solution of the steady Stokes problem requires compatibility between the choice of velocity and pressure approximation that has traditionally proven problematic for meshless methods. In this work, we present a discretization that couples a staggered scheme for pressure approximation with a divergence-free velocity reconstruction to obtain an adaptive, high-order, finite difference-like discretization that can be efficiently solved with conventional algebraic multigrid techniques. We use analytic benchmarks to demonstrate equal-order convergence for both velocity and pressure when solving problems with curvilinear geometries. In order to study problems in dense suspensions, we couple the solution for the flow to the equations of motion for freely suspended particles in an implicit monolithic scheme. The combination of high-order accuracy with fully-implicit schemes allows the accurate resolution of stiff lubrication forces directly from the solution of the Stokes problem without the need to introduce sub-grid lubrication models.

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Technical Reports Server (NTRS)

Chitsomboon, Tawit

1992-01-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

Implementation of a kappa-epsilon turbulence model to RPLUS3D code

NASA Astrophysics Data System (ADS)

Chitsomboon, Tawit

1992-02-01

The RPLUS3D code has been developed at the NASA Lewis Research Center to support the National Aerospace Plane (NASP) project. The code has the ability to solve three dimensional flowfields with finite rate combustion of hydrogen and air. The combustion process of the hydrogen-air system are simulated by an 18 reaction path, 8 species chemical kinetic mechanism. The code uses a Lower-Upper (LU) decomposition numerical algorithm as its basis, making it a very efficient and robust code. Except for the Jacobian matrix for the implicit chemistry source terms, there is no inversion of a matrix even though a fully implicit numerical algorithm is used. A k-epsilon turbulence model has recently been incorporated into the code. Initial validations have been conducted for a flow over a flat plate. Results of the validation studies are shown. Some difficulties in implementing the k-epsilon equations to the code are also discussed.

An efficient fully-implicit multislope MUSCL method for multiphase flow with gravity in discrete fractured media

NASA Astrophysics Data System (ADS)

Jiang, Jiamin; Younis, Rami M.

2017-06-01

The first-order methods commonly employed in reservoir simulation for computing the convective fluxes introduce excessive numerical diffusion leading to severe smoothing of displacement fronts. We present a fully-implicit cell-centered finite-volume (CCFV) framework that can achieve second-order spatial accuracy on smooth solutions, while at the same time maintain robustness and nonlinear convergence performance. A novel multislope MUSCL method is proposed to construct the required values at edge centroids in a straightforward and effective way by taking advantage of the triangular mesh geometry. In contrast to the monoslope methods in which a unique limited gradient is used, the multislope concept constructs specific scalar slopes for the interpolations on each edge of a given element. Through the edge centroids, the numerical diffusion caused by mesh skewness is reduced, and optimal second order accuracy can be achieved. Moreover, an improved smooth flux-limiter is introduced to ensure monotonicity on non-uniform meshes. The flux-limiter provides high accuracy without degrading nonlinear convergence performance. The CCFV framework is adapted to accommodate a lower-dimensional discrete fracture-matrix (DFM) model. Several numerical tests with discrete fractured system are carried out to demonstrate the efficiency and robustness of the numerical model.

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.

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.

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

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1994-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques, and a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical, and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data.

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 Numerical Model for Predicting Shoreline Changes.

DTIC Science & Technology

1980-07-01

minimal shorelines for finite - difference scheme of time lAt (B) . . . 27 11 Transport function Q(ao) = cos ao sin za o for selected values of z . 28 12...generate the preceding examples was based on the use of implicit finite differences . Such schemes, whether implicit or ex- plicit (or both), are...10(A) shows an initially straight shoreline. In any finite - difference scheme, after one time increment At, the shoreline is bounded below by the solid

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm

DOE PAGES

Chen, G.; Chacón, L.

2015-08-11

For decades, the Vlasov–Darwin model has been recognized to be attractive for particle-in-cell (PIC) kinetic plasma simulations in non-radiative electromagnetic regimes, to avoid radiative noise issues and gain computational efficiency. However, the Darwin model results in an elliptic set of field equations that renders conventional explicit time integration unconditionally unstable. We explore a fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions, which overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. The finite-difference scheme for Darwin field equations and particle equations of motion is space–time-centered, employing particle sub-cycling and orbit-averaging. This algorithm conserves total energy, local charge,more » canonical-momentum in the ignorable direction, and preserves the Coulomb gauge exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. Finally, we demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 2D–3V.« less

Implicit Geometry Meshing for the simulation of Rotary Friction Welding

NASA Astrophysics Data System (ADS)

Schmicker, D.; Persson, P.-O.; Strackeljan, J.

2014-08-01

The simulation of Rotary Friction Welding (RFW) is a challenging task, since it states a coupled problem of phenomena like large plastic deformations, heat flux, contact and friction. In particular the mesh generation and its restoration when using a Lagrangian description of motion is of significant severity. In this regard Implicit Geometry Meshing (IGM) algorithms are promising alternatives to the more conventional explicit methods. Because of the implicit description of the geometry during remeshing, the IGM procedure turns out to be highly robust and generates spatial discretizations of high quality regardless of the complexity of the flash shape and its inclusions. A model for efficient RFW simulation is presented, which is based on a Carreau fluid law, an Augmented Lagrange approach in mapping the incompressible deformations, a penalty contact approach, a fully regularized Coulomb-/fluid friction law and a hybrid time integration strategy. The implementation of the IGM algorithm using 6-node triangular finite elements is described in detail. The techniques are demonstrated on a fairly complex friction welding problem, demonstrating the performance and the potentials of the proposed method. The techniques are general and straight-forward to implement, and offer the potential of successful adoption to a wide range of other engineering problems.

Fully Coupled Nonlinear Fluid Flow and Poroelasticity in Arbitrarily Fractured Porous Media: A Hybrid-Dimensional Computational Model

NASA Astrophysics Data System (ADS)

Jin, L.; Zoback, M. D.

2017-10-01

We formulate the problem of fully coupled transient fluid flow and quasi-static poroelasticity in arbitrarily fractured, deformable porous media saturated with a single-phase compressible fluid. The fractures we consider are hydraulically highly conductive, allowing discontinuous fluid flux across them; mechanically, they act as finite-thickness shear deformation zones prior to failure (i.e., nonslipping and nonpropagating), leading to "apparent discontinuity" in strain and stress across them. Local nonlinearity arising from pressure-dependent permeability of fractures is also included. Taking advantage of typically high aspect ratio of a fracture, we do not resolve transversal variations and instead assume uniform flow velocity and simple shear strain within each fracture, rendering the coupled problem numerically more tractable. Fractures are discretized as lower dimensional zero-thickness elements tangentially conforming to unstructured matrix elements. A hybrid-dimensional, equal-low-order, two-field mixed finite element method is developed, which is free from stability issues for a drained coupled system. The fully implicit backward Euler scheme is employed for advancing the fully coupled solution in time, and the Newton-Raphson scheme is implemented for linearization. We show that the fully discretized system retains a canonical form of a fracture-free poromechanical problem; the effect of fractures is translated to the modification of some existing terms as well as the addition of several terms to the capacity, conductivity, and stiffness matrices therefore allowing the development of independent subroutines for treating fractures within a standard computational framework. Our computational model provides more realistic inputs for some fracture-dominated poromechanical problems like fluid-induced seismicity.

Toward transient finite element simulation of thermal deformation of machine tools in real-time

NASA Astrophysics Data System (ADS)

Naumann, Andreas; Ruprecht, Daniel; Wensch, Joerg

2018-01-01

Finite element models without simplifying assumptions can accurately describe the spatial and temporal distribution of heat in machine tools as well as the resulting deformation. In principle, this allows to correct for displacements of the Tool Centre Point and enables high precision manufacturing. However, the computational cost of FE models and restriction to generic algorithms in commercial tools like ANSYS prevents their operational use since simulations have to run faster than real-time. For the case where heat diffusion is slow compared to machine movement, we introduce a tailored implicit-explicit multi-rate time stepping method of higher order based on spectral deferred corrections. Using the open-source FEM library DUNE, we show that fully coupled simulations of the temperature field are possible in real-time for a machine consisting of a stock sliding up and down on rails attached to a stand.

A Penalty Method for the Numerical Solution of Hamilton-Jacobi-Bellman (HJB) Equations in Finance

NASA Astrophysics Data System (ADS)

Witte, J. H.; Reisinger, C.

2010-09-01

We present a simple and easy to implement method for the numerical solution of a rather general class of Hamilton-Jacobi-Bellman (HJB) equations. In many cases, the considered problems have only a viscosity solution, to which, fortunately, many intuitive (e.g. finite difference based) discretisations can be shown to converge. However, especially when using fully implicit time stepping schemes with their desireable stability properties, one is still faced with the considerable task of solving the resulting nonlinear discrete system. In this paper, we introduce a penalty method which approximates the nonlinear discrete system to an order of O(1/ρ), where ρ>0 is the penalty parameter, and we show that an iterative scheme can be used to solve the penalised discrete problem in finitely many steps. We include a number of examples from mathematical finance for which the described approach yields a rigorous numerical scheme and present numerical results.

Efficient Coupling of Fluid-Plasma and Monte-Carlo-Neutrals Models for Edge Plasma Transport

NASA Astrophysics Data System (ADS)

Dimits, A. M.; Cohen, B. I.; Friedman, A.; Joseph, I.; Lodestro, L. L.; Rensink, M. E.; Rognlien, T. D.; Sjogreen, B.; Stotler, D. P.; Umansky, M. V.

2017-10-01

UEDGE has been valuable for modeling transport in the tokamak edge and scrape-off layer due in part to its efficient fully implicit solution of coupled fluid neutrals and plasma models. We are developing an implicit coupling of the kinetic Monte-Carlo (MC) code DEGAS-2, as the neutrals model component, to the UEDGE plasma component, based on an extension of the Jacobian-free Newton-Krylov (JFNK) method to MC residuals. The coupling components build on the methods and coding already present in UEDGE. For the linear Krylov iterations, a procedure has been developed to ``extract'' a good preconditioner from that of UEDGE. This preconditioner may also be used to greatly accelerate the convergence rate of a relaxed fixed-point iteration, which may provide a useful ``intermediate'' algorithm. The JFNK method also requires calculation of Jacobian-vector products, for which any finite-difference procedure is inaccurate when a MC component is present. A semi-analytical procedure that retains the standard MC accuracy and fully kinetic neutrals physics is therefore being developed. Prepared for US DOE by LLNL under Contract DE-AC52-07NA27344 and LDRD project 15-ERD-059, by PPPL under Contract DE-AC02-09CH11466, and supported in part by the U.S. DOE, OFES.

Aerodynamic Design on Unstructured Grids for Turbulent Flows

NASA Technical Reports Server (NTRS)

Anderson, W. Kyle; Bonhaus, Daryl L.

1997-01-01

An aerodynamic design algorithm for turbulent flows using unstructured grids is described. The current approach uses adjoint (costate) variables for obtaining derivatives of the cost function. The solution of the adjoint equations is obtained using an implicit formulation in which the turbulence model is fully coupled with the flow equations when solving for the costate variables. The accuracy of the derivatives is demonstrated by comparison with finite-difference gradients and a few example computations are shown. In addition, a user interface is described which significantly reduces the time required for setting up the design problems. Recommendations on directions of further research into the Navier Stokes design process are made.

Scalable Implementation of Finite Elements by NASA _ Implicit (ScIFEi)

NASA Technical Reports Server (NTRS)

Warner, James E.; Bomarito, Geoffrey F.; Heber, Gerd; Hochhalter, Jacob D.

2016-01-01

Scalable Implementation of Finite Elements by NASA (ScIFEN) is a parallel finite element analysis code written in C++. ScIFEN is designed to provide scalable solutions to computational mechanics problems. It supports a variety of finite element types, nonlinear material models, and boundary conditions. This report provides an overview of ScIFEi (\\Sci-Fi"), the implicit solid mechanics driver within ScIFEN. A description of ScIFEi's capabilities is provided, including an overview of the tools and features that accompany the software as well as a description of the input and output le formats. Results from several problems are included, demonstrating the efficiency and scalability of ScIFEi by comparing to finite element analysis using a commercial code.

The NCOREL computer program for 3D nonlinear supersonic potential flow computations

NASA Technical Reports Server (NTRS)

Siclari, M. J.

1983-01-01

An innovative computational technique (NCOREL) was established for the treatment of three dimensional supersonic flows. The method is nonlinear in that it solves the nonconservative finite difference analog of the full potential equation and can predict the formation of supercritical cross flow regions, embedded and bow shocks. The method implicitly computes a conical flow at the apex (R = 0) of a spherical coordinate system and uses a fully implicit marching technique to obtain three dimensional cross flow solutions. This implies that the radial Mach number must remain supersonic. The cross flow solutions are obtained by using type dependent transonic relaxation techniques with the type dependency linked to the character of the cross flow velocity (i.e., subsonic/supersonic). The spherical coordinate system and marching on spherical surfaces is ideally suited to the computation of wing flows at low supersonic Mach numbers due to the elimination of the subsonic axial Mach number problems that exist in other marching codes that utilize Cartesian transverse marching planes.

Development of an upwind, finite-volume code with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Molvik, Gregory A.

1995-01-01

Under this grant, two numerical algorithms were developed to predict the flow of viscous, hypersonic, chemically reacting gases over three-dimensional bodies. Both algorithms take advantage of the benefits of upwind differencing, total variation diminishing techniques and of a finite-volume framework, but obtain their solution in two separate manners. The first algorithm is a zonal, time-marching scheme, and is generally used to obtain solutions in the subsonic portions of the flow field. The second algorithm is a much less expensive, space-marching scheme and can be used for the computation of the larger, supersonic portion of the flow field. Both codes compute their interface fluxes with a temporal Riemann solver and the resulting schemes are made fully implicit including the chemical source terms and boundary conditions. Strong coupling is used between the fluid dynamic, chemical and turbulence equations. These codes have been validated on numerous hypersonic test cases and have provided excellent comparison with existing data. This report summarizes the research that took place from August 1,1994 to January 1, 1995.

A Review of High-Order and Optimized Finite-Difference Methods for Simulating Linear Wave Phenomena

NASA Technical Reports Server (NTRS)

Zingg, David W.

1996-01-01

This paper presents a review of high-order and optimized finite-difference methods for numerically simulating the propagation and scattering of linear waves, such as electromagnetic, acoustic, or elastic waves. The spatial operators reviewed include compact schemes, non-compact schemes, schemes on staggered grids, and schemes which are optimized to produce specific characteristics. The time-marching methods discussed include Runge-Kutta methods, Adams-Bashforth methods, and the leapfrog method. In addition, the following fourth-order fully-discrete finite-difference methods are considered: a one-step implicit scheme with a three-point spatial stencil, a one-step explicit scheme with a five-point spatial stencil, and a two-step explicit scheme with a five-point spatial stencil. For each method studied, the number of grid points per wavelength required for accurate simulation of wave propagation over large distances is presented. Recommendations are made with respect to the suitability of the methods for specific problems and practical aspects of their use, such as appropriate Courant numbers and grid densities. Avenues for future research are suggested.

Finite-difference model for 3-D flow in bays and estuaries

USGS Publications Warehouse

Smith, Peter E.; Larock, Bruce E.; ,

1993-01-01

This paper describes a semi-implicit finite-difference model for the numerical solution of three-dimensional flow in bays and estuaries. The model treats the gravity wave and vertical diffusion terms in the governing equations implicitly, and other terms explicitly. The model achieves essentially second-order accurate and stable solutions in strongly nonlinear problems by using a three-time-level leapfrog-trapezoidal scheme for the time integration.

Implicit finite difference methods on composite grids

NASA Technical Reports Server (NTRS)

Mastin, C. Wayne

1987-01-01

Techniques for eliminating time lags in the implicit finite-difference solution of partial differential equations are investigated analytically, with a focus on transient fluid dynamics problems on overlapping multicomponent grids. The fundamental principles of the approach are explained, and the method is shown to be applicable to both rectangular and curvilinear grids. Numerical results for sample problems are compared with exact solutions in graphs, and good agreement is demonstrated.

The development of flux-split algorithms for flows with non-equilibrium thermodynamics and chemical reactions

NASA Technical Reports Server (NTRS)

Grossman, B.; Cinella, P.

1988-01-01

A finite-volume method for the numerical computation of flows with nonequilibrium thermodynamics and chemistry is presented. A thermodynamic model is described which simplifies the coupling between the chemistry and thermodynamics and also results in the retention of the homogeneity property of the Euler equations (including all the species continuity and vibrational energy conservation equations). Flux-splitting procedures are developed for the fully coupled equations involving fluid dynamics, chemical production and thermodynamic relaxation processes. New forms of flux-vector split and flux-difference split algorithms are embodied in a fully coupled, implicit, large-block structure, including all the species conservation and energy production equations. Several numerical examples are presented, including high-temperature shock tube and nozzle flows. The methodology is compared to other existing techniques, including spectral and central-differenced procedures, and favorable comparisons are shown regarding accuracy, shock-capturing and convergence rates.

Application of the θ-method to a telegraphic model of fluid flow in a dual-porosity medium

NASA Astrophysics Data System (ADS)

González-Calderón, Alfredo; Vivas-Cruz, Luis X.; Herrera-Hernández, Erik César

2018-01-01

This work focuses mainly on the study of numerical solutions, which are obtained using the θ-method, of a generalized Warren and Root model that includes a second-order wave-like equation in its formulation. The solutions approximately describe the single-phase hydraulic head in fractures by considering the finite velocity of propagation by means of a Cattaneo-like equation. The corresponding discretized model is obtained by utilizing a non-uniform grid and a non-uniform time step. A simple relationship is proposed to give the time-step distribution. Convergence is analyzed by comparing results from explicit, fully implicit, and Crank-Nicolson schemes with exact solutions: a telegraphic model of fluid flow in a single-porosity reservoir with relaxation dynamics, the Warren and Root model, and our studied model, which is solved with the inverse Laplace transform. We find that the flux and the hydraulic head have spurious oscillations that most often appear in small-time solutions but are attenuated as the solution time progresses. Furthermore, we show that the finite difference method is unable to reproduce the exact flux at time zero. Obtaining results for oilfield production times, which are in the order of months in real units, is only feasible using parallel implicit schemes. In addition, we propose simple parallel algorithms for the memory flux and for the explicit scheme.

An efficient semi-implicit method for three-dimensional non-hydrostatic flows in compliant arterial vessels.

PubMed

Fambri, Francesco; Dumbser, Michael; Casulli, Vincenzo

2014-11-01

Blood flow in arterial systems can be described by the three-dimensional Navier-Stokes equations within a time-dependent spatial domain that accounts for the elasticity of the arterial walls. In this article, blood is treated as an incompressible Newtonian fluid that flows through compliant vessels of general cross section. A three-dimensional semi-implicit finite difference and finite volume model is derived so that numerical stability is obtained at a low computational cost on a staggered grid. The key idea of the method consists in a splitting of the pressure into a hydrostatic and a non-hydrostatic part, where first a small quasi-one-dimensional nonlinear system is solved for the hydrostatic pressure and only in a second step the fully three-dimensional non-hydrostatic pressure is computed from a three-dimensional nonlinear system as a correction to the hydrostatic one. The resulting algorithm is robust, efficient, locally and globally mass conservative, and applies to hydrostatic and non-hydrostatic flows in one, two and three space dimensions. These features are illustrated on nontrivial test cases for flows in tubes with circular or elliptical cross section where the exact analytical solution is known. Test cases of steady and pulsatile flows in uniformly curved rigid and elastic tubes are presented. Wherever possible, axial velocity development and secondary flows are shown and compared with previously published results. Copyright © 2014 John Wiley & Sons, Ltd.

On the performance of explicit and implicit algorithms for transient thermal analysis

NASA Astrophysics Data System (ADS)

Adelman, H. M.; Haftka, R. T.

1980-09-01

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit and implicit algorithms are discussed. A promising set of implicit algorithms, known as the GEAR package is described. Four test problems, used for evaluating and comparing various algorithms, have been selected and finite element models of the configurations are discribed. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system and a model of the space shuttle orbiter wing. Calculations were carried out using the SPAR finite element program, the MITAS lumped parameter program and a special purpose finite element program incorporating the GEAR algorithms. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff. Careful attention to modeling detail such as avoiding thin or short high-conducting elements can sometimes reduce the stiffness to the extent that explicit methods become advantageous.

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Chacon, Luis

2005-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. A crucial element is the development of an effective multilevel treatment of the grid equation.ootnotetextL. Chac'on, G. Lapenta, A fully implicit, nonlinear adaptive grid strategy, J. Comput. Phys., accepted (2005) We will show that such an approach is competitive vs. uniform grids both from the accuracy (due to adaptivity) and the efficiency standpoints. Results for a variety of models 1D and 2D geometries, including nonlinear diffusion, radiation-diffusion, Burgers equation, and gas dynamics will be presented.

Solidification of a binary mixture

NASA Technical Reports Server (NTRS)

Antar, B. N.

1982-01-01

The time dependent concentration and temperature profiles of a finite layer of a binary mixture are investigated during solidification. The coupled time dependent Stefan problem is solved numerically using an implicit finite differencing algorithm with the method of lines. Specifically, the temporal operator is approximated via an implicit finite difference operator resulting in a coupled set of ordinary differential equations for the spatial distribution of the temperature and concentration for each time. Since the resulting differential equations set form a boundary value problem with matching conditions at an unknown spatial point, the method of invariant imbedding is used for its solution.

Optimal implicit 2-D finite differences to model wave propagation in poroelastic media

NASA Astrophysics Data System (ADS)

Itzá, Reymundo; Iturrarán-Viveros, Ursula; Parra, Jorge O.

2016-08-01

Numerical modeling of seismic waves in heterogeneous porous reservoir rocks is an important tool for the interpretation of seismic surveys in reservoir engineering. We apply globally optimal implicit staggered-grid finite differences (FD) to model 2-D wave propagation in heterogeneous poroelastic media at a low-frequency range (<10 kHz). We validate the numerical solution by comparing it to an analytical-transient solution obtaining clear seismic wavefields including fast P and slow P and S waves (for a porous media saturated with fluid). The numerical dispersion and stability conditions are derived using von Neumann analysis, showing that over a wide range of porous materials the Courant condition governs the stability and this optimal implicit scheme improves the stability of explicit schemes. High-order explicit FD can be replaced by some lower order optimal implicit FD so computational cost will not be as expensive while maintaining the accuracy. Here, we compute weights for the optimal implicit FD scheme to attain an accuracy of γ = 10-8. The implicit spatial differentiation involves solving tridiagonal linear systems of equations through Thomas' algorithm.

Solvent Reaction Field Potential inside an Uncharged Globular Protein: A Bridge between Implicit and Explicit Solvent Models?

PubMed Central

Baker, Nathan A.; McCammon, J. Andrew

2008-01-01

The solvent reaction field potential of an uncharged protein immersed in Simple Point Charge/Extended (SPC/E) explicit solvent was computed over a series of molecular dynamics trajectories, intotal 1560 ns of simulation time. A finite, positive potential of 13 to 24 kbTec−1 (where T = 300K), dependent on the geometry of the solvent-accessible surface, was observed inside the biomolecule. The primary contribution to this potential arose from a layer of positive charge density 1.0 Å from the solute surface, on average 0.008 ec/Å3, which we found to be the product of a highly ordered first solvation shell. Significant second solvation shell effects, including additional layers of charge density and a slight decrease in the short-range solvent-solvent interaction strength, were also observed. The impact of these findings on implicit solvent models was assessed by running similar explicit-solvent simulations on the fully charged protein system. When the energy due to the solvent reaction field in the uncharged system is accounted for, correlation between per-atom electrostatic energies for the explicit solvent model and a simple implicit (Poisson) calculation is 0.97, and correlation between per-atom energies for the explicit solvent model and a previously published, optimized Poisson model is 0.99. PMID:17949217

Solvent reaction field potential inside an uncharged globular protein: A bridge between implicit and explicit solvent models?

NASA Astrophysics Data System (ADS)

Cerutti, David S.; Baker, Nathan A.; McCammon, J. Andrew

2007-10-01

The solvent reaction field potential of an uncharged protein immersed in simple point charge/extended explicit solvent was computed over a series of molecular dynamics trajectories, in total 1560ns of simulation time. A finite, positive potential of 13-24 kbTec-1 (where T =300K), dependent on the geometry of the solvent-accessible surface, was observed inside the biomolecule. The primary contribution to this potential arose from a layer of positive charge density 1.0Å from the solute surface, on average 0.008ec/Å3, which we found to be the product of a highly ordered first solvation shell. Significant second solvation shell effects, including additional layers of charge density and a slight decrease in the short-range solvent-solvent interaction strength, were also observed. The impact of these findings on implicit solvent models was assessed by running similar explicit solvent simulations on the fully charged protein system. When the energy due to the solvent reaction field in the uncharged system is accounted for, correlation between per-atom electrostatic energies for the explicit solvent model and a simple implicit (Poisson) calculation is 0.97, and correlation between per-atom energies for the explicit solvent model and a previously published, optimized Poisson model is 0.99.

A parallel domain decomposition-based implicit method for the Cahn–Hilliard–Cook phase-field equation in 3D

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

Zheng, Xiang; Yang, Chao; State Key Laboratory of Computer Science, Chinese Academy of Sciences, Beijing 100190

2015-03-15

We present a numerical algorithm for simulating the spinodal decomposition described by the three dimensional Cahn–Hilliard–Cook (CHC) equation, which is a fourth-order stochastic partial differential equation with a noise term. The equation is discretized in space and time based on a fully implicit, cell-centered finite difference scheme, with an adaptive time-stepping strategy designed to accelerate the progress to equilibrium. At each time step, a parallel Newton–Krylov–Schwarz algorithm is used to solve the nonlinear system. We discuss various numerical and computational challenges associated with the method. The numerical scheme is validated by a comparison with an explicit scheme of high accuracymore » (and unreasonably high cost). We present steady state solutions of the CHC equation in two and three dimensions. The effect of the thermal fluctuation on the spinodal decomposition process is studied. We show that the existence of the thermal fluctuation accelerates the spinodal decomposition process and that the final steady morphology is sensitive to the stochastic noise. We also show the evolution of the energies and statistical moments. In terms of the parallel performance, it is found that the implicit domain decomposition approach scales well on supercomputers with a large number of processors.« less

Supercomputers for engineering analysis

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

Goudreau, G.L.; Benson, D.J.; Hallquist, J.O.

1986-07-01

The Cray-1 and Cray X-MP/48 experience in engineering computations at the Lawrence Livermore National Laboratory is surveyed. The fully vectorized explicit DYNA and implicit NIKE finite element codes are discussed with respect to solid and structural mechanics. The main efficiencies for production analyses are currently obtained by simple CFT compiler exploitation of pipeline architecture for inner do-loop optimization. Current developmet of outer-loop multitasking is also discussed. Applications emphasis will be on 3D examples spanning earth penetrator loads analysis, target lethality assessment, and crashworthiness. The use of a vectorized large deformation shell element in both DYNA and NIKE has substantially expandedmore » 3D nonlinear capability. 25 refs., 7 figs.« less

Error analysis of multipoint flux domain decomposition methods for evolutionary diffusion problems

NASA Astrophysics Data System (ADS)

Arrarás, A.; Portero, L.; Yotov, I.

2014-01-01

We study space and time discretizations for mixed formulations of parabolic problems. The spatial approximation is based on the multipoint flux mixed finite element method, which reduces to an efficient cell-centered pressure system on general grids, including triangles, quadrilaterals, tetrahedra, and hexahedra. The time integration is performed by using a domain decomposition time-splitting technique combined with multiterm fractional step diagonally implicit Runge-Kutta methods. The resulting scheme is unconditionally stable and computationally efficient, as it reduces the global system to a collection of uncoupled subdomain problems that can be solved in parallel without the need for Schwarz-type iteration. Convergence analysis for both the semidiscrete and fully discrete schemes is presented.

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

There is an increasing interest to develop the next generation simulation tools for the advanced nuclear energy systems. These tools will utilize the state-of-art numerical algorithms and computer science technology in order to maximize the predictive capability, support advanced reactor designs, reduce uncertainty and increase safety margins. In analyzing nuclear energy systems, we are interested in compressible low-Mach number, high heat flux flows with a wide range of Re, Ra, and Pr numbers. Under these conditions, the focus is placed on turbulent heat transfer, in contrast to other industries whose main interest is in capturing turbulent mixing. Our objective ismore » to develop singlepoint turbulence closure models for large-scale engineering CFD code, using Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES) tools, requireing very accurate and efficient numerical algorithms. The focus of this work is placed on fully-implicit, high-order spatiotemporal discretization based on the discontinuous Galerkin method solving the conservative form of the compressible Navier-Stokes equations. The method utilizes a local reconstruction procedure derived from weak formulation of the problem, which is inspired by the recovery diffusion flux algorithm of van Leer and Nomura [?] and by the piecewise parabolic reconstruction [?] in the finite volume method. The developed methodology is integrated into the Jacobianfree Newton-Krylov framework [?] to allow a fully-implicit solution of the problem.« less

Algorithm development for Maxwell's equations for computational electromagnetism

NASA Technical Reports Server (NTRS)

Goorjian, Peter M.

1990-01-01

A new algorithm has been developed for solving Maxwell's equations for the electromagnetic field. It solves the equations in the time domain with central, finite differences. The time advancement is performed implicitly, using an alternating direction implicit procedure. The space discretization is performed with finite volumes, using curvilinear coordinates with electromagnetic components along those directions. Sample calculations are presented of scattering from a metal pin, a square and a circle to demonstrate the capabilities of the new algorithm.

Parallelization of implicit finite difference schemes in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Decker, Naomi H.; Naik, Vijay K.; Nicoules, Michel

1990-01-01

Implicit finite difference schemes are often the preferred numerical schemes in computational fluid dynamics, requiring less stringent stability bounds than the explicit schemes. Each iteration in an implicit scheme involves global data dependencies in the form of second and higher order recurrences. Efficient parallel implementations of such iterative methods are considerably more difficult and non-intuitive. The parallelization of the implicit schemes that are used for solving the Euler and the thin layer Navier-Stokes equations and that require inversions of large linear systems in the form of block tri-diagonal and/or block penta-diagonal matrices is discussed. Three-dimensional cases are emphasized and schemes that minimize the total execution time are presented. Partitioning and scheduling schemes for alleviating the effects of the global data dependencies are described. An analysis of the communication and the computation aspects of these methods is presented. The effect of the boundary conditions on the parallel schemes is also discussed.

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.

Random walk numerical simulation for hopping transport at finite carrier concentrations: diffusion coefficient and transport energy concept.

PubMed

Gonzalez-Vazquez, J P; Anta, Juan A; Bisquert, Juan

2009-11-28

The random walk numerical simulation (RWNS) method is used to compute diffusion coefficients for hopping transport in a fully disordered medium at finite carrier concentrations. We use Miller-Abrahams jumping rates and an exponential distribution of energies to compute the hopping times in the random walk simulation. The computed diffusion coefficient shows an exponential dependence with respect to Fermi-level and Arrhenius behavior with respect to temperature. This result indicates that there is a well-defined transport level implicit to the system dynamics. To establish the origin of this transport level we construct histograms to monitor the energies of the most visited sites. In addition, we construct "corrected" histograms where backward moves are removed. Since these moves do not contribute to transport, these histograms provide a better estimation of the effective transport level energy. The analysis of this concept in connection with the Fermi-level dependence of the diffusion coefficient and the regime of interest for the functioning of dye-sensitised solar cells is thoroughly discussed.

A conservative implicit finite difference algorithm for the unsteady transonic full potential equation

NASA Technical Reports Server (NTRS)

Steger, J. L.; Caradonna, F. X.

1980-01-01

An implicit finite difference procedure is developed to solve the unsteady full potential equation in conservation law form. Computational efficiency is maintained by use of approximate factorization techniques. The numerical algorithm is first order in time and second order in space. A circulation model and difference equations are developed for lifting airfoils in unsteady flow; however, thin airfoil body boundary conditions have been used with stretching functions to simplify the development of the numerical algorithm.

An unstructured-mesh finite-volume MPDATA for compressible atmospheric dynamics

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

Kühnlein, Christian, E-mail: christian.kuehnlein@ecmwf.int; Smolarkiewicz, Piotr K., E-mail: piotr.smolarkiewicz@ecmwf.int

An advancement of the unstructured-mesh finite-volume MPDATA (Multidimensional Positive Definite Advection Transport Algorithm) is presented that formulates the error-compensative pseudo-velocity of the scheme to rely only on face-normal advective fluxes to the dual cells, in contrast to the full vector employed in previous implementations. This is essentially achieved by expressing the temporal truncation error underlying the pseudo-velocity in a form consistent with the flux-divergence of the governing conservation law. The development is especially important for integrating fluid dynamics equations on non-rectilinear meshes whenever face-normal advective mass fluxes are employed for transport compatible with mass continuity—the latter being essential for flux-formmore » schemes. In particular, the proposed formulation enables large-time-step semi-implicit finite-volume integration of the compressible Euler equations using MPDATA on arbitrary hybrid computational meshes. Furthermore, it facilitates multiple error-compensative iterations of the finite-volume MPDATA and improved overall accuracy. The advancement combines straightforwardly with earlier developments, such as the nonoscillatory option, the infinite-gauge variant, and moving curvilinear meshes. A comprehensive description of the scheme is provided for a hybrid horizontally-unstructured vertically-structured computational mesh for efficient global atmospheric flow modelling. The proposed finite-volume MPDATA is verified using selected 3D global atmospheric benchmark simulations, representative of hydrostatic and non-hydrostatic flow regimes. Besides the added capabilities, the scheme retains fully the efficacy of established finite-volume MPDATA formulations.« less

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

Nonlinearly preconditioned semismooth Newton methods for variational inequality solution of two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Yang, Haijian; Sun, Shuyu; Yang, Chao

2017-03-01

Most existing methods for solving two-phase flow problems in porous media do not take the physically feasible saturation fractions between 0 and 1 into account, which often destroys the numerical accuracy and physical interpretability of the simulation. To calculate the solution without the loss of this basic requirement, we introduce a variational inequality formulation of the saturation equilibrium with a box inequality constraint, and use a conservative finite element method for the spatial discretization and a backward differentiation formula with adaptive time stepping for the temporal integration. The resulting variational inequality system at each time step is solved by using a semismooth Newton algorithm. To accelerate the Newton convergence and improve the robustness, we employ a family of adaptive nonlinear elimination methods as a nonlinear preconditioner. Some numerical results are presented to demonstrate the robustness and efficiency of the proposed algorithm. A comparison is also included to show the superiority of the proposed fully implicit approach over the classical IMplicit Pressure-Explicit Saturation (IMPES) method in terms of the time step size and the total execution time measured on a parallel computer.

Improving sub-grid scale accuracy of boundary features in regional finite-difference models

USGS Publications Warehouse

Panday, Sorab; Langevin, Christian D.

2012-01-01

As an alternative to grid refinement, the concept of a ghost node, which was developed for nested grid applications, has been extended towards improving sub-grid scale accuracy of flow to conduits, wells, rivers or other boundary features that interact with a finite-difference groundwater flow model. The formulation is presented for correcting the regular finite-difference groundwater flow equations for confined and unconfined cases, with or without Newton Raphson linearization of the nonlinearities, to include the Ghost Node Correction (GNC) for location displacement. The correction may be applied on the right-hand side vector for a symmetric finite-difference Picard implementation, or on the left-hand side matrix for an implicit but asymmetric implementation. The finite-difference matrix connectivity structure may be maintained for an implicit implementation by only selecting contributing nodes that are a part of the finite-difference connectivity. Proof of concept example problems are provided to demonstrate the improved accuracy that may be achieved through sub-grid scale corrections using the GNC schemes.

Fully implicit Particle-in-cell algorithms for multiscale plasma simulation

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

Chacon, Luis

The outline of the paper is as follows: Particle-in-cell (PIC) methods for fully ionized collisionless plasmas, explicit vs. implicit PIC, 1D ES implicit PIC (charge and energy conservation, moment-based acceleration), and generalization to Multi-D EM PIC: Vlasov-Darwin model (review and motivation for Darwin model, conservation properties (energy, charge, and canonical momenta), and numerical benchmarks). The author demonstrates a fully implicit, fully nonlinear, multidimensional PIC formulation that features exact local charge conservation (via a novel particle mover strategy), exact global energy conservation (no particle self-heating or self-cooling), adaptive particle orbit integrator to control errors in momentum conservation, and canonical momenta (EM-PICmore » only, reduced dimensionality). The approach is free of numerical instabilities: ω peΔt >> 1, and Δx >> λ D. It requires many fewer dofs (vs. explicit PIC) for comparable accuracy in challenging problems. Significant CPU gains (vs explicit PIC) have been demonstrated. The method has much potential for efficiency gains vs. explicit in long-time-scale applications. Moment-based acceleration is effective in minimizing N FE, leading to an optimal algorithm.« less

Coupled Thermo-Hydro-Mechanical Numerical Framework for Simulating Unconventional Formations

NASA Astrophysics Data System (ADS)

Garipov, T. T.; White, J. A.; Lapene, A.; Tchelepi, H.

2016-12-01

Unconventional deposits are found in all world oil provinces. Modeling these systems is challenging, however, due to complex thermo-hydro-mechanical processes that govern their behavior. As a motivating example, we consider in situ thermal processing of oil shale deposits. When oil shale is heated to sufficient temperatures, kerogen can be converted to oil and gas products over a relatively short timespan. This phase change dramatically impact both the mechanical and hydrologic properties of the rock, leading to strongly coupled THMC interactions. Here, we present a numerical framework for simulating tightly-coupled chemistry, geomechanics, and multiphase flow within a reservoir simulator (the AD-GPRS General Purpose Research Simulator). We model changes in constitutive behavior of the rock using a thermoplasticity model that accounts for microstructural evolution. The multi-component, multiphase flow and transport processes of both mass and heat are modeled at the macroscopic (e.g., Darcy) scale. The phase compositions and properties are described by a cubic equation of state; Arrhenius-type chemical reactions are used to represent kerogen conversion. The system of partial differential equations is discretized using a combination of finite-volumes and finite-elements, respectively, for the flow and mechanics problems. Fully implicit and sequentially implicit method are used to solve resulting nonlinear problem. The proposed framework is verified against available analytical and numerical benchmark cases. We demonstrate the efficiency, performance, and capabilities of the proposed simulation framework by analyzing near well deformation in an oil shale formation.

An advanced constitutive model in the sheet metal forming simulation: the Teodosiu microstructural model and the Cazacu Barlat yield criterion

NASA Astrophysics Data System (ADS)

Alves, J. L.; Oliveira, M. C.; Menezes, L. F.

2004-06-01

Two constitutive models used to describe the plastic behavior of sheet metals in the numerical simulation of sheet metal forming process are studied: a recently proposed advanced constitutive model based on the Teodosiu microstructural model and the Cazacu Barlat yield criterion is compared with a more classical one, based on the Swift law and the Hill 1948 yield criterion. These constitutive models are implemented into DD3IMP, a finite element home code specifically developed to simulate sheet metal forming processes, which generically is a 3-D elastoplastic finite element code with an updated Lagrangian formulation, following a fully implicit time integration scheme, large elastoplastic strains and rotations. Solid finite elements and parametric surfaces are used to model the blank sheet and tool surfaces, respectively. Some details of the numerical implementation of the constitutive models are given. Finally, the theory is illustrated with the numerical simulation of the deep drawing of a cylindrical cup. The results show that the proposed advanced constitutive model predicts with more exactness the final shape (medium height and ears profile) of the formed part, as one can conclude from the comparison with the experimental results.

THERMO-HYDRO-MECHANICAL MODELING OF WORKING FLUID INJECTION AND THERMAL ENERGY EXTRACTION IN EGS FRACTURES AND ROCK MATRIX

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

Robert Podgorney; Chuan Lu; Hai Huang

2012-01-01

Development of enhanced geothermal systems (EGS) will require creation of a reservoir of sufficient volume to enable commercial-scale heat transfer from the reservoir rocks to the working fluid. A key assumption associated with reservoir creation/stimulation is that sufficient rock volumes can be hydraulically fractured via both tensile and shear failure, and more importantly by reactivation of naturally existing fractures (by shearing), to create the reservoir. The advancement of EGS greatly depends on our understanding of the dynamics of the intimately coupled rock-fracture-fluid-heat system and our ability to reliably predict how reservoirs behave under stimulation and production. Reliable performance predictions ofmore » EGS reservoirs require accurate and robust modeling for strongly coupled thermal-hydrological-mechanical (THM) processes. Conventionally, these types of problems have been solved using operator-splitting methods, usually by coupling a subsurface flow and heat transport simulators with a solid mechanics simulator via input files. An alternative approach is to solve the system of nonlinear partial differential equations that govern multiphase fluid flow, heat transport, and rock mechanics simultaneously, using a fully coupled, fully implicit solution procedure, in which all solution variables (pressure, enthalpy, and rock displacement fields) are solved simultaneously. This paper describes numerical simulations used to investigate the poro- and thermal- elastic effects of working fluid injection and thermal energy extraction on the properties of the fractures and rock matrix of a hypothetical EGS reservoir, using a novel simulation software FALCON (Podgorney et al., 2011), a finite element based simulator solving fully coupled multiphase fluid flow, heat transport, rock deformation, and fracturing using a global implicit approach. Investigations are also conducted on how these poro- and thermal-elastic effects are related to fracture permeability evolution.« less

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST.

PubMed

Xu, X Q

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (psi,theta,micro) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

Neoclassical simulation of tokamak plasmas using the continuum gyrokinetic code TEMPEST

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2008-07-01

We present gyrokinetic neoclassical simulations of tokamak plasmas with a self-consistent electric field using a fully nonlinear (full- f ) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five-dimensional computational grid in phase space. The present implementation is a method of lines approach where the phase-space derivatives are discretized with finite differences, and implicit backward differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving the gyrokinetic Poisson equation with self-consistent poloidal variation. With a four-dimensional (ψ,θ,γ,μ) version of the TEMPEST code, we compute the radial particle and heat fluxes, the geodesic-acoustic mode, and the development of the neoclassical electric field, which we compare with neoclassical theory using a Lorentz collision model. The present work provides a numerical scheme for self-consistently studying important dynamical aspects of neoclassical transport and electric field in toroidal magnetic fusion devices.

An implicit spatial and high-order temporal finite difference scheme for 2D acoustic modelling

NASA Astrophysics Data System (ADS)

Wang, Enjiang; Liu, Yang

2018-01-01

The finite difference (FD) method exhibits great superiority over other numerical methods due to its easy implementation and small computational requirement. We propose an effective FD method, characterised by implicit spatial and high-order temporal schemes, to reduce both the temporal and spatial dispersions simultaneously. For the temporal derivative, apart from the conventional second-order FD approximation, a special rhombus FD scheme is included to reach high-order accuracy in time. Compared with the Lax-Wendroff FD scheme, this scheme can achieve nearly the same temporal accuracy but requires less floating-point operation times and thus less computational cost when the same operator length is adopted. For the spatial derivatives, we adopt the implicit FD scheme to improve the spatial accuracy. Apart from the existing Taylor series expansion-based FD coefficients, we derive the least square optimisation based implicit spatial FD coefficients. Dispersion analysis and modelling examples demonstrate that, our proposed method can effectively decrease both the temporal and spatial dispersions, thus can provide more accurate wavefields.

An implicit numerical model for multicomponent compressible two-phase flow in porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2015-11-01

We introduce a new implicit approach to model multicomponent compressible two-phase flow in porous media with species transfer between the phases. In the implicit discretization of the species transport equation in our formulation we calculate for the first time the derivative of the molar concentration of component i in phase α (cα, i) with respect to the total molar concentration (ci) under the conditions of a constant volume V and temperature T. The species transport equation is discretized by the finite volume (FV) method. The fluxes are calculated based on powerful features of the mixed finite element (MFE) method which provides the pressure at grid-cell interfaces in addition to the pressure at the grid-cell center. The efficiency of the proposed model is demonstrated by comparing our results with three existing implicit compositional models. Our algorithm has low numerical dispersion despite the fact it is based on first-order space discretization. The proposed algorithm is very robust.

Analyse et caracterisation d'interactions fluide-structure instationnaires en grands deplacements

NASA Astrophysics Data System (ADS)

Cori, Jean-Francois

Flapping wings for flying and oscillating fins for swimming stand out as the most complex yet efficient propulsion methods found in nature. Understanding the phenomena involved is a great challenge generating significant interests, especially in the growing field of Micro Air Vehicles. The thrust and lift are induced by oscillating foils thanks to a complex phenomenon of unsteady fluid-structure interaction (FSI). The aim of the dissertation is to develop an efficient CFD framework for simulating the FSI process involved in the propulsion or the power extraction of an oscillating flexible airfoil in a viscous incompressible flow. The numerical method relies on direct implicit monolithic formulation using high-order implicit time integrators. We use an Arbitrary Lagrangian Eulerian (ALE) formulation of the equations designed to satisfy the Geometric Conservation Law (GCL) and to guarantee that the high order temporal accuracy of the time integrators observed on fixed meshes is preserved on ALE deforming meshes. Hyperelastic structural Saint-Venant Kirchhoff model, viscous incompressible Navier-Stokes equations for the flow, Newton's law for the point mass and equilibrium equations at the interface form one large monolithic system. The fully implicit FSI approach uses coincidents nodes on the fluid-structure interface, so that loads, velocities and displacements are evaluated at the same location and at the same time. The problem is solved in an implicit manner using a Newton-Raphson pseudo-solid finite element approach. High-order implicit Runge-Kutta time integrators are implemented (up to 5th order) to improve the accuracy and reduce the computational cost. In this context of stiff interaction problems, the highly stable fully implicit one-step approach is an original alternative to traditional multistep or explicit one-step finite element approaches. The methodology has been verified with three different test-cases. Thorough time-step refinement studies for a rigid oscillating airfoil on deforming meshes, for flow induced vibrations of a flexible strip and for a self-propulsed flapping airfoil indicate that the stability of the proposed approach is always observed even with large time steps, spurious oscillations on the structure are avoided without any damping and the high order accuracy of the IRK schemes is maintained. We have applied our powerful FSI framework on three interesting applications, with a detailed dimensional analysis to obtain their characteristic parameters. Firstly, we have studied the vibrational characteristics of a well-documented fluid-structure interaction case : a flexible strip fixed behind a rigid square cylinder. Our results compare favorably with previous works. The accuracy of the IRK time integrators (even for the pressure field of incompressible flow), their unconditional stability and their non-dissipative nature produced results revealing new, never previously reported, higher frequency structural forces weakly coupled with the fluid. Secondly, we have explored the propulsive and power extraction characteristics of rigid and flexible flapping airfoils. For the power extraction, we found an excellent agreement with literature results. A parametric study indicates the optimal motion parameters to get high propulsive efficiencies. An optimal flexibility seems to improve power extraction efficiency. Finally, a survey on flapping propulsion has given initial results for a self-propulsed airfoil and has opened a new way of studying propulsive efficiency. (Abstract shortened by UMI.)

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.

Inexact adaptive Newton methods

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

Bertiger, W.I.; Kelsey, F.J.

1985-02-01

The Inexact Adaptive Newton method (IAN) is a modification of the Adaptive Implicit Method/sup 1/ (AIM) with improved Newton convergence. Both methods simplify the Jacobian at each time step by zeroing coefficients in regions where saturations are changing slowly. The methods differ in how the diagonal block terms are treated. On test problems with up to 3,000 cells, IAN consistently saves approximately 30% of the CPU time when compared to the fully implicit method. AIM shows similar savings on some problems, but takes as much CPU time as fully implicit on other test problems due to poor Newton convergence.

On the construction and application of implicit factored schemes for conservation laws. [in computational fluid dynamics

NASA Technical Reports Server (NTRS)

Warming, R. F.; Beam, R. M.

1978-01-01

Efficient, noniterative, implicit finite difference algorithms are systematically developed for nonlinear conservation laws including purely hyperbolic systems and mixed hyperbolic parabolic systems. Utilization of a rational fraction or Pade time differencing formulas, yields a direct and natural derivation of an implicit scheme in a delta form. Attention is given to advantages of the delta formation and to various properties of one- and two-dimensional algorithms.

Fully coupled approach to modeling shallow water flow, sediment transport, and bed evolution in rivers

NASA Astrophysics Data System (ADS)

Li, Shuangcai; Duffy, Christopher J.

2011-03-01

Our ability to predict complex environmental fluid flow and transport hinges on accurate and efficient simulations of multiple physical phenomenon operating simultaneously over a wide range of spatial and temporal scales, including overbank floods, coastal storm surge events, drying and wetting bed conditions, and simultaneous bed form evolution. This research implements a fully coupled strategy for solving shallow water hydrodynamics, sediment transport, and morphological bed evolution in rivers and floodplains (PIHM_Hydro) and applies the model to field and laboratory experiments that cover a wide range of spatial and temporal scales. The model uses a standard upwind finite volume method and Roe's approximate Riemann solver for unstructured grids. A multidimensional linear reconstruction and slope limiter are implemented, achieving second-order spatial accuracy. Model efficiency and stability are treated using an explicit-implicit method for temporal discretization with operator splitting. Laboratory-and field-scale experiments were compiled where coupled processes across a range of scales were observed and where higher-order spatial and temporal accuracy might be needed for accurate and efficient solutions. These experiments demonstrate the ability of the fully coupled strategy in capturing dynamics of field-scale flood waves and small-scale drying-wetting processes.

Beyond Euler's Method: Implicit Finite Differences in an Introductory ODE Course

ERIC Educational Resources Information Center

Kull, Trent C.

2011-01-01

A typical introductory course in ordinary differential equations (ODEs) exposes students to exact solution methods. However, many differential equations must be approximated with numerical methods. Textbooks commonly include explicit methods such as Euler's and Improved Euler's. Implicit methods are typically introduced in more advanced courses…

A diagonal implicit scheme for computing flows with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Eberhardt, Scott; Imlay, Scott

1990-01-01

A new algorithm for solving steady, finite-rate chemistry, flow problems is presented. The new scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The source Jacobian matrix is replaced by a diagonal matrix which is tailored to account for the fastest reactions in the chemical system. A point-implicit procedure is discussed and then the algorithm is included into the LU-SGS scheme. Solutions are presented for hypervelocity reentry and Hydrogen-Oxygen combustion. For the LU-SGS scheme a CFL number in excess of 10,000 has been achieved.

Hybrid Upwinding for Two-Phase Flow in Heterogeneous Porous Media with Buoyancy and Capillarity

NASA Astrophysics Data System (ADS)

Hamon, F. P.; Mallison, B.; Tchelepi, H.

2016-12-01

In subsurface flow simulation, efficient discretization schemes for the partial differential equations governing multiphase flow and transport are critical. For highly heterogeneous porous media, the temporal discretization of choice is often the unconditionally stable fully implicit (backward-Euler) method. In this scheme, the simultaneous update of all the degrees of freedom requires solving large algebraic nonlinear systems at each time step using Newton's method. This is computationally expensive, especially in the presence of strong capillary effects driven by abrupt changes in porosity and permeability between different rock types. Therefore, discretization schemes that reduce the simulation cost by improving the nonlinear convergence rate are highly desirable. To speed up nonlinear convergence, we present an efficient fully implicit finite-volume scheme for immiscible two-phase flow in the presence of strong capillary forces. In this scheme, the discrete viscous, buoyancy, and capillary spatial terms are evaluated separately based on physical considerations. We build on previous work on Implicit Hybrid Upwinding (IHU) by using the upstream saturations with respect to the total velocity to compute the relative permeabilities in the viscous term, and by determining the directionality of the buoyancy term based on the phase density differences. The capillary numerical flux is decomposed into a rock- and geometry-dependent transmissibility factor, a nonlinear capillary diffusion coefficient, and an approximation of the saturation gradient. Combining the viscous, buoyancy, and capillary terms, we obtain a numerical flux that is consistent, bounded, differentiable, and monotone for homogeneous one-dimensional flow. The proposed scheme also accounts for spatially discontinuous capillary pressure functions. Specifically, at the interface between two rock types, the numerical scheme accurately honors the entry pressure condition by solving a local nonlinear problem to compute the numerical flux. Heterogeneous numerical tests demonstrate that this extended IHU scheme is non-oscillatory and convergent upon refinement. They also illustrate the superior accuracy and nonlinear convergence rate of the IHU scheme compared with the standard phase-based upstream weighting approach.

Multi-dimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations in curvilinear geometry

NASA Astrophysics Data System (ADS)

Chen, Guangye; Chacon, Luis

2015-11-01

We discuss a new, conservative, fully implicit 2D3V Vlasov-Darwin particle-in-cell algorithm in curvilinear geometry for non-radiative, electromagnetic kinetic plasma simulations. Unlike standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. Here, we extend these algorithms to curvilinear geometry. The algorithm retains its exact conservation properties in curvilinear grids. The nonlinear iteration is effectively accelerated with a fluid preconditioner for weakly to modestly magnetized plasmas, which allows efficient use of large timesteps, O (√{mi/me}c/veT) larger than the explicit CFL. In this presentation, we will introduce the main algorithmic components of the approach, and demonstrate the accuracy and efficiency properties of the algorithm with various numerical experiments in 1D (slow shock) and 2D (island coalescense).

An interactive adaptive remeshing algorithm for the two-dimensional Euler equations

NASA Technical Reports Server (NTRS)

Slack, David C.; Walters, Robert W.; Lohner, R.

1990-01-01

An interactive adaptive remeshing algorithm utilizing a frontal grid generator and a variety of time integration schemes for the two-dimensional Euler equations on unstructured meshes is presented. Several device dependent interactive graphics interfaces have been developed along with a device independent DI-3000 interface which can be employed on any computer that has the supporting software including the Cray-2 supercomputers Voyager and Navier. The time integration methods available include: an explicit four stage Runge-Kutta and a fully implicit LU decomposition. A cell-centered finite volume upwind scheme utilizing Roe's approximate Riemann solver is developed. To obtain higher order accurate results a monotone linear reconstruction procedure proposed by Barth is utilized. Results for flow over a transonic circular arc and flow through a supersonic nozzle are examined.

Assessment of a 3-D boundary layer code to predict heat transfer and flow losses in a turbine

NASA Technical Reports Server (NTRS)

Anderson, O. L.

1984-01-01

Zonal concepts are utilized to delineate regions of application of three-dimensional boundary layer (DBL) theory. The zonal approach requires three distinct analyses. A modified version of the 3-DBL code named TABLET is used to analyze the boundary layer flow. This modified code solves the finite difference form of the compressible 3-DBL equations in a nonorthogonal surface coordinate system which includes coriolis forces produced by coordinate rotation. These equations are solved using an efficient, implicit, fully coupled finite difference procedure. The nonorthogonal surface coordinate system is calculated using a general analysis based on the transfinite mapping of Gordon which is valid for any arbitrary surface. Experimental data is used to determine the boundary layer edge conditions. The boundary layer edge conditions are determined by integrating the boundary layer edge equations, which are the Euler equations at the edge of the boundary layer, using the known experimental wall pressure distribution. Starting solutions along the inflow boundaries are estimated by solving the appropriate limiting form of the 3-DBL equations.

Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

NASA Astrophysics Data System (ADS)

Litaker, Eric T.

1994-12-01

The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

Application of the implicit MacCormack scheme to the PNS equations

NASA Technical Reports Server (NTRS)

Lawrence, S. L.; Tannehill, J. C.; Chaussee, D. S.

1983-01-01

The two-dimensional parabolized Navier-Stokes equations are solved using MacCormack's (1981) implicit finite-difference scheme. It is shown that this method for solving the parabolized Navier-Stokes equations does not require the inversion of block tridiagonal systems of algebraic equations and allows the original explicit scheme to be employed in those regions where implicit treatment is not needed. The finite-difference algorithm is discussed and the computational results for two laminar test cases are presented. Results obtained using this method for the case of a flat plate boundary layer are compared with those obtained using the conventional Beam-Warming scheme, as well as those obtained from a boundary layer code. The computed results for a more severe test of the method, the hypersonic flow past a 15 deg compression corner, are found to compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.

A gradient enhanced plasticity-damage microplane model for concrete

NASA Astrophysics Data System (ADS)

Zreid, Imadeddin; Kaliske, Michael

2018-03-01

Computational modeling of concrete poses two main types of challenges. The first is the mathematical description of local response for such a heterogeneous material under all stress states, and the second is the stability and efficiency of the numerical implementation in finite element codes. The paper at hand presents a comprehensive approach addressing both issues. Adopting the microplane theory, a combined plasticity-damage model is formulated and regularized by an implicit gradient enhancement. The plasticity part introduces a new microplane smooth 3-surface cap yield function, which provides a stable numerical solution within an implicit finite element algorithm. The damage part utilizes a split, which can describe the transition of loading between tension and compression. Regularization of the model by the implicit gradient approach eliminates the mesh sensitivity and numerical instabilities. Identification methods for model parameters are proposed and several numerical examples of plain and reinforced concrete are carried out for illustration.

Computational plasticity algorithm for particle dynamics simulations

NASA Astrophysics Data System (ADS)

Krabbenhoft, K.; Lyamin, A. V.; Vignes, C.

2018-01-01

The problem of particle dynamics simulation is interpreted in the framework of computational plasticity leading to an algorithm which is mathematically indistinguishable from the common implicit scheme widely used in the finite element analysis of elastoplastic boundary value problems. This algorithm provides somewhat of a unification of two particle methods, the discrete element method and the contact dynamics method, which usually are thought of as being quite disparate. In particular, it is shown that the former appears as the special case where the time stepping is explicit while the use of implicit time stepping leads to the kind of schemes usually labelled contact dynamics methods. The framing of particle dynamics simulation within computational plasticity paves the way for new approaches similar (or identical) to those frequently employed in nonlinear finite element analysis. These include mixed implicit-explicit time stepping, dynamic relaxation and domain decomposition schemes.

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.

Solving phase appearance/disappearance two-phase flow problems with high resolution staggered grid and fully implicit schemes by the Jacobian-free Newton–Krylov Method

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

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-04-01

The phase appearance/disappearance issue presents serious numerical challenges in two-phase flow simulations. Many existing reactor safety analysis codes use different kinds of treatments for the phase appearance/disappearance problem. However, to our best knowledge, there are no fully satisfactory solutions. Additionally, the majority of the existing reactor system analysis codes were developed using low-order numerical schemes in both space and time. In many situations, it is desirable to use high-resolution spatial discretization and fully implicit time integration schemes to reduce numerical errors. In this work, we adapted a high-resolution spatial discretization scheme on staggered grid mesh and fully implicit time integrationmore » methods (such as BDF1 and BDF2) to solve the two-phase flow problems. The discretized nonlinear system was solved by the Jacobian-free Newton Krylov (JFNK) method, which does not require the derivation and implementation of analytical Jacobian matrix. These methods were tested with a few two-phase flow problems with phase appearance/disappearance phenomena considered, such as a linear advection problem, an oscillating manometer problem, and a sedimentation problem. The JFNK method demonstrated extremely robust and stable behaviors in solving the two-phase flow problems with phase appearance/disappearance. No special treatments such as water level tracking or void fraction limiting were used. High-resolution spatial discretization and second- order fully implicit method also demonstrated their capabilities in significantly reducing numerical errors.« less

Parallel Implementation of a High Order Implicit Collocation Method for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Halem, Milton (Technical Monitor)

2000-01-01

We combine a high order compact finite difference approximation and collocation techniques to numerically solve the two dimensional heat equation. The resulting method is implicit arid can be parallelized with a strategy that allows parallelization across both time and space. We compare the parallel implementation of the new method with a classical implicit method, namely the Crank-Nicolson method, where the parallelization is done across space only. Numerical experiments are carried out on the SGI Origin 2000.

Numerical study of shock-wave/boundary layer interactions in premixed hydrogen-air hypersonic flows

NASA Technical Reports Server (NTRS)

Yungster, Shaye

1991-01-01

A computational study of shock wave/boundary layer interactions involving premixed combustible gases, and the resulting combustion processes is presented. The analysis is carried out using a new fully implicit, total variation diminishing (TVD) code developed for solving the fully coupled Reynolds-averaged Navier-Stokes equations and species continuity equations in an efficient manner. To accelerate the convergence of the basic iterative procedure, this code is combined with vector extrapolation methods. The chemical nonequilibrium processes are simulated by means of a finite-rate chemistry model for hydrogen-air combustion. Several validation test cases are presented and the results compared with experimental data or with other computational results. The code is then applied to study shock wave/boundary layer interactions in a ram accelerator configuration. Results indicate a new combustion mechanism in which a shock wave induces combustion in the boundary layer, which then propagates outwards and downstream. At higher Mach numbers, spontaneous ignition in part of the boundary layer is observed, which eventually extends along the entire boundary layer at still higher values of the Mach number.

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

NASA Astrophysics Data System (ADS)

Xing, F.; Masson, R.; Lopez, S.

2017-09-01

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non-immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is discretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence.

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.

Neoclassical Simulation of Tokamak Plasmas using Continuum Gyrokinetc Code TEMPEST

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

Xu, X Q

We present gyrokinetic neoclassical simulations of tokamak plasmas with self-consistent electric field for the first time using a fully nonlinear (full-f) continuum code TEMPEST in a circular geometry. A set of gyrokinetic equations are discretized on a five dimensional computational grid in phase space. The present implementation is a Method of Lines approach where the phase-space derivatives are discretized with finite differences and implicit backwards differencing formulas are used to advance the system in time. The fully nonlinear Boltzmann model is used for electrons. The neoclassical electric field is obtained by solving gyrokinetic Poisson equation with self-consistent poloidal variation. Withmore » our 4D ({psi}, {theta}, {epsilon}, {mu}) version of the TEMPEST code we compute radial particle and heat flux, the Geodesic-Acoustic Mode (GAM), and the development of neoclassical electric field, which we compare with neoclassical theory with a Lorentz collision model. The present work provides a numerical scheme and a new capability for self-consistently studying important aspects of neoclassical transport and rotations in toroidal magnetic fusion devices.« less

Numerical study of shock-wave/boundary layer interactions in premixed hydrogen-air hypersonic flows

NASA Technical Reports Server (NTRS)

Yungster, Shaye

1990-01-01

A computational study of shock wave/boundary layer interactions involving premixed combustible gases, and the resulting combustion processes is presented. The analysis is carried out using a new fully implicit, total variation diminishing (TVD) code developed for solving the fully coupled Reynolds-averaged Navier-Stokes equations and species continuity equations in an efficient manner. To accelerate the convergence of the basic iterative procedure, this code is combined with vector extrapolation methods. The chemical nonequilibrium processes are simulated by means of a finite-rate chemistry model for hydrogen-air combustion. Several validation test cases are presented and the results compared with experimental data or with other computational results. The code is then applied to study shock wave/boundary layer interactions in a ram accelerator configuration. Results indicate a new combustion mechanism in which a shock wave induces combustion in the boundary layer, which then propagates outwards and downstream. At higher Mach numbers, spontaneous ignition in part of the boundary layer is observed, which eventually extends along the entire boundary layer at still higher values of the Mach number.

Efficiency Study of Implicit and Explicit Time Integration Operators for Finite Element Applications

DTIC Science & Technology

1977-07-01

cffiAciency, wherein Beta =0 provides anl exp~licit algorithm, wvhile Beta &0 provides anl implicit algorithm. Both algorithmns arc used in the same...Hlueneme CA: CO, Code C44A Port j IHuenemne, CA NAVSEC Cod,. 6034 (Library), Washington DC NAVSI*CGRUAC’I’ PWO, ’rorri Sta, OkinawaI NAVSIIIPRBFTAC Library

Fully implicit moving mesh adaptive algorithm

NASA Astrophysics Data System (ADS)

Serazio, C.; Chacon, L.; Lapenta, G.

2006-10-01

In many problems of interest, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former is best dealt with with fully implicit methods, which are able to step over fast frequencies to resolve the dynamical time scale of interest. The latter requires grid adaptivity for efficiency. Moving-mesh grid adaptive methods are attractive because they can be designed to minimize the numerical error for a given resolution. However, the required grid governing equations are typically very nonlinear and stiff, and of considerably difficult numerical treatment. Not surprisingly, fully coupled, implicit approaches where the grid and the physics equations are solved simultaneously are rare in the literature, and circumscribed to 1D geometries. In this study, we present a fully implicit algorithm for moving mesh methods that is feasible for multidimensional geometries. Crucial elements are the development of an effective multilevel treatment of the grid equation, and a robust, rigorous error estimator. For the latter, we explore the effectiveness of a coarse grid correction error estimator, which faithfully reproduces spatial truncation errors for conservative equations. We will show that the moving mesh approach is competitive vs. uniform grids both in accuracy (due to adaptivity) and efficiency. Results for a variety of models 1D and 2D geometries will be presented. L. Chac'on, G. Lapenta, J. Comput. Phys., 212 (2), 703 (2006) G. Lapenta, L. Chac'on, J. Comput. Phys., accepted (2006)

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.

Recent applications of the transonic wing analysis computer code, TWING

NASA Technical Reports Server (NTRS)

Subramanian, N. R.; Holst, T. L.; Thomas, S. D.

1982-01-01

An evaluation of the transonic-wing-analysis computer code TWING is given. TWING utilizes a fully implicit approximate factorization iteration scheme to solve the full potential equation in conservative form. A numerical elliptic-solver grid-generation scheme is used to generate the required finite-difference mesh. Several wing configurations were analyzed, and the limits of applicability of this code was evaluated. Comparisons of computed results were made with available experimental data. Results indicate that the code is robust, accurate (when significant viscous effects are not present), and efficient. TWING generally produces solutions an order of magnitude faster than other conservative full potential codes using successive-line overrelaxation. The present method is applicable to a wide range of isolated wing configurations including high-aspect-ratio transport wings and low-aspect-ratio, high-sweep, fighter configurations.

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.

A computer program for two-dimensional and axisymmetric nonreacting perfect gas and equilibrium chemically reacting laminar, transitional and-or turbulent boundary layer flows

NASA Technical Reports Server (NTRS)

Miner, E. W.; Anderson, E. C.; Lewis, C. H.

1971-01-01

A computer program is described in detail for laminar, transitional, and/or turbulent boundary-layer flows of non-reacting (perfect gas) and reacting gas mixtures in chemical equilibrium. An implicit finite difference scheme was developed for both two dimensional and axisymmetric flows over bodies, and in rocket nozzles and hypervelocity wind tunnel nozzles. The program, program subroutines, variables, and input and output data are described. Also included is the output from a sample calculation of fully developed turbulent, perfect gas flow over a flat plate. Input data coding forms and a FORTRAN source listing of the program are included. A method is discussed for obtaining thermodynamic and transport property data which are required to perform boundary-layer calculations for reacting gases in chemical equilibrium.

External heat transfer predictions in a highly loaded transonic linear turbine guide vane cascade using an upwind biased Navier-Stokes solver

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

Gehrer, A.; Jericha, H.

External heat transfer predictions are performed for two-dimensional turbine blade cascades. The Reynolds-averaged Navier-Stokes equations with algebraic (Arnone and Pacciani, 1998), one-equation (Spalart and Allmaras, 1994), and two-equation (low-Re {kappa}-{epsilon}, Biswas and Fukuyama, 1994) turbulence closures are solved with a fully implicit time-marching finite volume method. Comparisons with measurements (Arts et al., 1990; Arts, 1994) for a highly loaded transonic turbine nozzle guide vane cascade show good agreement in some cases, but also reveal problems with transition prediction and turbulence modeling. Special attention has been focused on the low-Re {kappa}-{epsilon} model concerning the influence of the inlet boundary condition formore » the {epsilon}-equation and problems in the stagnation point region.« less

Coupled Hydro-Mechanical Modeling of Fluid Geological Storage

NASA Astrophysics Data System (ADS)

Castelletto, N.; Garipov, T.; Tchelepi, H. A.

2013-12-01

The accurate modeling of the complex coupled physical processes occurring during the injection and the post-injection period is a key factor for assessing the safety and the feasibility of anthropogenic carbon dioxide (CO2) sequestration in subsurface formations. In recent years, it has become widely accepted the importance of the coupling between fluid flow and geomechanical response in constraining the sustainable pressure buildup caused by fluid injection relative to the caprock sealing capacity, induced seismicity effects and ground surface stability [e.g., Rutqvist, 2012; Castelletto et al., 2013]. Here, we present a modeling approach based on a suitable combination of Finite Volumes (FVs) and Finite Elements (FEs) to solve the coupled system of partial differential equations governing the multiphase flow in a deformable porous medium. Specifically, a FV method is used for the flow problem while the FE method is adopted to address the poro-elasto-plasticity equations. The aim of the present work is to compare the performance and the robustness of unconditionally stable sequential-implicit schemes [Kim et al., 2011] and the fully-implicit method in solving the algebraic systems arising from the discretization of the governing equations, for both normally conditioned and severely ill-conditioned problems. The two approaches are tested against well-known analytical solutions and experimented with in a realistic application of CO2 injection in a synthetic aquifer. References: - Castelletto N., G. Gambolati, and P. Teatini (2013), Geological CO2 sequestration in multi-compartment reservoirs: Geomechanical challenges, J. Geophys. Res. Solid Earth, 118, 2417-2428, doi:10.1002/jgrb.50180. - Kim J., H. A. Tchelepi, and R. Juanes (2011), Stability, accuracy and efficiency of sequential methods for coupled flow and geomechanics, SPE J., 16(2), 249-262. - Rutqvist J. (2012), The geomechanics of CO2 storage in deep sedimentary formations, Geotech. Geol. Eng., 30, 525-551.

Finite Volume Method for Pricing European Call Option with Regime-switching Volatility

NASA Astrophysics Data System (ADS)

Lista Tauryawati, Mey; Imron, Chairul; Putri, Endah RM

2018-03-01

In this paper, we present a finite volume method for pricing European call option using Black-Scholes equation with regime-switching volatility. In the first step, we formulate the Black-Scholes equations with regime-switching volatility. we use a finite volume method based on fitted finite volume with spatial discretization and an implicit time stepping technique for the case. We show that the regime-switching scheme can revert to the non-switching Black Scholes equation, both in theoretical evidence and numerical simulations.

Noniterative implicit method for tracking particles in mixed Lagrangian-Eulerian formulations

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Dasgupta, A.

1993-01-01

The existing implicit methods for the current initial value problems (IVPs) concerning particle-laden flows are complicated and iterative in nature. This paper presents a noniterative implicit method which can be used with pressure-based as well as with density-based algorithms. The method is illustrated by analyzing a dilute dispersion of noninteracting solid particles in an isothermal flow in a passage bounded by one straight wall and one wavy wall, in which all particles are spherical and have a finite velociy relative to the continuum phase at the inflow boundary.

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

BIGHORN Computational Fluid Dynamics Theory, Methodology, and Code Verification & Validation Benchmark Problems

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

Xia, Yidong; Andrs, David; Martineau, Richard Charles

This document presents the theoretical background for a hybrid finite-element / finite-volume fluid flow solver, namely BIGHORN, based on the Multiphysics Object Oriented Simulation Environment (MOOSE) computational framework developed at the Idaho National Laboratory (INL). An overview of the numerical methods used in BIGHORN are discussed and followed by a presentation of the formulation details. The document begins with the governing equations for the compressible fluid flow, with an outline of the requisite constitutive relations. A second-order finite volume method used for solving the compressible fluid flow problems is presented next. A Pressure-Corrected Implicit Continuous-fluid Eulerian (PCICE) formulation for timemore » integration is also presented. The multi-fluid formulation is being developed. Although multi-fluid is not fully-developed, BIGHORN has been designed to handle multi-fluid problems. Due to the flexibility in the underlying MOOSE framework, BIGHORN is quite extensible, and can accommodate both multi-species and multi-phase formulations. This document also presents a suite of verification & validation benchmark test problems for BIGHORN. The intent for this suite of problems is to provide baseline comparison data that demonstrates the performance of the BIGHORN solution methods on problems that vary in complexity from laminar to turbulent flows. Wherever possible, some form of solution verification has been attempted to identify sensitivities in the solution methods, and suggest best practices when using BIGHORN.« less

Transient modeling/analysis of hyperbolic heat conduction problems employing mixed implicit-explicit alpha method

NASA Technical Reports Server (NTRS)

Tamma, Kumar K.; D'Costa, Joseph F.

1991-01-01

This paper describes the evaluation of mixed implicit-explicit finite element formulations for hyperbolic heat conduction problems involving non-Fourier effects. In particular, mixed implicit-explicit formulations employing the alpha method proposed by Hughes et al. (1987, 1990) are described for the numerical simulation of hyperbolic heat conduction models, which involves time-dependent relaxation effects. Existing analytical approaches for modeling/analysis of such models involve complex mathematical formulations for obtaining closed-form solutions, while in certain numerical formulations the difficulties include severe oscillatory solution behavior (which often disguises the true response) in the vicinity of the thermal disturbances, which propagate with finite velocities. In view of these factors, the alpha method is evaluated to assess the control of the amount of numerical dissipation for predicting the transient propagating thermal disturbances. Numerical test models are presented, and pertinent conclusions are drawn for the mixed-time integration simulation of hyperbolic heat conduction models involving non-Fourier effects.

Numerical Simulation of a Solar Domestic Hot Water System

NASA Astrophysics Data System (ADS)

Mongibello, L.; Bianco, N.; Di Somma, M.; Graditi, G.; Naso, V.

2014-11-01

An innovative transient numerical model is presented for the simulation of a solar Domestic Hot Water (DHW) system. The solar collectors have been simulated by using a zerodimensional analytical model. The temperature distributions in the heat transfer fluid and in the water inside the tank have been evaluated by one-dimensional models. The reversion elimination algorithm has been used to include the effects of natural convection among the water layers at different heights in the tank on the thermal stratification. A finite difference implicit scheme has been implemented to solve the energy conservation equation in the coil heat exchanger, and the energy conservation equation in the tank has been solved by using the finite difference Euler implicit scheme. Energy conservation equations for the solar DHW components models have been coupled by means of a home-made implicit algorithm. Results of the simulation performed using as input data the experimental values of the ambient temperature and the solar irradiance in a summer day are presented and discussed.

Nonlinear three-dimensional verification of the SPECYL and PIXIE3D magnetohydrodynamics codes for fusion plasmas

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Chacón, L.; Cappello, S.

2010-08-01

With the increasing impact of scientific discovery via advanced computation, there is presently a strong emphasis on ensuring the mathematical correctness of computational simulation tools. Such endeavor, termed verification, is now at the center of most serious code development efforts. In this study, we address a cross-benchmark nonlinear verification study between two three-dimensional magnetohydrodynamics (3D MHD) codes for fluid modeling of fusion plasmas, SPECYL [S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996)] and PIXIE3D [L. Chacón, Phys. Plasmas 15, 056103 (2008)], in their common limit of application: the simple viscoresistive cylindrical approximation. SPECYL is a serial code in cylindrical geometry that features a spectral formulation in space and a semi-implicit temporal advance, and has been used extensively to date for reversed-field pinch studies. PIXIE3D is a massively parallel code in arbitrary curvilinear geometry that features a conservative, solenoidal finite-volume discretization in space, and a fully implicit temporal advance. The present study is, in our view, a first mandatory step in assessing the potential of any numerical 3D MHD code for fluid modeling of fusion plasmas. Excellent agreement is demonstrated over a wide range of parameters for several fusion-relevant cases in both two- and three-dimensional geometries.

Nonlinear three-dimensional verification of the SPECYL and PIXIE3D magnetohydrodynamics codes for fusion plasmas

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

Bonfiglio, Daniele; Chacon, Luis; Cappello, Susanna

2010-01-01

With the increasing impact of scientific discovery via advanced computation, there is presently a strong emphasis on ensuring the mathematical correctness of computational simulation tools. Such endeavor, termed verification, is now at the center of most serious code development efforts. In this study, we address a cross-benchmark nonlinear verification study between two three-dimensional magnetohydrodynamics (3D MHD) codes for fluid modeling of fusion plasmas, SPECYL [S. Cappello and D. Biskamp, Nucl. Fusion 36, 571 (1996)] and PIXIE3D [L. Chacon, Phys. Plasmas 15, 056103 (2008)], in their common limit of application: the simple viscoresistive cylindrical approximation. SPECYL is a serial code inmore » cylindrical geometry that features a spectral formulation in space and a semi-implicit temporal advance, and has been used extensively to date for reversed-field pinch studies. PIXIE3D is a massively parallel code in arbitrary curvilinear geometry that features a conservative, solenoidal finite-volume discretization in space, and a fully implicit temporal advance. The present study is, in our view, a first mandatory step in assessing the potential of any numerical 3D MHD code for fluid modeling of fusion plasmas. Excellent agreement is demonstrated over a wide range of parameters for several fusion-relevant cases in both two- and three-dimensional geometries.« less

SUPG Finite Element Simulations of Compressible Flows for Aerothermodynamic Applications

NASA Technical Reports Server (NTRS)

Kirk, Benjamin S.

2007-01-01

This viewgraph presentation reviews the Streamline-Upwind Petrov-Galerkin (SUPG) Finite Element Simulation. It covers the background, governing equations, weak formulation, shock capturing, inviscid flux discretization, time discretization, linearization, and implicit solution strategies. It also reviews some applications such as Type IV Shock Interaction, Forward-Facing Cavity and AEDC Sharp Double Cone.

Development Of A Navier-Stokes Computer Code

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Kwak, Dochan

1993-01-01

Report discusses aspects of development of CENS3D computer code, solving three-dimensional Navier-Stokes equations of compressible, viscous, unsteady flow. Implements implicit finite-difference or finite-volume numerical-integration scheme, called "lower-upper symmetric-Gauss-Seidel" (LU-SGS), offering potential for very low computer time per iteration and for fast convergence.

Implicit Theories of Intelligence and Personality, Self-Efficacy in Problem Solving, and the Perception of Skills and Competences in High School Students in Sicily, Italy

ERIC Educational Resources Information Center

Pirrone, Concetta; Commodari, Elena

2013-01-01

Various theories of intelligence and personality (TIP) help explain the implicit beliefs that an individual develops about the functioning of his intelligence and personality. Such beliefs are defined "implicit" because the individual might not be fully aware of his or her belief system. The results from scientific research on the TIP…

Application of viscous-inviscid interaction methods to transonic turbulent flows

NASA Technical Reports Server (NTRS)

Lee, D.; Pletcher, R. H.

1986-01-01

Two different viscous-inviscid interaction schemes were developed for the analysis of steady, turbulent, transonic, separated flows over axisymmetric bodies. The viscous and inviscid solutions are coupled through the displacement concept using a transpiration velocity approach. In the semi-inverse interaction scheme, the viscous and inviscid equations are solved in an explicitly separate manner and the displacement thickness distribution is iteratively updated by a simple coupling algorithm. In the simultaneous interaction method, local solutions of viscous and inviscid equations are treated simultaneously, and the displacement thickness is treated as an unknown and is obtained as a part of the solution through a global iteration procedure. The inviscid flow region is described by a direct finite-difference solution of a velocity potential equation in conservative form. The potential equation is solved on a numerically generated mesh by an approximate factorization (AF2) scheme in the semi-inverse interaction method and by a successive line overrelaxation (SLOR) scheme in the simultaneous interaction method. The boundary-layer equations are used for the viscous flow region. The continuity and momentum equations are solved inversely in a coupled manner using a fully implicit finite-difference scheme.

Effects of Nonequilibrium Chemistry and Darcy-Forchheimer Pyrolysis Flow for Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2013-01-01

The fully implicit ablation and thermal response code simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid.This work describes new modeling capabilities that are added to a special version of code. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Two groups of parametric studies of the phenolic impregnated carbon ablator are performed. In the first group, an Orion flight environment for a proposed lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results indicate that the presence of chemical nonequilibrium pyrolysis gas flow does not significantly alter the in-depth thermal response performance predicted using the chemical equilibrium gas model.

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

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

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Fully implicit adaptive mesh refinement MHD algorithm

NASA Astrophysics Data System (ADS)

Philip, Bobby

2005-10-01

In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. The former results in stiffness due to the presence of very fast waves. The latter requires one to resolve the localized features that the system develops. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. To our knowledge, a scalable, fully implicit AMR algorithm has not been accomplished before for MHD. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technologyootnotetextL. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite --FAC-- algorithms) for scalability. We will demonstrate that the concept is indeed feasible, featuring optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations will be presented on a variety of problems.

Engine dynamic analysis with general nonlinear finite element codes. Part 2: Bearing element implementation overall numerical characteristics and benchmaking

NASA Technical Reports Server (NTRS)

Padovan, J.; Adams, M.; Fertis, J.; Zeid, I.; Lam, P.

1982-01-01

Finite element codes are used in modelling rotor-bearing-stator structure common to the turbine industry. Engine dynamic simulation is used by developing strategies which enable the use of available finite element codes. benchmarking the elements developed are benchmarked by incorporation into a general purpose code (ADINA); the numerical characteristics of finite element type rotor-bearing-stator simulations are evaluated through the use of various types of explicit/implicit numerical integration operators. Improving the overall numerical efficiency of the procedure is improved.

On improving the iterative convergence properties of an implicit approximate-factorization finite difference algorithm. [considering transonic flow

NASA Technical Reports Server (NTRS)

Desideri, J. A.; Steger, J. L.; Tannehill, J. C.

1978-01-01

The iterative convergence properties of an approximate-factorization implicit finite-difference algorithm are analyzed both theoretically and numerically. Modifications to the base algorithm were made to remove the inconsistency in the original implementation of artificial dissipation. In this way, the steady-state solution became independent of the time-step, and much larger time-steps can be used stably. To accelerate the iterative convergence, large time-steps and a cyclic sequence of time-steps were used. For a model transonic flow problem governed by the Euler equations, convergence was achieved with 10 times fewer time-steps using the modified differencing scheme. A particular form of instability due to variable coefficients is also analyzed.

Formulation of the relativistic moment implicit particle-in-cell method

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

Noguchi, Koichi; Tronci, Cesare; Zuccaro, Gianluca

2007-04-15

A new formulation is presented for the implicit moment method applied to the time-dependent relativistic Vlasov-Maxwell system. The new approach is based on a specific formulation of the implicit moment method that allows us to retain the same formalism that is valid in the classical case despite the formidable complication introduced by the nonlinear nature of the relativistic equations of motion. To demonstrate the validity of the new formulation, an implicit finite difference algorithm is developed to solve the Maxwell's equations and equations of motion. A number of benchmark problems are run: two stream instability, ion acoustic wave damping, Weibelmore » instability, and Poynting flux acceleration. The numerical results are all in agreement with analytical solutions.« less

Implicit Plasma Kinetic Simulation Using The Jacobian-Free Newton-Krylov Method

NASA Astrophysics Data System (ADS)

Taitano, William; Knoll, Dana; Chacon, Luis

2009-11-01

The use of fully implicit time integration methods in kinetic simulation is still area of algorithmic research. A brute-force approach to simultaneously including the field equations and the particle distribution function would result in an intractable linear algebra problem. A number of algorithms have been put forward which rely on an extrapolation in time. They can be thought of as linearly implicit methods or one-step Newton methods. However, issues related to time accuracy of these methods still remain. We are pursuing a route to implicit plasma kinetic simulation which eliminates extrapolation, eliminates phase-space from the linear algebra problem, and converges the entire nonlinear system within a time step. We accomplish all this using the Jacobian-Free Newton-Krylov algorithm. The original research along these lines considered particle methods to advance the distribution function [1]. In the current research we are advancing the Vlasov equations on a grid. Results will be presented which highlight algorithmic details for single species electrostatic problems and coupled ion-electron electrostatic problems. [4pt] [1] H. J. Kim, L. Chac'on, G. Lapenta, ``Fully implicit particle in cell algorithm,'' 47th Annual Meeting of the Division of Plasma Physics, Oct. 24-28, 2005, Denver, CO

A fully vectorized numerical solution of the incompressible Navier-Stokes equations. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Patel, N.

1983-01-01

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Two-Dimensional Mathematical Modeling of the Pack Carburizing Process

NASA Astrophysics Data System (ADS)

Sarkar, S.; Gupta, G. S.

2008-10-01

Pack carburization is the oldest method among the case-hardening treatments, and sufficient attempts have not been made to understand this process in terms of heat and mass transfer, effect of alloying elements, dimensions of the sample, etc. Thus, a two-dimensional mathematical model in cylindrical coordinate is developed for simulating the pack carburization process for chromium-bearing steel in this study. Heat and mass balance equations are solved simultaneously, where the surface temperature of the sample varies with time, but the carbon potential at the surface during the process remains constant. The fully implicit finite volume technique is used to solve the governing equations. Good agreement has been found between the predicted and published data. The effect of temperature, carburizing time, dimensions of the sample, etc. on the pack carburizing process shows some interesting results. It is found that the two-dimensional model gives better insight into understanding the carburizing process.

Characterization of chaotic electroconvection near flat electrodes under oscillatory voltages

NASA Astrophysics Data System (ADS)

Kim, Jeonglae; Davidson, Scott; Mani, Ali

2017-11-01

Onset of hydrodynamic instability and chaotic electroconvection in aqueous systems are studied by directly solving the two-dimensional coupled Poisson-Nernst-Planck and Navier-Stokes equations. An aqueous binary electrolyte is bounded by two planar electrodes where time-harmonic voltage is applied at a constant oscillation frequency. The governing equations are solved using a fully-conservative second-order-accurate finite volume discretization and a second-order implicit Euler time advancement. At a sufficiently high amplitude of applied voltage, the system exhibits chaotic behaviors involving strong hydrodynamic mixing and enhanced electroconvection. The system responses are characterized as a function of oscillation frequency, voltage magnitude, and the ratio of diffusivities of two ion species. Our results indicate that electroconvection is most enhanced for frequencies on the order of inverse system RC time scale. We will discuss the dependence of this optimal frequency on the asymmetry of the diffusion coefficients of ionic species. Supported by the Stanford's Precourt Institute.

Coherent states formulation of polymer field theory

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

Man, Xingkun; Villet, Michael C.; Materials Research Laboratory, University of California, Santa Barbara, California 93106

2014-01-14

We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards’ well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations.more » The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.« less

Implementation of an improved adaptive-implicit method in a thermal compositional simulator

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

Tan, T.B.

1988-11-01

A multicomponent thermal simulator with an adaptive-implicit-method (AIM) formulation/inexact-adaptive-Newton (IAN) method is presented. The final coefficient matrix retains the original banded structure so that conventional iterative methods can be used. Various methods for selection of the eliminated unknowns are tested. AIM/IAN method has a lower work count per Newtonian iteration than fully implicit methods, but a wrong choice of unknowns will result in excessive Newtonian iterations. For the problems tested, the residual-error method described in the paper for selecting implicit unknowns, together with the IAN method, had an improvement of up to 28% of the CPU time over the fullymore » implicit method.« less

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.

Comparison of three explicit multigrid methods for the Euler and Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Chima, Rodrick V.; Turkel, Eli; Schaffer, Steve

1987-01-01

Three explicit multigrid methods, Ni's method, Jameson's finite-volume method, and a finite-difference method based on Brandt's work, are described and compared for two model problems. All three methods use an explicit multistage Runge-Kutta scheme on the fine grid, and this scheme is also described. Convergence histories for inviscid flow over a bump in a channel for the fine-grid scheme alone show that convergence rate is proportional to Courant number and that implicit residual smoothing can significantly accelerate the scheme. Ni's method was slightly slower than the implicitly-smoothed scheme alone. Brandt's and Jameson's methods are shown to be equivalent in form but differ in their node versus cell-centered implementations. They are about 8.5 times faster than Ni's method in terms of CPU time. Results for an oblique shock/boundary layer interaction problem verify the accuracy of the finite-difference code. All methods slowed considerably on the stretched viscous grid but Brandt's method was still 2.1 times faster than Ni's method.

Parallelized implicit propagators for the finite-difference Schrödinger equation

NASA Astrophysics Data System (ADS)

Parker, Jonathan; Taylor, K. T.

1995-08-01

We describe the application of block Gauss-Seidel and block Jacobi iterative methods to the design of implicit propagators for finite-difference models of the time-dependent Schrödinger equation. The block-wise iterative methods discussed here are mixed direct-iterative methods for solving simultaneous equations, in the sense that direct methods (e.g. LU decomposition) are used to invert certain block sub-matrices, and iterative methods are used to complete the solution. We describe parallel variants of the basic algorithm that are well suited to the medium- to coarse-grained parallelism of work-station clusters, and MIMD supercomputers, and we show that under a wide range of conditions, fine-grained parallelism of the computation can be achieved. Numerical tests are conducted on a typical one-electron atom Hamiltonian. The methods converge robustly to machine precision (15 significant figures), in some cases in as few as 6 or 7 iterations. The rate of convergence is nearly independent of the finite-difference grid-point separations.

Stability analysis of Eulerian-Lagrangian methods for the one-dimensional shallow-water equations

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1990-01-01

In this paper stability and error analyses are discussed for some finite difference methods when applied to the one-dimensional shallow-water equations. Two finite difference formulations, which are based on a combined Eulerian-Lagrangian approach, are discussed. In the first part of this paper the results of numerical analyses for an explicit Eulerian-Lagrangian method (ELM) have shown that the method is unconditionally stable. This method, which is a generalized fixed grid method of characteristics, covers the Courant-Isaacson-Rees method as a special case. Some artificial viscosity is introduced by this scheme. However, because the method is unconditionally stable, the artificial viscosity can be brought under control either by reducing the spatial increment or by increasing the size of time step. The second part of the paper discusses a class of semi-implicit finite difference methods for the one-dimensional shallow-water equations. This method, when the Eulerian-Lagrangian approach is used for the convective terms, is also unconditionally stable and highly accurate for small space increments or large time steps. The semi-implicit methods seem to be more computationally efficient than the explicit ELM; at each time step a single tridiagonal system of linear equations is solved. The combined explicit and implicit ELM is best used in formulating a solution strategy for solving a network of interconnected channels. The explicit ELM is used at channel junctions for each time step. The semi-implicit method is then applied to the interior points in each channel segment. Following this solution strategy, the channel network problem can be reduced to a set of independent one-dimensional open-channel flow problems. Numerical results support properties given by the stability and error analyses. ?? 1990.

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

Sierra Thermal /Fluid Team

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes thermal energy transport, species transport, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for manufacturing process flows via the incompressible Navier-Stokes equations specialized to a low Reynolds number (Re %3C 1) regime. Enhanced modeling support of manufacturing processing is made possible through use of either arbitrarymore » Lagrangian- Eulerian (ALE) and level set based free and moving boundary tracking in conjunction with quasi-static nonlinear elastic solid mechanics for mesh control. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton- Krylov methods and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based upon the Sierra Framework.« less

Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD

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

Lin, P. T.; Shadid, J. N.; Hu, J. J.

Here, we explore the current performance and scaling of a fully-implicit stabilized unstructured finite element (FE) variational multiscale (VMS) capability for large-scale simulations of 3D incompressible resistive magnetohydrodynamics (MHD). The large-scale linear systems that are generated by a Newton nonlinear solver approach are iteratively solved by preconditioned Krylov subspace methods. The efficiency of this approach is critically dependent on the scalability and performance of the algebraic multigrid preconditioner. Our study considers the performance of the numerical methods as recently implemented in the second-generation Trilinos implementation that is 64-bit compliant and is not limited by the 32-bit global identifiers of themore » original Epetra-based Trilinos. The study presents representative results for a Poisson problem on 1.6 million cores of an IBM Blue Gene/Q platform to demonstrate very large-scale parallel execution. Additionally, results for a more challenging steady-state MHD generator and a transient solution of a benchmark MHD turbulence calculation for the full resistive MHD system are also presented. These results are obtained on up to 131,000 cores of a Cray XC40 and one million cores of a BG/Q system.« less

Performance of fully-coupled algebraic multigrid preconditioners for large-scale VMS resistive MHD

DOE PAGES

Lin, P. T.; Shadid, J. N.; Hu, J. J.; ...

2017-11-06

Here, we explore the current performance and scaling of a fully-implicit stabilized unstructured finite element (FE) variational multiscale (VMS) capability for large-scale simulations of 3D incompressible resistive magnetohydrodynamics (MHD). The large-scale linear systems that are generated by a Newton nonlinear solver approach are iteratively solved by preconditioned Krylov subspace methods. The efficiency of this approach is critically dependent on the scalability and performance of the algebraic multigrid preconditioner. Our study considers the performance of the numerical methods as recently implemented in the second-generation Trilinos implementation that is 64-bit compliant and is not limited by the 32-bit global identifiers of themore » original Epetra-based Trilinos. The study presents representative results for a Poisson problem on 1.6 million cores of an IBM Blue Gene/Q platform to demonstrate very large-scale parallel execution. Additionally, results for a more challenging steady-state MHD generator and a transient solution of a benchmark MHD turbulence calculation for the full resistive MHD system are also presented. These results are obtained on up to 131,000 cores of a Cray XC40 and one million cores of a BG/Q system.« less

Fully 3D modeling of tokamak vertical displacement events with realistic parameters

NASA Astrophysics Data System (ADS)

Pfefferle, David; Ferraro, Nathaniel; Jardin, Stephen; Bhattacharjee, Amitava

2016-10-01

In this work, we model the complex multi-domain and highly non-linear physics of Vertical Displacement Events (VDEs), one of the most damaging off-normal events in tokamaks, with the implicit 3D extended MHD code M3D-C1. The code has recently acquired the capability to include finite thickness conducting structures within the computational domain. By exploiting the possibility of running a linear 3D calculation on top of a non-linear 2D simulation, we monitor the non-axisymmetric stability and assess the eigen-structure of kink modes as the simulation proceeds. Once a stability boundary is crossed, a fully 3D non-linear calculation is launched for the remainder of the simulation, starting from an earlier time of the 2D run. This procedure, along with adaptive zoning, greatly increases the efficiency of the calculation, and allows to perform VDE simulations with realistic parameters and high resolution. Simulations are being validated with NSTX data where both axisymmetric (toroidally averaged) and non-axisymmetric induced and conductive (halo) currents have been measured. This work is supported by US DOE Grant DE-AC02-09CH11466.

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

Development of an Implicit, Charge and Energy Conserving 2D Electromagnetic PIC Code on Advanced Architectures

NASA Astrophysics Data System (ADS)

Payne, Joshua; Taitano, William; Knoll, Dana; Liebs, Chris; Murthy, Karthik; Feltman, Nicolas; Wang, Yijie; McCarthy, Colleen; Cieren, Emanuel

2012-10-01

In order to solve problems such as the ion coalescence and slow MHD shocks fully kinetically we developed a fully implicit 2D energy and charge conserving electromagnetic PIC code, PlasmaApp2D. PlasmaApp2D differs from previous implicit PIC implementations in that it will utilize advanced architectures such as GPUs and shared memory CPU systems, with problems too large to fit into cache. PlasmaApp2D will be a hybrid CPU-GPU code developed primarily to run on the DARWIN cluster at LANL utilizing four 12-core AMD Opteron CPUs and two NVIDIA Tesla GPUs per node. MPI will be used for cross-node communication, OpenMP will be used for on-node parallelism, and CUDA will be used for the GPUs. Development progress and initial results will be presented.

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.

Fourth order Douglas implicit scheme for solving three dimension reaction diffusion equation with non-linear source term

NASA Astrophysics Data System (ADS)

Hasnain, Shahid; Saqib, Muhammad; Mashat, Daoud Suleiman

2017-07-01

This research paper represents a numerical approximation to non-linear three dimension reaction diffusion equation with non-linear source term from population genetics. Since various initial and boundary value problems exist in three dimension reaction diffusion phenomena, which are studied numerically by different numerical methods, here we use finite difference schemes (Alternating Direction Implicit and Fourth Order Douglas Implicit) to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with analytical results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. Numerical results showed that Fourth Order Douglas Implicit scheme is very efficient and reliable for solving 3-D non-linear reaction diffusion equation.

Impact of the Parameter Identification of Plastic Potentials on the Finite Element Simulation of Sheet Metal Forming

NASA Astrophysics Data System (ADS)

Rabahallah, M.; Bouvier, S.; Balan, T.; Bacroix, B.; Teodosiu, C.

2007-04-01

In this work, an implicit, backward Euler time integration scheme is developed for an anisotropic, elastic-plastic model based on strain-rate potentials. The constitutive algorithm includes a sub-stepping procedure to deal with the strong nonlinearity of the plastic potentials when applied to FCC materials. The algorithm is implemented in the static implicit version of the Abaqus finite element code. Several recent plastic potentials have been implemented in this framework. The most accurate potentials require the identification of about twenty material parameters. Both mechanical tests and micromechanical simulations have been used for their identification, for a number of BCC and FCC materials. The impact of the identification procedure on the prediction of ears in cup drawing is investigated.

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.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. I - Nonstiff strongly dynamic problems

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

An implicit finite difference method of fourth order accuracy in space and time is introduced for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The basic form of the method is a two-level scheme which is unconditionally stable and nondissipative. The scheme uses only three mesh points at level t and three mesh points at level t + delta t. The dissipative version of the basic method given is conditionally stable under the CFL (Courant-Friedrichs-Lewy) condition. This version is particularly useful for the numerical solution of problems with strong but nonstiff dynamic features, where the CFL restriction is reasonable on accuracy grounds. Numerical results are provided to illustrate properties of the proposed method.

The assessment of nanofluid in a Von Karman flow with temperature relied viscosity

NASA Astrophysics Data System (ADS)

Tanveer, Anum; Salahuddin, T.; Khan, Mumtaz; Alshomrani, Ali Saleh; Malik, M. Y.

2018-06-01

This work endeavor to study the heat and mass transfer viscous nanofluid features in a Von Karman flow invoking the variable viscosity mechanism. Moreover, we have extended our study in view of heat generation and uniform suction effects. The flow triggering non-linear partial differential equations are inscribed in the non-dimensional form by manipulating suitable transformations. The resulting non-linear ordinary differential equations are solved numerically via implicit finite difference scheme in conjecture with the Newton's linearization scheme afterwards. The sought solutions are plotted graphically to present comparison between MATLAB routine bvp4c and implicit finite difference schemes. Impact of different parameters on the concentration/temperature/velocity profiles are highlighted. Further Nusselt number, skin friction and Sherwood number characteristics are discussed for better exposition.

Boundary conditions for the solution of compressible Navier-Stokes equations by an implicit factored method

NASA Technical Reports Server (NTRS)

Shih, T. I.-P.; Smith, G. E.; Springer, G. S.; Rimon, Y.

1983-01-01

A method is presented for formulating the boundary conditions in implicit finite-difference form needed for obtaining solutions to the compressible Navier-Stokes equations by the Beam and Warming implicit factored method. The usefulness of the method was demonstrated (a) by establishing the boundary conditions applicable to the analysis of the flow inside an axisymmetric piston-cylinder configuration and (b) by calculating velocities and mass fractions inside the cylinder for different geometries and different operating conditions. Stability, selection of time step and grid sizes, and computer time requirements are discussed in reference to the piston-cylinder problem analyzed.

Three-Dimensional Viscous Alternating Direction Implicit Algorithm and Strategies for Shape Optimization

NASA Technical Reports Server (NTRS)

Pandya, Mohagna J.; Baysal, Oktay

1997-01-01

A gradient-based shape optimization based on quasi-analytical sensitivities has been extended for practical three-dimensional aerodynamic applications. The flow analysis has been rendered by a fully implicit, finite-volume formulation of the Euler and Thin-Layer Navier-Stokes (TLNS) equations. Initially, the viscous laminar flow analysis for a wing has been compared with an independent computational fluid dynamics (CFD) code which has been extensively validated. The new procedure has been demonstrated in the design of a cranked arrow wing at Mach 2.4 with coarse- and fine-grid based computations performed with Euler and TLNS equations. The influence of the initial constraints on the geometry and aerodynamics of the optimized shape has been explored. Various final shapes generated for an identical initial problem formulation but with different optimization path options (coarse or fine grid, Euler or TLNS), have been aerodynamically evaluated via a common fine-grid TLNS-based analysis. The initial constraint conditions show significant bearing on the optimization results. Also, the results demonstrate that to produce an aerodynamically efficient design, it is imperative to include the viscous physics in the optimization procedure with the proper resolution. Based upon the present results, to better utilize the scarce computational resources, it is recommended that, a number of viscous coarse grid cases using either a preconditioned bi-conjugate gradient (PbCG) or an alternating-direction-implicit (ADI) method, should initially be employed to improve the optimization problem definition, the design space and initial shape. Optimized shapes should subsequently be analyzed using a high fidelity (viscous with fine-grid resolution) flow analysis to evaluate their true performance potential. Finally, a viscous fine-grid-based shape optimization should be conducted, using an ADI method, to accurately obtain the final optimized shape.

A Novel Implementation of Massively Parallel Three Dimensional Monte Carlo Radiation Transport

NASA Astrophysics Data System (ADS)

Robinson, P. B.; Peterson, J. D. L.

2005-12-01

The goal of our summer project was to implement the difference formulation for radiation transport into Cosmos++, a multidimensional, massively parallel, magneto hydrodynamics code for astrophysical applications (Peter Anninos - AX). The difference formulation is a new method for Symbolic Implicit Monte Carlo thermal transport (Brooks and Szöke - PAT). Formerly, simultaneous implementation of fully implicit Monte Carlo radiation transport in multiple dimensions on multiple processors had not been convincingly demonstrated. We found that a combination of the difference formulation and the inherent structure of Cosmos++ makes such an implementation both accurate and straightforward. We developed a "nearly nearest neighbor physics" technique to allow each processor to work independently, even with a fully implicit code. This technique coupled with the increased accuracy of an implicit Monte Carlo solution and the efficiency of parallel computing systems allows us to demonstrate the possibility of massively parallel thermal transport. This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48

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

Numerical Simulation of the Interaction of a Vortex with Stationary Airfoil in Transonic Flow,

DTIC Science & Technology

1984-01-12

Goorjian, P. M., "Implicit Vortex Wakes ," AIAA Journal, Vol. 15, No. 4, April Finite- Difference Computations of Unsteady Transonic 1977, pp. 581-590... Difference Simulations of Three- tion of Wing- Vortex Interaction in Transonic Flow Dimensional Flow," AIAA Journal, Vol. 18, No. 2, Using Implicit...assumptions are made in p = density modeling the nonlinear vortex wake structure. Numerical algorithms based on the Euler equations p_ = free stream density

Finite spaces and schemes

NASA Astrophysics Data System (ADS)

Sancho de Salas, Fernando

2017-12-01

A ringed finite space is a ringed space whose underlying topological space is finite. The category of ringed finite spaces contains, fully faithfully, the category of finite topological spaces and the category of affine schemes. Any ringed space, endowed with a finite open covering, produces a ringed finite space. We introduce the notions of schematic finite space and schematic morphism, showing that they behave, with respect to quasi-coherence, like schemes and morphisms of schemes do. Finally, we construct a fully faithful and essentially surjective functor from a localization of a full subcategory of the category of schematic finite spaces and schematic morphisms to the category of quasi-compact and quasi-separated schemes.

Effects of Non-Equilibrium Chemistry and Darcy-Forchheimer Flow of Pyrolysis Gas for a Charring Ablator

NASA Technical Reports Server (NTRS)

Chen, Yih-Kanq; Milos, Frank S.

2011-01-01

The Fully Implicit Ablation and Thermal Response code, FIAT, simulates pyrolysis and ablation of thermal protection materials and systems. The governing equations, which include energy conservation, a three-component decomposition model, and a surface energy balance, are solved with a moving grid. This work describes new modeling capabilities that are added to a special version of FIAT. These capabilities include a time-dependent pyrolysis gas flow momentum equation with Darcy-Forchheimer terms and pyrolysis gas species conservation equations with finite-rate homogeneous chemical reactions. The total energy conservation equation is also enhanced for consistency with these new additions. Parametric studies are performed using this enhanced version of FIAT. Two groups of analyses of Phenolic Impregnated Carbon Ablator (PICA) are presented. In the first group, an Orion flight environment for a proposed Lunar-return trajectory is considered. In the second group, various test conditions for arcjet models are examined. The central focus of these parametric studies is to understand the effect of pyrolysis gas momentum transfer on PICA material in-depth thermal responses with finite-rate, equilibrium, or frozen homogeneous gas chemistry. Results are presented, discussed, and compared with those predicted by the baseline PICA/FIAT ablation and thermal response model developed by the Orion Thermal Protection System Advanced Development Project.

Data assimilation and prognostic whole ice sheet modelling with the variationally derived, higher order, open source, and fully parallel ice sheet model VarGlaS

NASA Astrophysics Data System (ADS)

Brinkerhoff, D. J.; Johnson, J. V.

2013-07-01

We introduce a novel, higher order, finite element ice sheet model called VarGlaS (Variational Glacier Simulator), which is built on the finite element framework FEniCS. Contrary to standard procedure in ice sheet modelling, VarGlaS formulates ice sheet motion as the minimization of an energy functional, conferring advantages such as a consistent platform for making numerical approximations, a coherent relationship between motion and heat generation, and implicit boundary treatment. VarGlaS also solves the equations of enthalpy rather than temperature, avoiding the solution of a contact problem. Rather than include a lengthy model spin-up procedure, VarGlaS possesses an automated framework for model inversion. These capabilities are brought to bear on several benchmark problems in ice sheet modelling, as well as a 500 yr simulation of the Greenland ice sheet at high resolution. VarGlaS performs well in benchmarking experiments and, given a constant climate and a 100 yr relaxation period, predicts a mass evolution of the Greenland ice sheet that matches present-day observations of mass loss. VarGlaS predicts a thinning in the interior and thickening of the margins of the ice sheet.

Aeroelasticity and structural optimization of composite helicopter rotor blades with swept tips

NASA Technical Reports Server (NTRS)

Yuan, K. A.; Friedmann, P. P.

1995-01-01

This report describes the development of an aeroelastic analysis capability for composite helicopter rotor blades with straight and swept tips, and its application to the simulation of helicopter vibration reduction through structural optimization. A new aeroelastic model is developed in this study which is suitable for composite rotor blades with swept tips in hover and in forward flight. The hingeless blade is modeled by beam type finite elements. A single finite element is used to model the swept tip. Arbitrary cross-sectional shape, generally anisotropic material behavior, transverse shears and out-of-plane warping are included in the blade model. The nonlinear equations of motion, derived using Hamilton's principle, are based on a moderate deflection theory. Composite blade cross-sectbnal properties are calculated by a separate linear, two-dimensional cross section analysis. The aerodynamic loads are obtained from quasi-steady, incompressible aerodynamics, based on an implicit formulation. The trim and steady state blade aeroelastic response are solved in a fully coupled manner. In forward flight, where the blade equations of motion are periodic, the coupled trim-aeroelastic response solution is obtained from the harmonic balance method. Subsequently, the periodic system is linearized about the steady state response, and its stability is determined from Floquet theory.

A variable resolution nonhydrostatic global atmospheric semi-implicit semi-Lagrangian model

NASA Astrophysics Data System (ADS)

Pouliot, George Antoine

2000-10-01

The objective of this project is to develop a variable-resolution finite difference adiabatic global nonhydrostatic semi-implicit semi-Lagrangian (SISL) model based on the fully compressible nonhydrostatic atmospheric equations. To achieve this goal, a three-dimensional variable resolution dynamical core was developed and tested. The main characteristics of the dynamical core can be summarized as follows: Spherical coordinates were used in a global domain. A hydrostatic/nonhydrostatic switch was incorporated into the dynamical equations to use the fully compressible atmospheric equations. A generalized horizontal variable resolution grid was developed and incorporated into the model. For a variable resolution grid, in contrast to a uniform resolution grid, the order of accuracy of finite difference approximations is formally lost but remains close to the order of accuracy associated with the uniform resolution grid provided the grid stretching is not too significant. The SISL numerical scheme was implemented for the fully compressible set of equations. In addition, the generalized minimum residual (GMRES) method with restart and preconditioner was used to solve the three-dimensional elliptic equation derived from the discretized system of equations. The three-dimensional momentum equation was integrated in vector-form to incorporate the metric terms in the calculations of the trajectories. Using global re-analysis data for a specific test case, the model was compared to similar SISL models previously developed. Reasonable agreement between the model and the other independently developed models was obtained. The Held-Suarez test for dynamical cores was used for a long integration and the model was successfully integrated for up to 1200 days. Idealized topography was used to test the variable resolution component of the model. Nonhydrostatic effects were simulated at grid spacings of 400 meters with idealized topography and uniform flow. Using a high-resolution topographic data set and the variable resolution grid, sets of experiments with increasing resolution were performed over specific regions of interest. Using realistic initial conditions derived from re-analysis fields, nonhydrostatic effects were significant for grid spacings on the order of 0.1 degrees with orographic forcing. If the model code was adapted for use in a message passing interface (MPI) on a parallel supercomputer today, it was estimated that a global grid spacing of 0.1 degrees would be achievable for a global model. In this case, nonhydrostatic effects would be significant for most areas. A variable resolution grid in a global model provides a unified and flexible approach to many climate and numerical weather prediction problems. The ability to configure the model from very fine to very coarse resolutions allows for the simulation of atmospheric phenomena at different scales using the same code. We have developed a dynamical core illustrating the feasibility of using a variable resolution in a global model.

Development of Implicit Methods in CFD NASA Ames Research Center 1970's - 1980's

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.

2010-01-01

The focus here is on the early development (mid 1970's-1980's) at NASA Ames Research Center of implicit methods in Computational Fluid Dynamics (CFD). A class of implicit finite difference schemes of the Beam and Warming approximate factorization type will be addressed. The emphasis will be on the Euler equations. A review of material pertinent to the solution of the Euler equations within the framework of implicit methods will be presented. The eigensystem of the equations will be used extensively in developing a framework for various methods applied to the Euler equations. The development and analysis of various aspects of this class of schemes will be given along with the motivations behind many of the choices. Various acceleration and efficiency modifications such as matrix reduction, diagonalization and flux split schemes will be presented.

On a fourth order accurate implicit finite difference scheme for hyperbolic conservation laws. II - Five-point schemes

NASA Technical Reports Server (NTRS)

Harten, A.; Tal-Ezer, H.

1981-01-01

This paper presents a family of two-level five-point implicit schemes for the solution of one-dimensional systems of hyperbolic conservation laws, which generalized the Crank-Nicholson scheme to fourth order accuracy (4-4) in both time and space. These 4-4 schemes are nondissipative and unconditionally stable. Special attention is given to the system of linear equations associated with these 4-4 implicit schemes. The regularity of this system is analyzed and efficiency of solution-algorithms is examined. A two-datum representation of these 4-4 implicit schemes brings about a compactification of the stencil to three mesh points at each time-level. This compact two-datum representation is particularly useful in deriving boundary treatments. Numerical results are presented to illustrate some properties of the proposed scheme.

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.

Implicit method for the computation of unsteady flows on unstructured grids

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, D. J.

1995-01-01

An implicit method for the computation of unsteady flows on unstructured grids is presented. Following a finite difference approximation for the time derivative, the resulting nonlinear system of equations is solved at each time step by using an agglomeration multigrid procedure. The method allows for arbitrarily large time steps and is efficient in terms of computational effort and storage. Inviscid and viscous unsteady flows are computed to validate the procedure. The issue of the mass matrix which arises with vertex-centered finite volume schemes is addressed. The present formulation allows the mass matrix to be inverted indirectly. A mesh point movement and reconnection procedure is described that allows the grids to evolve with the motion of bodies. As an example of flow over bodies in relative motion, flow over a multi-element airfoil system undergoing deployment is computed.

Numerical study of supersonic combustion using a finite rate chemistry model

NASA Technical Reports Server (NTRS)

Chitsomboon, T.; Tiwari, S. N.; Kumar, A.; Drummond, J. P.

1986-01-01

The governing equations of two-dimensional chemically reacting flows are presented together with a global two-step chemistry model for H2-air combustion. The explicit unsplit MacCormack finite difference algorithm is used to advance the discrete system of the governing equations in time until convergence is attained. The source terms in the species equations are evaluated implicitly to alleviate stiffness associated with fast reactions. With implicit source terms, the species equations give rise to a block-diagonal system which can be solved very efficiently on vector-processing computers. A supersonic reacting flow in an inlet-combustor configuration is calculated for the case where H2 is injected into the flow from the side walls and the strut. Results of the calculation are compared against the results obtained by using a complete reaction model.

An implict LU scheme for the Euler equations applied to arbitrary cascades. [new method of factoring

NASA Technical Reports Server (NTRS)

Buratynski, E. K.; Caughey, D. A.

1984-01-01

An implicit scheme for solving the Euler equations is derived and demonstrated. The alternating-direction implicit (ADI) technique is modified, using two implicit-operator factors corresponding to lower-block-diagonal (L) or upper-block-diagonal (U) algebraic systems which can be easily inverted. The resulting LU scheme is implemented in finite-volume mode and applied to 2D subsonic and transonic cascade flows with differing degrees of geometric complexity. The results are presented graphically and found to be in good agreement with those of other numerical and analytical approaches. The LU method is also 2.0-3.4 times faster than ADI, suggesting its value in calculating 3D problems.

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.

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.

A nonlinear dynamic finite element approach for simulating muscular hydrostats.

PubMed

Vavourakis, V; Kazakidi, A; Tsakiris, D P; Ekaterinaris, J A

2014-01-01

An implicit nonlinear finite element model for simulating biological muscle mechanics is developed. The numerical method is suitable for dynamic simulations of three-dimensional, nonlinear, nearly incompressible, hyperelastic materials that undergo large deformations. These features characterise biological muscles, which consist of fibres and connective tissues. It can be assumed that the stress distribution inside the muscles is the superposition of stresses along the fibres and the connective tissues. The mechanical behaviour of the surrounding tissues is determined by adopting a Mooney-Rivlin constitutive model, while the mechanical description of fibres is considered to be the sum of active and passive stresses. Due to the nonlinear nature of the problem, evaluation of the Jacobian matrix is carried out in order to subsequently utilise the standard Newton-Raphson iterative procedure and to carry out time integration with an implicit scheme. The proposed methodology is implemented into our in-house, open source, finite element software, which is validated by comparing numerical results with experimental measurements and other numerical results. Finally, the numerical procedure is utilised to simulate primitive octopus arm manoeuvres, such as bending and reaching.

Modeling the absorption spectrum of the permanganate ion in vacuum and in aqueous solution

NASA Astrophysics Data System (ADS)

Olsen, Jógvan Magnus Haugaard; Hedegård, Erik Donovan

The absorption spectrum of the MnO$_{4}$$^{-}$ ion has been a test-bed for quantum-chemical methods over the last decades. Its correct description requires highly-correlated multiconfigurational methods, which are incompatible with the inclusion of finite-temperature and solvent effects due to their high computational demands. Therefore, implicit solvent models are usually employed. Here we show that implicit solvent models are not sufficiently accurate to model the solvent shift of MnO$_{4}$$^{-}$, and we analyze the origins of their failure. We obtain the correct solvent shift for MnO$_{4}$$^{-}$ in aqueous solution by employing the polarizable embedding (PE) model combined with a range-separated complete active space short-range density functional theory method (CAS-srDFT). Finite-temperature effects are taken into account by averaging over structures obtained from ab initio molecular dynamics simulations. The explicit treatment of finite-temperature and solvent effects facilitates the interpretation of the bands in the low-energy region of the MnO$_{4}$$^{-}$ absorption spectrum, whose assignment has been elusive.

A fully implicit Hall MHD algorithm based on the ion Ohm's law

NASA Astrophysics Data System (ADS)

Chacón, Luis

2010-11-01

Hall MHD is characterized by extreme hyperbolic numerical stiffness stemming from fast dispersive waves. Implicit algorithms are potentially advantageous, but of very difficult efficient implementation due to the condition numbers of associated matrices. Here, we explore the extension of a successful fully implicit, fully nonlinear algorithm for resistive MHD,ootnotetextL. Chac'on, Phys. Plasmas, 15 (2008) based on Jacobian-free Newton-Krylov methods with physics-based preconditioning, to Hall MHD. Traditionally, Hall MHD has been formulated using the electron equation of motion (EOM) to determine the electric field in the plasma (the so-called Ohm's law). However, given that the center-of-mass EOM, the ion EOM, and the electron EOM are linearly dependent, one could equivalently employ the ion EOM as the Ohm's law for a Hall MHD formulation. While, from a physical standpoint, there is no a priori advantage for using one Ohm's law vs. the other, we argue in this poster that there is an algorithmic one. We will show that, while the electron Ohm's law prevents the extension of the resistive MHD preconditioning strategy to Hall MHD, an ion Ohm's law allows it trivially. Verification and performance numerical results on relevant problems will be presented.

Multigrid Methods for Fully Implicit Oil Reservoir Simulation

NASA Technical Reports Server (NTRS)

Molenaar, J.

1996-01-01

In this paper we consider the simultaneous flow of oil and water in reservoir rock. This displacement process is modeled by two basic equations: the material balance or continuity equations and the equation of motion (Darcy's law). For the numerical solution of this system of nonlinear partial differential equations there are two approaches: the fully implicit or simultaneous solution method and the sequential solution method. In the sequential solution method the system of partial differential equations is manipulated to give an elliptic pressure equation and a hyperbolic (or parabolic) saturation equation. In the IMPES approach the pressure equation is first solved, using values for the saturation from the previous time level. Next the saturations are updated by some explicit time stepping method; this implies that the method is only conditionally stable. For the numerical solution of the linear, elliptic pressure equation multigrid methods have become an accepted technique. On the other hand, the fully implicit method is unconditionally stable, but it has the disadvantage that in every time step a large system of nonlinear algebraic equations has to be solved. The most time-consuming part of any fully implicit reservoir simulator is the solution of this large system of equations. Usually this is done by Newton's method. The resulting systems of linear equations are then either solved by a direct method or by some conjugate gradient type method. In this paper we consider the possibility of applying multigrid methods for the iterative solution of the systems of nonlinear equations. There are two ways of using multigrid for this job: either we use a nonlinear multigrid method or we use a linear multigrid method to deal with the linear systems that arise in Newton's method. So far only a few authors have reported on the use of multigrid methods for fully implicit simulations. Two-level FAS algorithm is presented for the black-oil equations, and linear multigrid for two-phase flow problems with strong heterogeneities and anisotropies is studied. Here we consider both possibilities. Moreover we present a novel way for constructing the coarse grid correction operator in linear multigrid algorithms. This approach has the advantage in that it preserves the sparsity pattern of the fine grid matrix and it can be extended to systems of equations in a straightforward manner. We compare the linear and nonlinear multigrid algorithms by means of a numerical experiment.

Connecting Free Energy Surfaces in Implicit and Explicit Solvent: an Efficient Method to Compute Conformational and Solvation Free Energies

PubMed Central

Deng, Nanjie; Zhang, Bin W.; Levy, Ronald M.

2015-01-01

The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions and protein-ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ~3 kcal/mol at only ~8 % of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the explicit/implicit thermodynamic cycle. PMID:26236174

Connecting free energy surfaces in implicit and explicit solvent: an efficient method to compute conformational and solvation free energies.

PubMed

Deng, Nanjie; Zhang, Bin W; Levy, Ronald M

2015-06-09

The ability to accurately model solvent effects on free energy surfaces is important for understanding many biophysical processes including protein folding and misfolding, allosteric transitions, and protein–ligand binding. Although all-atom simulations in explicit solvent can provide an accurate model for biomolecules in solution, explicit solvent simulations are hampered by the slow equilibration on rugged landscapes containing multiple basins separated by barriers. In many cases, implicit solvent models can be used to significantly speed up the conformational sampling; however, implicit solvent simulations do not fully capture the effects of a molecular solvent, and this can lead to loss of accuracy in the estimated free energies. Here we introduce a new approach to compute free energy changes in which the molecular details of explicit solvent simulations are retained while also taking advantage of the speed of the implicit solvent simulations. In this approach, the slow equilibration in explicit solvent, due to the long waiting times before barrier crossing, is avoided by using a thermodynamic cycle which connects the free energy basins in implicit solvent and explicit solvent using a localized decoupling scheme. We test this method by computing conformational free energy differences and solvation free energies of the model system alanine dipeptide in water. The free energy changes between basins in explicit solvent calculated using fully explicit solvent paths agree with the corresponding free energy differences obtained using the implicit/explicit thermodynamic cycle to within 0.3 kcal/mol out of ∼3 kcal/mol at only ∼8% of the computational cost. We note that WHAM methods can be used to further improve the efficiency and accuracy of the implicit/explicit thermodynamic cycle.

A review of hybrid implicit explicit finite difference time domain method

NASA Astrophysics Data System (ADS)

Chen, Juan

2018-06-01

The finite-difference time-domain (FDTD) method has been extensively used to simulate varieties of electromagnetic interaction problems. However, because of its Courant-Friedrich-Levy (CFL) condition, the maximum time step size of this method is limited by the minimum size of cell used in the computational domain. So the FDTD method is inefficient to simulate the electromagnetic problems which have very fine structures. To deal with this problem, the Hybrid Implicit Explicit (HIE)-FDTD method is developed. The HIE-FDTD method uses the hybrid implicit explicit difference in the direction with fine structures to avoid the confinement of the fine spatial mesh on the time step size. So this method has much higher computational efficiency than the FDTD method, and is extremely useful for the problems which have fine structures in one direction. In this paper, the basic formulations, time stability condition and dispersion error of the HIE-FDTD method are presented. The implementations of several boundary conditions, including the connect boundary, absorbing boundary and periodic boundary are described, then some applications and important developments of this method are provided. The goal of this paper is to provide an historical overview and future prospects of the HIE-FDTD method.

An Implicit Characteristic Based Method for Electromagnetics

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

An implicit characteristic-based approach for numerical solution of Maxwell's time-dependent curl equations in flux conservative form is introduced. This method combines a characteristic based finite difference spatial approximation with an implicit lower-upper approximate factorization (LU/AF) time integration scheme. This approach is advantageous for three-dimensional applications because the characteristic differencing enables a two-factor approximate factorization that retains its unconditional stability in three space dimensions, and it does not require solution of tridiagonal systems. Results are given both for a Fourier analysis of stability, damping and dispersion properties, and for one-dimensional model problems involving propagation and scattering for free space and dielectric materials using both uniform and nonuniform grids. The explicit Finite Difference Time Domain Method (FDTD) algorithm is used as a convenient reference algorithm for comparison. The one-dimensional results indicate that for low frequency problems on a highly resolved uniform or nonuniform grid, this LU/AF algorithm can produce accurate solutions at Courant numbers significantly greater than one, with a corresponding improvement in efficiency for simulating a given period of time. This approach appears promising for development of dispersion optimized LU/AF schemes for three dimensional applications.

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

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

Asymptotic analysis of discrete schemes for non-equilibrium radiation diffusion

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

Cui, Xia, E-mail: cui_xia@iapcm.ac.cn; Yuan, Guang-wei; Shen, Zhi-jun

Motivated by providing well-behaved fully discrete schemes in practice, this paper extends the asymptotic analysis on time integration methods for non-equilibrium radiation diffusion in [2] to space discretizations. Therein studies were carried out on a two-temperature model with Larsen's flux-limited diffusion operator, both the implicitly balanced (IB) and linearly implicit (LI) methods were shown asymptotic-preserving. In this paper, we focus on asymptotic analysis for space discrete schemes in dimensions one and two. First, in construction of the schemes, in contrast to traditional first-order approximations, asymmetric second-order accurate spatial approximations are devised for flux-limiters on boundary, and discrete schemes with second-ordermore » accuracy on global spatial domain are acquired consequently. Then by employing formal asymptotic analysis, the first-order asymptotic-preserving property for these schemes and furthermore for the fully discrete schemes is shown. Finally, with the help of manufactured solutions, numerical tests are performed, which demonstrate quantitatively the fully discrete schemes with IB time evolution indeed have the accuracy and asymptotic convergence as theory predicts, hence are well qualified for both non-equilibrium and equilibrium radiation diffusion. - Highlights: • Provide AP fully discrete schemes for non-equilibrium radiation diffusion. • Propose second order accurate schemes by asymmetric approach for boundary flux-limiter. • Show first order AP property of spatially and fully discrete schemes with IB evolution. • Devise subtle artificial solutions; verify accuracy and AP property quantitatively. • Ideas can be generalized to 3-dimensional problems and higher order implicit schemes.« less

Flowfield-Dependent Mixed Explicit-Implicit (FDMEL) Algorithm for Computational Fluid Dynamics

NASA Technical Reports Server (NTRS)

Garcia, S. M.; Chung, T. J.

1997-01-01

Despite significant achievements in computational fluid dynamics, there still remain many fluid flow phenomena not well understood. For example, the prediction of temperature distributions is inaccurate when temperature gradients are high, particularly in shock wave turbulent boundary layer interactions close to the wall. Complexities of fluid flow phenomena include transition to turbulence, relaminarization separated flows, transition between viscous and inviscid incompressible and compressible flows, among others, in all speed regimes. The purpose of this paper is to introduce a new approach, called the Flowfield-Dependent Mixed Explicit-Implicit (FDMEI) method, in an attempt to resolve these difficult issues in Computational Fluid Dynamics (CFD). In this process, a total of six implicitness parameters characteristic of the current flowfield are introduced. They are calculated from the current flowfield or changes of Mach numbers, Reynolds numbers, Peclet numbers, and Damkoehler numbers (if reacting) at each nodal point and time step. This implies that every nodal point or element is provided with different or unique numerical scheme according to their current flowfield situations, whether compressible, incompressible, viscous, inviscid, laminar, turbulent, reacting, or nonreacting. In this procedure, discontinuities or fluctuations of an variables between adjacent nodal points are determined accurately. If these implicitness parameters are fixed to certain numbers instead of being calculated from the flowfield information, then practically all currently available schemes of finite differences or finite elements arise as special cases. Some benchmark problems to be presented in this paper will show the validity, accuracy, and efficiency of the proposed methodology.

Finite element computation of compressible flows with the SUPG formulation

NASA Technical Reports Server (NTRS)

Le Beau, G. J.; Tezduyar, T. E.

1991-01-01

Finite element computation of compressible Euler equations is presented in the context of the streamline-upwind/Petrov-Galerkin (SUPG) formulation. The SUPG formulation, which is based on adding stabilizing terms to the Galerkin formulation, is further supplemented with a shock capturing operator which addresses the difficulty in maintaining a satisfactory solution near discontinuities in the solution field. The shock capturing operator, which has been derived from work done in entropy variables for a similar operator, is shown to lead to an appropriate level of additional stabilization near shocks, without resulting in excessive numerical diffusion. An implicit treatment of the impermeable wall boundary condition is also presented. This treatment of the no-penetration condition offers increased stability for large Courant numbers, and accelerated convergence of the computations for both implicit and explicit applications. Several examples are presented to demonstrate the ability of this method to solve the equations governing compressible fluid flow.

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.

Calculation of three-dimensional compressible laminar and turbulent boundary layers. An implicit finite-difference procedure for solving the three-dimensional compressible laminar, transitional, and turbulent boundary-layer equations

NASA Technical Reports Server (NTRS)

Harris, J. E.

1975-01-01

An implicit finite-difference procedure is presented for solving the compressible three-dimensional boundary-layer equations. The method is second-order accurate, unconditionally stable (conditional stability for reverse cross flow), and efficient from the viewpoint of computer storage and processing time. The Reynolds stress terms are modeled by (1) a single-layer mixing length model and (2) a two-layer eddy viscosity model. These models, although simple in concept, accurately predicted the equilibrium turbulent flow for the conditions considered. Numerical results are compared with experimental wall and profile data for a cone at an angle of attack larger than the cone semiapex angle. These comparisons clearly indicate that the numerical procedure and turbulence models accurately predict the experimental data with as few as 21 nodal points in the plane normal to the wall boundary.

Modeling highly transient flow, mass, and heat transport in the Chattahoochee River near Atlanta, Georgia

USGS Publications Warehouse

Jobson, Harvey E.; Keefer, Thomas N.

1979-01-01

A coupled flow-temperature model has been developed and verified for a 27.9-km reach of the Chattahoochee River between Buford Dam and Norcross, Ga. Flow in this reach of the Chattahoochee is continuous but highly regulated by Buford Dam, a flood-control and hydroelectric facility located near Buford, Ga. Calibration and verification utilized two sets of data collected under highly unsteady discharge conditions. Existing solution techniques, with certain minor improvements, were applied to verify the existing technology of flow and transport modeling. A linear, implicit finite-difference flow model was coupled with implicit, finite-difference transport and temperature models. Both the conservative and nonconservative forms of the transport equation were solved, and the difference in the predicted concentrations of dye were found to be insignificant. The temperature model, therefore, was based on the simpler nonconservative form of the transport equation. (Woodard-USGS)

Comprehensive Numerical Analysis of Finite Difference Time Domain Methods for Improving Optical Waveguide Sensor Accuracy

PubMed Central

Samak, M. Mosleh E. Abu; Bakar, A. Ashrif A.; Kashif, Muhammad; Zan, Mohd Saiful Dzulkifly

2016-01-01

This paper discusses numerical analysis methods for different geometrical features that have limited interval values for typically used sensor wavelengths. Compared with existing Finite Difference Time Domain (FDTD) methods, the alternating direction implicit (ADI)-FDTD method reduces the number of sub-steps by a factor of two to three, which represents a 33% time savings in each single run. The local one-dimensional (LOD)-FDTD method has similar numerical equation properties, which should be calculated as in the previous method. Generally, a small number of arithmetic processes, which result in a shorter simulation time, are desired. The alternating direction implicit technique can be considered a significant step forward for improving the efficiency of unconditionally stable FDTD schemes. This comparative study shows that the local one-dimensional method had minimum relative error ranges of less than 40% for analytical frequencies above 42.85 GHz, and the same accuracy was generated by both methods.

Pentadiagonal alternating-direction-implicit finite-difference time-domain method for two-dimensional Schrödinger equation

NASA Astrophysics Data System (ADS)

Tay, Wei Choon; Tan, Eng Leong

2014-07-01

In this paper, we have proposed a pentadiagonal alternating-direction-implicit (Penta-ADI) finite-difference time-domain (FDTD) method for the two-dimensional Schrödinger equation. Through the separation of complex wave function into real and imaginary parts, a pentadiagonal system of equations for the ADI method is obtained, which results in our Penta-ADI method. The Penta-ADI method is further simplified into pentadiagonal fundamental ADI (Penta-FADI) method, which has matrix-operator-free right-hand-sides (RHS), leading to the simplest and most concise update equations. As the Penta-FADI method involves five stencils in the left-hand-sides (LHS) of the pentadiagonal update equations, special treatments that are required for the implementation of the Dirichlet's boundary conditions will be discussed. Using the Penta-FADI method, a significantly higher efficiency gain can be achieved over the conventional Tri-ADI method, which involves a tridiagonal system of equations.

Flow model for open-channel reach or network

USGS Publications Warehouse

Schaffranek, R.W.

1987-01-01

Formulation of a one-dimensional model for simulating unsteady flow in a single open-channel reach or in a network of interconnected channels is presented. The model is both general and flexible in that it can be used to simulate a wide range of flow conditions for various channel configurations. It is based on a four-point (box), implicit, finite-difference approximation of the governing nonlinear flow equations with user-definable weighting coefficients to permit varying the solution scheme from box-centered to fully forward. Unique transformation equations are formulated that permit correlation of the unknowns at the extremities of the channels, thereby reducing coefficient matrix and execution time requirements. Discharges and water-surface elevations computed at intermediate locations within a channel are determined following solution of the transformation equations. The matrix of transformation and boundary-condition equations is solved by Gauss elimination using maximum pivot strategy. Two diverse applications of the model are presented to illustrate its broad utility. (USGS)

Entropy-based artificial viscosity stabilization for non-equilibrium Grey Radiation-Hydrodynamics

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

Delchini, Marc O., E-mail: delchinm@email.tamu.edu; Ragusa, Jean C., E-mail: jean.ragusa@tamu.edu; Morel, Jim, E-mail: jim.morel@tamu.edu

2015-09-01

The entropy viscosity method is extended to the non-equilibrium Grey Radiation-Hydrodynamic equations. The method employs a viscous regularization to stabilize the numerical solution. The artificial viscosity coefficient is modulated by the entropy production and peaks at shock locations. The added dissipative terms are consistent with the entropy minimum principle. A new functional form of the entropy residual, suitable for the Radiation-Hydrodynamic equations, is derived. We demonstrate that the viscous regularization preserves the equilibrium diffusion limit. The equations are discretized with a standard Continuous Galerkin Finite Element Method and a fully implicit temporal integrator within the MOOSE multiphysics framework. The methodmore » of manufactured solutions is employed to demonstrate second-order accuracy in both the equilibrium diffusion and streaming limits. Several typical 1-D radiation-hydrodynamic test cases with shocks (from Mach 1.05 to Mach 50) are presented to establish the ability of the technique to capture and resolve shocks.« less

Study on the extrusion of nickel-based spark plug electrodes by numerical simulation

NASA Astrophysics Data System (ADS)

Saby, Q.; Courbon, C.; Salvatore, F.; Fabre, D.; Romeyer, F.

2018-05-01

Interest in metal forming simulation has grown rapidly during the last decades and is now well established even in industry. It provides a flexible and relatively cheap method to perform sensitivity analyses, getting a better insight into the forming process and use it as an optimisation tool. As far as wear is concerned, numerical simulation can be seen as a relevant approach to assess the thermomechanical loadings applied to the active die surface and therefore predict their wear behaviour. In this study, a Finite-Element (FE) based model has been developed in order to investigate the cold forming process of a nickel-based sparkplug electrode. A fully thermo-mechanically coupled implicit formulation has been used in order to model the forward extrusion step with a special emphasis on the contact conditions at the workpiece-die interface. Contact pressure, relative sliding velocity and temperature profiles have been extracted versus time and qualitatively compared to the wear phenomena observed on the worn production dies.

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.

Four-Dimensional Continuum Gyrokinetic Code: Neoclassical Simulation of Fusion Edge Plasmas

NASA Astrophysics Data System (ADS)

Xu, X. Q.

2005-10-01

We are developing a continuum gyrokinetic code, TEMPEST, to simulate edge plasmas. Our code represents velocity space via a grid in equilibrium energy and magnetic moment variables, and configuration space via poloidal magnetic flux and poloidal angle. The geometry is that of a fully diverted tokamak (single or double null) and so includes boundary conditions for both closed magnetic flux surfaces and open field lines. The 4-dimensional code includes kinetic electrons and ions, and electrostatic field-solver options, and simulates neoclassical transport. The present implementation is a Method of Lines approach where spatial finite-differences (higher order upwinding) and implicit time advancement are used. We present results of initial verification and validation studies: transition from collisional to collisionless limits of parallel end-loss in the scrape-off layer, self-consistent electric field, and the effect of the real X-point geometry and edge plasma conditions on the standard neoclassical theory, including a comparison of our 4D code with other kinetic neoclassical codes and experiments.

Development of cost-effective surfactant flooding technology. Annual report for the period, September 30, 1993--September 29, 1994

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

Pope, G.; Sepehrnoori, K.

1995-08-01

This research consists of the parallel development of a new chemical flooding simulator and the application of our existing UTCHEM simulation code to model surfactant flooding. The new code is based upon a completely new numerical method that combines for the first time higher-order finite-difference methods, flux limiters, and implicit algorithms. Results indicate that this approach has significant advantages in some problems and will likely enable us to simulate much larger and more realistic chemical floods once it is fully developed. Additional improvements have also been made to the UTCHEM code, and it has been applied to the study ofmore » stochastic reservoirs with and without horizontal wells to evaluate methods to reduce the cost and risk of surfactant flooding. During the second year of this contract, we have already made significant progress on both of these tasks and are ahead of schedule on both of them.« less

An implicit fast Fourier transform method for integration of the time dependent Schrodinger equation

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

Riley, M.E.; Ritchie, A.B.

1997-12-31

One finds that the conventional exponentiated split operator procedure is subject to difficulties when solving the time-dependent Schrodinger equation for Coulombic systems. By rearranging the kinetic and potential energy terms in the temporal propagator of the finite difference equations, one can find a propagation algorithm for three dimensions that looks much like the Crank-Nicholson and alternating direction implicit methods for one- and two-space-dimensional partial differential equations. The authors report investigations of this novel implicit split operator procedure. The results look promising for a purely numerical approach to certain electron quantum mechanical problems. A charge exchange calculation is presented as anmore » example of the power of the method.« less

On-the-fly Numerical Surface Integration for Finite-Difference Poisson-Boltzmann Methods.

PubMed

Cai, Qin; Ye, Xiang; Wang, Jun; Luo, Ray

2011-11-01

Most implicit solvation models require the definition of a molecular surface as the interface that separates the solute in atomic detail from the solvent approximated as a continuous medium. Commonly used surface definitions include the solvent accessible surface (SAS), the solvent excluded surface (SES), and the van der Waals surface. In this study, we present an efficient numerical algorithm to compute the SES and SAS areas to facilitate the applications of finite-difference Poisson-Boltzmann methods in biomolecular simulations. Different from previous numerical approaches, our algorithm is physics-inspired and intimately coupled to the finite-difference Poisson-Boltzmann methods to fully take advantage of its existing data structures. Our analysis shows that the algorithm can achieve very good agreement with the analytical method in the calculation of the SES and SAS areas. Specifically, in our comprehensive test of 1,555 molecules, the average unsigned relative error is 0.27% in the SES area calculations and 1.05% in the SAS area calculations at the grid spacing of 1/2Å. In addition, a systematic correction analysis can be used to improve the accuracy for the coarse-grid SES area calculations, with the average unsigned relative error in the SES areas reduced to 0.13%. These validation studies indicate that the proposed algorithm can be applied to biomolecules over a broad range of sizes and structures. Finally, the numerical algorithm can also be adapted to evaluate the surface integral of either a vector field or a scalar field defined on the molecular surface for additional solvation energetics and force calculations.

Mixed time integration methods for transient thermal analysis of structures

NASA Technical Reports Server (NTRS)

Liu, W. K.

1982-01-01

The computational methods used to predict and optimize the thermal structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a different yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. The computer implementation aspects and numerical evaluation of these mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally useful method of estimating the critical time step for linear quadrilateral element is also given. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

Mixed time integration methods for transient thermal analysis of structures

NASA Technical Reports Server (NTRS)

Liu, W. K.

1983-01-01

The computational methods used to predict and optimize the thermal-structural behavior of aerospace vehicle structures are reviewed. In general, two classes of algorithms, implicit and explicit, are used in transient thermal analysis of structures. Each of these two methods has its own merits. Due to the different time scales of the mechanical and thermal responses, the selection of a time integration method can be a difficult yet critical factor in the efficient solution of such problems. Therefore mixed time integration methods for transient thermal analysis of structures are being developed. The computer implementation aspects and numerical evaluation of these mixed time implicit-explicit algorithms in thermal analysis of structures are presented. A computationally-useful method of estimating the critical time step for linear quadrilateral element is also given. Numerical tests confirm the stability criterion and accuracy characteristics of the methods. The superiority of these mixed time methods to the fully implicit method or the fully explicit method is also demonstrated.

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

DOE PAGES

Chacon, L.; Chen, G.

2016-04-19

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. Anmore » asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.« less

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

NASA Astrophysics Data System (ADS)

Chacón, L.; Chen, G.

2016-07-01

We extend a recently proposed fully implicit PIC algorithm for the Vlasov-Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (ϕ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ ṡ A = 0 exactly. An asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.

A curvilinear, fully implicit, conservative electromagnetic PIC algorithm in multiple dimensions

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

Chacon, L.; Chen, G.

Here, we extend a recently proposed fully implicit PIC algorithm for the Vlasov–Darwin model in multiple dimensions (Chen and Chacón (2015) [1]) to curvilinear geometry. As in the Cartesian case, the approach is based on a potential formulation (Φ, A), and overcomes many difficulties of traditional semi-implicit Darwin PIC algorithms. Conservation theorems for local charge and global energy are derived in curvilinear representation, and then enforced discretely by a careful choice of the discretization of field and particle equations. Additionally, the algorithm conserves canonical-momentum in any ignorable direction, and preserves the Coulomb gauge ∇ • A = 0 exactly. Anmore » asymptotically well-posed fluid preconditioner allows efficient use of large cell sizes, which are determined by accuracy considerations, not stability, and can be orders of magnitude larger than required in a standard explicit electromagnetic PIC simulation. We demonstrate the accuracy and efficiency properties of the algorithm with numerical experiments in mapped meshes in 1D-3V and 2D-3V.« less

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.

An investigation of several numerical procedures for time-asymptotic compressible Navier-Stokes solutions

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.; Blanchard, D. K.; Cooke, C. H.; Rubin, S. G.

1975-01-01

The status of an investigation of four numerical techniques for the time-dependent compressible Navier-Stokes equations is presented. Results for free shear layer calculations in the Reynolds number range from 1000 to 81000 indicate that a sequential alternating-direction implicit (ADI) finite-difference procedure requires longer computing times to reach steady state than a low-storage hopscotch finite-difference procedure. A finite-element method with cubic approximating functions was found to require excessive computer storage and computation times. A fourth method, an alternating-direction cubic spline technique which is still being tested, is also described.

A simple level set method for solving Stefan problems

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

Chen, S.; Merriman, B.; Osher, S.

1997-07-15

Discussed in this paper is an implicit finite difference scheme for solving a heat equation and a simple level set method for capturing the interface between solid and liquid phases which are used to solve Stefan problems.

Implicit Priors in Galaxy Cluster Mass and Scaling Relation Determinations

NASA Technical Reports Server (NTRS)

Mantz, A.; Allen, S. W.

2011-01-01

Deriving the total masses of galaxy clusters from observations of the intracluster medium (ICM) generally requires some prior information, in addition to the assumptions of hydrostatic equilibrium and spherical symmetry. Often, this information takes the form of particular parametrized functions used to describe the cluster gas density and temperature profiles. In this paper, we investigate the implicit priors on hydrostatic masses that result from this fully parametric approach, and the implications of such priors for scaling relations formed from those masses. We show that the application of such fully parametric models of the ICM naturally imposes a prior on the slopes of the derived scaling relations, favoring the self-similar model, and argue that this prior may be influential in practice. In contrast, this bias does not exist for techniques which adopt an explicit prior on the form of the mass profile but describe the ICM non-parametrically. Constraints on the slope of the cluster mass-temperature relation in the literature show a separation based the approach employed, with the results from fully parametric ICM modeling clustering nearer the self-similar value. Given that a primary goal of scaling relation analyses is to test the self-similar model, the application of methods subject to strong, implicit priors should be avoided. Alternative methods and best practices are discussed.

Can we undo our first impressions?: The role of reinterpretation in reversing implicit evaluations

PubMed Central

Mann, Thomas C.; Ferguson, Melissa J.

2015-01-01

Little work has examined whether implicit evaluations can be effectively “undone” after learning new revelations. Across 7 experiments, participants fully reversed their implicit evaluation of a novel target person after reinterpreting earlier information. Revision occurred across multiple implicit evaluation measures (Experiments 1a and 1b), and only when the new information prompted a reinterpretation of prior learning versus did not (Experiment 2). The updating required active consideration of the information, as it emerged only with at least moderate cognitive resources (Experiment 3). Self-reported reinterpretation predicted (Experiment 4) and mediated (Experiment 5) revised implicit evaluations beyond the separate influence of how thoughtfully participants considered the new information in general. Finally, the revised evaluations were durable three days later (Experiment 6). We discuss how these results inform existing theoretical models, and consider implications for future research. PMID:25798625

Can we undo our first impressions? The role of reinterpretation in reversing implicit evaluations.

PubMed

Mann, Thomas C; Ferguson, Melissa J

2015-06-01

Little work has examined whether implicit evaluations can be effectively "undone" after learning new revelations. Across 7 experiments, participants fully reversed their implicit evaluation of a novel target person after reinterpreting earlier information. Revision occurred across multiple implicit evaluation measures (Experiments 1a and 1b), and only when the new information prompted a reinterpretation of prior learning versus did not (Experiment 2). The updating required active consideration of the information, as it emerged only with at least moderate cognitive resources (Experiment 3). Self-reported reinterpretation predicted (Experiment 4) and mediated (Experiment 5) revised implicit evaluations beyond the separate influence of how thoughtfully participants considered the new information in general. Finally, the revised evaluations were durable 3 days later (Experiment 6). We discuss how these results inform existing theoretical models, and consider implications for future research. (c) 2015 APA, all rights reserved).

An implicit flux-split algorithm to calculate hypersonic flowfields in chemical equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1987-01-01

An implicit, finite-difference, shock-capturing algorithm that calculates inviscid, hypersonic flows in chemical equilibrium is presented. The flux vectors and flux Jacobians are differenced using a first-order, flux-split technique. The equilibrium composition of the gas is determined by minimizing the Gibbs free energy at every node point. The code is validated by comparing results over an axisymmetric hemisphere against previously published results. The algorithm is also applied to more practical configurations. The accuracy, stability, and versatility of the algorithm have been promising.

Flexible parallel implicit modelling of coupled thermal-hydraulic-mechanical processes in fractured rocks

NASA Astrophysics Data System (ADS)

Cacace, Mauro; Jacquey, Antoine B.

2017-09-01

Theory and numerical implementation describing groundwater flow and the transport of heat and solute mass in fully saturated fractured rocks with elasto-plastic mechanical feedbacks are developed. In our formulation, fractures are considered as being of lower dimension than the hosting deformable porous rock and we consider their hydraulic and mechanical apertures as scaling parameters to ensure continuous exchange of fluid mass and energy within the fracture-solid matrix system. The coupled system of equations is implemented in a new simulator code that makes use of a Galerkin finite-element technique. The code builds on a flexible, object-oriented numerical framework (MOOSE, Multiphysics Object Oriented Simulation Environment) which provides an extensive scalable parallel and implicit coupling to solve for the multiphysics problem. The governing equations of groundwater flow, heat and mass transport, and rock deformation are solved in a weak sense (either by classical Newton-Raphson or by free Jacobian inexact Newton-Krylow schemes) on an underlying unstructured mesh. Nonlinear feedbacks among the active processes are enforced by considering evolving fluid and rock properties depending on the thermo-hydro-mechanical state of the system and the local structure, i.e. degree of connectivity, of the fracture system. A suite of applications is presented to illustrate the flexibility and capability of the new simulator to address problems of increasing complexity and occurring at different spatial (from centimetres to tens of kilometres) and temporal scales (from minutes to hundreds of years).

3D Hall MHD-EPIC Simulations of Ganymede's Magnetosphere

NASA Astrophysics Data System (ADS)

Zhou, H.; Toth, G.; Jia, X.

2017-12-01

Fully kinetic modeling of a complete 3D magnetosphere is still computationally expensive and not feasible on current computers. While magnetohydrodynamic (MHD) models have been successfully applied to a wide range of plasma simulation, they cannot capture some important kinetic effects. We have recently developed a new modeling tool to embed the implicit particle-in-cell (PIC) model iPIC3D into the Block-Adaptive-Tree-Solarwind-Roe-Upwind-Scheme (BATS-R-US) magnetohydrodynamic model. This results in a kinetic model of the regions where kinetic effects are important. In addition to the MHD-EPIC modeling of the magnetosphere, the improved model presented here is now able to represent the moon as a resistive body. We use a stretched spherical grid with adaptive mesh refinement (AMR) to capture the resistive body and its boundary. A semi-implicit scheme is employed for solving the magnetic induction equation to allow time steps that are not limited by the resistivity. We have applied the model to Ganymede, the only moon in the solar system known to possess a strong intrinsic magnetic field, and included finite resistivity beneath the moon`s surface to model the electrical properties of the interior in a self-consistent manner. The kinetic effects of electrons and ions on the dayside magnetopause and tail current sheet are captured with iPIC3D. Magnetic reconnections under different upstream background conditions of several Galileo flybys are simulated to study the global reconnection rate and the magnetospheric dynamics

Implicit Learning of Recursive Context-Free Grammars

PubMed Central

Rohrmeier, Martin; Fu, Qiufang; Dienes, Zoltan

2012-01-01

Context-free grammars are fundamental for the description of linguistic syntax. However, most artificial grammar learning experiments have explored learning of simpler finite-state grammars, while studies exploring context-free grammars have not assessed awareness and implicitness. This paper explores the implicit learning of context-free grammars employing features of hierarchical organization, recursive embedding and long-distance dependencies. The grammars also featured the distinction between left- and right-branching structures, as well as between centre- and tail-embedding, both distinctions found in natural languages. People acquired unconscious knowledge of relations between grammatical classes even for dependencies over long distances, in ways that went beyond learning simpler relations (e.g. n-grams) between individual words. The structural distinctions drawn from linguistics also proved important as performance was greater for tail-embedding than centre-embedding structures. The results suggest the plausibility of implicit learning of complex context-free structures, which model some features of natural languages. They support the relevance of artificial grammar learning for probing mechanisms of language learning and challenge existing theories and computational models of implicit learning. PMID:23094021

Tidal, Residual, Intertidal Mudflat (TRIM) Model and its Applications to San Francisco Bay, California

USGS Publications Warehouse

Cheng, R.T.; Casulli, V.; Gartner, J.W.

1993-01-01

A numerical model using a semi-implicit finite-difference method for solving the two-dimensional shallow-water equations is presented. The gradient of the water surface elevation in the momentum equations and the velocity divergence in the continuity equation are finite-differenced implicitly, the remaining terms are finite-differenced explicitly. The convective terms are treated using an Eulerian-Lagrangian method. The combination of the semi-implicit finite-difference solution for the gravity wave propagation, and the Eulerian-Lagrangian treatment of the convective terms renders the numerical model unconditionally stable. When the baroclinic forcing is included, a salt transport equation is coupled to the momentum equations, and the numerical method is subject to a weak stability condition. The method of solution and the properties of the numerical model are given. This numerical model is particularly suitable for applications to coastal plain estuaries and tidal embayments in which tidal currents are dominant, and tidally generated residual currents are important. The model is applied to San Francisco Bay, California where extensive historical tides and current-meter data are available. The model calibration is considered by comparing time-series of the field data and of the model results. Alternatively, and perhaps more meaningfully, the model is calibrated by comparing the harmonic constants of tides and tidal currents derived from field data with those derived from the model. The model is further verified by comparing the model results with an independent data set representing the wet season. The strengths and the weaknesses of the model are assessed based on the results of model calibration and verification. Using the model results, the properties of tides and tidal currents in San Francisco Bay are characterized and discussed. Furthermore, using the numerical model, estimates of San Francisco Bay's volume, surface area, mean water depth, tidal prisms, and tidal excursions at spring and neap tides are computed. Additional applications of the model reveal, qualitatively the spatial distribution of residual variables. ?? 1993 Academic Press. All rights reserved.

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.

Numerical implementation, verification and validation of two-phase flow four-equation drift flux model with Jacobian-free Newton–Krylov method

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-08-24

This study presents a numerical investigation on using the Jacobian-free Newton–Krylov (JFNK) method to solve the two-phase flow four-equation drift flux model with realistic constitutive correlations (‘closure models’). The drift flux model is based on Isshi and his collaborators’ work. Additional constitutive correlations for vertical channel flow, such as two-phase flow pressure drop, flow regime map, wall boiling and interfacial heat transfer models, were taken from the RELAP5-3D Code Manual and included to complete the model. The staggered grid finite volume method and fully implicit backward Euler method was used for the spatial discretization and time integration schemes, respectively. Themore » Jacobian-free Newton–Krylov method shows no difficulty in solving the two-phase flow drift flux model with a discrete flow regime map. In addition to the Jacobian-free approach, the preconditioning matrix is obtained by using the default finite differencing method provided in the PETSc package, and consequently the labor-intensive implementation of complex analytical Jacobian matrix is avoided. Extensive and successful numerical verification and validation have been performed to prove the correct implementation of the models and methods. Code-to-code comparison with RELAP5-3D has further demonstrated the successful implementation of the drift flux model.« less

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.

A quantification method for numerical dissipation in quasi-DNS and under-resolved DNS, and effects of numerical dissipation in quasi-DNS and under-resolved DNS of turbulent channel flows

NASA Astrophysics Data System (ADS)

Komen, E. M. J.; Camilo, L. H.; Shams, A.; Geurts, B. J.; Koren, B.

2017-09-01

LES for industrial applications with complex geometries is mostly characterised by: a) a finite volume CFD method using a non-staggered arrangement of the flow variables and second order accurate spatial and temporal discretisation schemes, b) an implicit top-hat filter, where the filter length is equal to the local computational cell size, and c) eddy-viscosity type LES models. LES based on these three main characteristics is indicated as industrial LES in this paper. It becomes increasingly clear that the numerical dissipation in CFD codes typically used in industrial applications with complex geometries may inhibit the predictive capabilities of explicit LES. Therefore, there is a need to quantify the numerical dissipation rate in such CFD codes. In this paper, we quantify the numerical dissipation rate in physical space based on an analysis of the transport equation for the mean turbulent kinetic energy. Using this method, we quantify the numerical dissipation rate in a quasi-Direct Numerical Simulation (DNS) and in under-resolved DNS of, as a basic demonstration case, fully-developed turbulent channel flow. With quasi-DNS, we indicate a DNS performed using a second order accurate finite volume method typically used in industrial applications. Furthermore, we determine and explain the trends in the performance of industrial LES for fully-developed turbulent channel flow for four different Reynolds numbers for three different LES mesh resolutions. The presented explanation of the mechanisms behind the observed trends is based on an analysis of the turbulent kinetic energy budgets. The presented quantitative analyses demonstrate that the numerical errors in the industrial LES computations of the considered turbulent channel flows result in a net numerical dissipation rate which is larger than the subgrid-scale dissipation rate. No new computational methods are presented in this paper. Instead, the main new elements in this paper are our detailed quantification method for the numerical dissipation rate, the application of this method to a quasi-DNS and under-resolved DNS of fully-developed turbulent channel flow, and the explanation of the effects of the numerical dissipation on the observed trends in the performance of industrial LES for fully-developed turbulent channel flows.

A positivity-preserving, implicit defect-correction multigrid method for turbulent combustion

NASA Astrophysics Data System (ADS)

Wasserman, M.; Mor-Yossef, Y.; Greenberg, J. B.

2016-07-01

A novel, robust multigrid method for the simulation of turbulent and chemically reacting flows is developed. A survey of previous attempts at implementing multigrid for the problems at hand indicated extensive use of artificial stabilization to overcome numerical instability arising from non-linearity of turbulence and chemistry model source-terms, small-scale physics of combustion, and loss of positivity. These issues are addressed in the current work. The highly stiff Reynolds-averaged Navier-Stokes (RANS) equations, coupled with turbulence and finite-rate chemical kinetics models, are integrated in time using the unconditionally positive-convergent (UPC) implicit method. The scheme is successfully extended in this work for use with chemical kinetics models, in a fully-coupled multigrid (FC-MG) framework. To tackle the degraded performance of multigrid methods for chemically reacting flows, two major modifications are introduced with respect to the basic, Full Approximation Storage (FAS) approach. First, a novel prolongation operator that is based on logarithmic variables is proposed to prevent loss of positivity due to coarse-grid corrections. Together with the extended UPC implicit scheme, the positivity-preserving prolongation operator guarantees unconditional positivity of turbulence quantities and species mass fractions throughout the multigrid cycle. Second, to improve the coarse-grid-correction obtained in localized regions of high chemical activity, a modified defect correction procedure is devised, and successfully applied for the first time to simulate turbulent, combusting flows. The proposed modifications to the standard multigrid algorithm create a well-rounded and robust numerical method that provides accelerated convergence, while unconditionally preserving the positivity of model equation variables. Numerical simulations of various flows involving premixed combustion demonstrate that the proposed MG method increases the efficiency by a factor of up to eight times with respect to an equivalent single-grid method, and by two times with respect to an artificially-stabilized MG method.

P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems

NASA Technical Reports Server (NTRS)

Kang, Kab S.

2002-01-01

The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning

magnum.fe: A micromagnetic finite-element simulation code based on FEniCS

NASA Astrophysics Data System (ADS)

Abert, Claas; Exl, Lukas; Bruckner, Florian; Drews, André; Suess, Dieter

2013-11-01

We have developed a finite-element micromagnetic simulation code based on the FEniCS package called magnum.fe. Here we describe the numerical methods that are applied as well as their implementation with FEniCS. We apply a transformation method for the solution of the demagnetization-field problem. A semi-implicit weak formulation is used for the integration of the Landau-Lifshitz-Gilbert equation. Numerical experiments show the validity of simulation results. magnum.fe is open source and well documented. The broad feature range of the FEniCS package makes magnum.fe a good choice for the implementation of novel micromagnetic finite-element algorithms.

Finite Deformations and Internal Forces in Elastic-Plastic Crystals: Interpretations From Nonlinear Elasticity and Anharmonic Lattice Statics

DTIC Science & Technology

2009-09-01

Sec. 2, while the latter ase—which implicitly includes the effects of image forces of efects in neighboring volume elements—may be more practical rom...versetzungen und eigenspannungen,” Arch . Ration. Mech. Anal., 4, pp. 273–334. 25 Lee, E. H., 1969, “Elastic-Plastic Deformation at Finite Strains,” ASME J...Rev., 73, pp. 373–382. 27 Kroner, E., and Seeger, A., 1959, “Nicht-Lineare Elastizitatstheorie der Verset- zungen und Eigenspannungen,” Arch . Ration

Computational Fluid Dynamics: Algorithms and Supercomputers

DTIC Science & Technology

1988-03-01

1985. 1.2. Pulliam, T., and Steger, J. , Implicit Finite Difference Simulations of Three Dimensional Compressible Flow, AIAA Journal , Vol. 18, No. 2...approaches infinity, assuming N is bounded. The question as to actual performance when M is finite and N varies, is a different matter. (Note: the CYBER...PARTICLE-IN-CELL 9i% 3.b7 j.48 WEATHER FORECAST 98% 3.77 3.55 SEISMIC MIGRATION 98% 3.85 3.45 MONTE CARLO 99% 3.85 3.75 LATTICE GAUGE 100% 4.00 3.77

Finite Element Analysis of M15 and M19 Mines Under Wheeled Vehicle Load

DTIC Science & Technology

2008-03-01

the plate statically. An implicit finite element option in a code called LSDYNA was used to model the pressure generated in the explosive by the...figure 4 for the M19 mines. Maximum pressure in the explosive for each mine calculated by LSDYNA code shown for a variety of plate sizes and weights...Director U.S. Army TRADOC Analysis Center-WSMR ATTN: ATRC-WSS-R White Sands Missile Range, NM 88002 Chemical Propulsion Information Agency ATTN

Unified gas-kinetic scheme with multigrid convergence for rarefied flow study

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2017-09-01

The unified gas kinetic scheme (UGKS) is based on direct modeling of gas dynamics on the mesh size and time step scales. With the modeling of particle transport and collision in a time-dependent flux function in a finite volume framework, the UGKS can connect the flow physics smoothly from the kinetic particle transport to the hydrodynamic wave propagation. In comparison with the direct simulation Monte Carlo (DSMC) method, the current equation-based UGKS can implement implicit techniques in the updates of macroscopic conservative variables and microscopic distribution functions. The implicit UGKS significantly increases the convergence speed for steady flow computations, especially in the highly rarefied and near continuum regimes. In order to further improve the computational efficiency, for the first time, a geometric multigrid technique is introduced into the implicit UGKS, where the prediction step for the equilibrium state and the evolution step for the distribution function are both treated with multigrid acceleration. More specifically, a full approximate nonlinear system is employed in the prediction step for fast evaluation of the equilibrium state, and a correction linear equation is solved in the evolution step for the update of the gas distribution function. As a result, convergent speed has been greatly improved in all flow regimes from rarefied to the continuum ones. The multigrid implicit UGKS (MIUGKS) is used in the non-equilibrium flow study, which includes microflow, such as lid-driven cavity flow and the flow passing through a finite-length flat plate, and high speed one, such as supersonic flow over a square cylinder. The MIUGKS shows 5-9 times efficiency increase over the previous implicit scheme. For the low speed microflow, the efficiency of MIUGKS is several orders of magnitude higher than the DSMC. Even for the hypersonic flow at Mach number 5 and Knudsen number 0.1, the MIUGKS is still more than 100 times faster than the DSMC method for obtaining a convergent steady state solution.

Adaptive implicit-explicit and parallel element-by-element iteration schemes

NASA Technical Reports Server (NTRS)

Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.

1989-01-01

Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.

Algorithm For Hypersonic Flow In Chemical Equilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

A mass, momentum, and energy conserving, fully implicit, scalable algorithm for the multi-dimensional, multi-species Rosenbluth-Fokker-Planck equation

NASA Astrophysics Data System (ADS)

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

2015-09-01

In this study, we demonstrate a fully implicit algorithm for the multi-species, multidimensional Rosenbluth-Fokker-Planck equation which is exactly mass-, momentum-, and energy-conserving, and which preserves positivity. Unlike most earlier studies, we base our development on the Rosenbluth (rather than Landau) form of the Fokker-Planck collision operator, which reduces complexity while allowing for an optimal fully implicit treatment. Our discrete conservation strategy employs nonlinear constraints that force the continuum symmetries of the collision operator to be satisfied upon discretization. We converge the resulting nonlinear system iteratively using Jacobian-free Newton-Krylov methods, effectively preconditioned with multigrid methods for efficiency. Single- and multi-species numerical examples demonstrate the advertised accuracy properties of the scheme, and the superior algorithmic performance of our approach. In particular, the discretization approach is numerically shown to be second-order accurate in time and velocity space and to exhibit manifestly positive entropy production. That is, H-theorem behavior is indicated for all the examples we have tested. The solution approach is demonstrated to scale optimally with respect to grid refinement (with CPU time growing linearly with the number of mesh points), and timestep (showing very weak dependence of CPU time with time-step size). As a result, the proposed algorithm delivers several orders-of-magnitude speedup vs. explicit algorithms.

Simulation of ITG instabilities with fully kinetic ions and drift-kinetic electrons in tokamaks

NASA Astrophysics Data System (ADS)

Hu, Youjun; Chen, Yang; Parker, Scott

2017-10-01

A turbulence simulation model with fully kinetic ions and drift-kinetic electrons is being developed in the toroidal electromagnetic turbulence code GEM. This is motivated by the observation that gyrokinetic ions are not well justified in simulating turbulence in tokamak edges with steep density profile, where ρi / L is not small enough to be used a small parameter needed by the gyrokinetic ordering (here ρi is the gyro-radius of ions and L is the scale length of density profile). In this case, the fully kinetic ion model may be useful. Our model uses an implicit scheme to suppress high-frequency compressional Alfven waves and waves associated with the gyro-motion of ions. The ion orbits are advanced by using the well-known Boris scheme, which reproduces correct drift-motion even with large time-step comparable to the ion gyro-period. The field equation in this model is Ampere's law with the magnetic field eliminated by using an implicit scheme of Faraday's law. The current contributed by ions are computed by using an implicit δf method. A flux tube approximation is adopted, which makes the field equation much easier to solve. Numerical results of electromagnetic ITG obtained from this model will be presented and compared with the gyrokinetic results. This work is supported by U.S. Department of Energy, Office of Fusion Energy Sciences under Award No. DE-SC0008801.

Numerical aerodynamic simulation facility. [for flows about three-dimensional configurations

NASA Technical Reports Server (NTRS)

Bailey, F. R.; Hathaway, A. W.

1978-01-01

Critical to the advancement of computational aerodynamics capability is the ability to simulate flows about three-dimensional configurations that contain both compressible and viscous effects, including turbulence and flow separation at high Reynolds numbers. Analyses were conducted of two solution techniques for solving the Reynolds averaged Navier-Stokes equations describing the mean motion of a turbulent flow with certain terms involving the transport of turbulent momentum and energy modeled by auxiliary equations. The first solution technique is an implicit approximate factorization finite-difference scheme applied to three-dimensional flows that avoids the restrictive stability conditions when small grid spacing is used. The approximate factorization reduces the solution process to a sequence of three one-dimensional problems with easily inverted matrices. The second technique is a hybrid explicit/implicit finite-difference scheme which is also factored and applied to three-dimensional flows. Both methods are applicable to problems with highly distorted grids and a variety of boundary conditions and turbulence models.

Modeling of high pressure arc-discharge with a fully-implicit Navier-Stokes stabilized finite element flow solver

NASA Astrophysics Data System (ADS)

Sahai, A.; Mansour, N. N.; Lopez, B.; Panesi, M.

2017-05-01

This work addresses the modeling of high pressure electric discharge in an arc-heated wind tunnel. The combined numerical solution of Poisson’s equation, radiative transfer equations, and the set of Favre-averaged thermochemical nonequilibrium Navier-Stokes equations allows for the determination of the electric, radiation, and flow fields, accounting for their mutual interaction. Semi-classical statistical thermodynamics is used to determine the plasma thermodynamic properties, while transport properties are obtained from kinetic principles with the Chapman-Enskog method. A multi-temperature formulation is used to account for thermal non-equilibrium. Finally, the turbulence closure of the flow equations is obtained by means of the Spalart-Allmaras model, which requires the solution of an additional scalar transport equation. A Streamline upwind Petrov-Galerkin stabilized finite element formulation is employed to solve the Navier-Stokes equation. The electric field equation is solved using the standard Galerkin formulation. A stable formulation for the radiative transfer equations is obtained using the least-squares finite element method. The developed simulation framework has been applied to investigate turbulent plasma flows in the 20 MW Aerodynamic Heating Facility at NASA Ames Research Center. The current model is able to predict the process of energy addition and re-distribution due to Joule heating and thermal radiation, resulting in a hot central core surrounded by colder flow. The use of an unsteady three-dimensional treatment also allows the asymmetry due to a dynamic electric arc attachment point in the cathode chamber to be captured accurately. The current work paves the way for detailed estimation of operating characteristics for arc-heated wind tunnels which are critical in testing thermal protection systems.

An implicit time-marching method for studying unsteady flow with massive separation

NASA Technical Reports Server (NTRS)

Osswald, G. A.; Ghia, K. N.; Chia, U.

1985-01-01

A fully implicit time-marching method is developed such that all spatial derivatives are approximated using central differences, but no use is made of any artificial dissipation. The numerical method solves the discretized equations using Alternating Direction Implicit-Block Gaussian Elimination technique. The method is implemented in the unsteady analysis, which solves the incompressible Navier-Stokes equations in terms of vorticity and stream function in generalized orthogonal coordinates. A clustered conformal C-grid is employed, and every effort is made to resolve the various length scales in the flow problem. The metric discontinuity at the branch-cut is treated appropriately using analytic continuation. Introduction of the BGE reordering permits implicit treatment of the branch cut in the numerical method. The vorticity singularity at the cusped trailing edge is also appropriately treated. This accurate and efficient implicit method is used to study flow at Re = 1000, past a 12-percent thick symmetric Joukowski airfoil at high angle of attack 30 and 53 deg.

An implicit-iterative solution of the heat conduction equation with a radiation boundary condition

NASA Technical Reports Server (NTRS)

Williams, S. D.; Curry, D. M.

1977-01-01

For the problem of predicting one-dimensional heat transfer between conducting and radiating mediums by an implicit finite difference method, four different formulations were used to approximate the surface radiation boundary condition while retaining an implicit formulation for the interior temperature nodes. These formulations are an explicit boundary condition, a linearized boundary condition, an iterative boundary condition, and a semi-iterative boundary method. The results of these methods in predicting surface temperature on the space shuttle orbiter thermal protection system model under a variety of heating rates were compared. The iterative technique caused the surface temperature to be bounded at each step. While the linearized and explicit methods were generally more efficient, the iterative and semi-iterative techniques provided a realistic surface temperature response without requiring step size control techniques.

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.

Exploring the disruptive effects of psychopathy and aggression on group processes and group effectiveness.

PubMed

Baysinger, Michael A; Scherer, Kelly T; LeBreton, James M

2014-01-01

The present research examines the influence of implicit and explicit personality characteristics on group process and effectiveness. Individuals from 112 groups participated in 2 problem-solving tasks and completed measures of group process and effectiveness. Results indicated that groups characterized by higher levels of psychopathy and implicit aggression tended to have more dysfunctional interactions and negative perceptions of the group. In addition, task participation and negative socioemotional behaviors fully mediated the relationship between group personality traits and group commitment and cohesion, and negative socioemotional behaviors fully mediated the relationship between group personality and performance on both tasks. Implications of antisocial traits for group interactions and performance, as well as for future theory and research, are discussed. PsycINFO Database Record (c) 2014 APA, all rights reserved

Using exact solutions to develop an implicit scheme for the baroclinic primitive equations

NASA Technical Reports Server (NTRS)

Marchesin, D.

1984-01-01

The exact solutions presently obtained by means of a novel method for nonlinear initial value problems are used in the development of numerical schemes for the computer solution of these problems. The method is applied to a new, fully implicit scheme on a vertical slice of the isentropic baroclinic equations. It was not possible to find a global scale phenomenon that could be simulated by the baroclinic primitive equations on a vertical slice.

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.

Computational modeling of chemo-electro-mechanical coupling: A novel implicit monolithic finite element approach

PubMed Central

Wong, J.; Göktepe, S.; Kuhl, E.

2014-01-01

Summary Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, while the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of four days on a standard desktop computer. PMID:23798328

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

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

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

Topology optimization of finite strain viscoplastic systems under transient loads [Dynamic topology optimization based on finite strain visco-plasticity

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

Semi-implicit integration factor methods on sparse grids for high-dimensional systems

NASA Astrophysics Data System (ADS)

Wang, Dongyong; Chen, Weitao; Nie, Qing

2015-07-01

Numerical methods for partial differential equations in high-dimensional spaces are often limited by the curse of dimensionality. Though the sparse grid technique, based on a one-dimensional hierarchical basis through tensor products, is popular for handling challenges such as those associated with spatial discretization, the stability conditions on time step size due to temporal discretization, such as those associated with high-order derivatives in space and stiff reactions, remain. Here, we incorporate the sparse grids with the implicit integration factor method (IIF) that is advantageous in terms of stability conditions for systems containing stiff reactions and diffusions. We combine IIF, in which the reaction is treated implicitly and the diffusion is treated explicitly and exactly, with various sparse grid techniques based on the finite element and finite difference methods and a multi-level combination approach. The overall method is found to be efficient in terms of both storage and computational time for solving a wide range of PDEs in high dimensions. In particular, the IIF with the sparse grid combination technique is flexible and effective in solving systems that may include cross-derivatives and non-constant diffusion coefficients. Extensive numerical simulations in both linear and nonlinear systems in high dimensions, along with applications of diffusive logistic equations and Fokker-Planck equations, demonstrate the accuracy, efficiency, and robustness of the new methods, indicating potential broad applications of the sparse grid-based integration factor method.

A space-time lower-upper symmetric Gauss-Seidel scheme for the time-spectral method

NASA Astrophysics Data System (ADS)

Zhan, Lei; Xiong, Juntao; Liu, Feng

2016-05-01

The time-spectral method (TSM) offers the advantage of increased order of accuracy compared to methods using finite-difference in time for periodic unsteady flow problems. Explicit Runge-Kutta pseudo-time marching and implicit schemes have been developed to solve iteratively the space-time coupled nonlinear equations resulting from TSM. Convergence of the explicit schemes is slow because of the stringent time-step limit. Many implicit methods have been developed for TSM. Their computational efficiency is, however, still limited in practice because of delayed implicit temporal coupling, multiple iterative loops, costly matrix operations, or lack of strong diagonal dominance of the implicit operator matrix. To overcome these shortcomings, an efficient space-time lower-upper symmetric Gauss-Seidel (ST-LU-SGS) implicit scheme with multigrid acceleration is presented. In this scheme, the implicit temporal coupling term is split as one additional dimension of space in the LU-SGS sweeps. To improve numerical stability for periodic flows with high frequency, a modification to the ST-LU-SGS scheme is proposed. Numerical results show that fast convergence is achieved using large or even infinite Courant-Friedrichs-Lewy (CFL) numbers for unsteady flow problems with moderately high frequency and with the use of moderately high numbers of time intervals. The ST-LU-SGS implicit scheme is also found to work well in calculating periodic flow problems where the frequency is not known a priori and needed to be determined by using a combined Fourier analysis and gradient-based search algorithm.

Analysis of Transformation Plasticity in Steel Using a Finite Element Method Coupled with a Phase Field Model

PubMed Central

Cho, Yi-Gil; Kim, Jin-You; Cho, Hoon-Hwe; Cha, Pil-Ryung; Suh, Dong-Woo; Lee, Jae Kon; Han, Heung Nam

2012-01-01

An implicit finite element model was developed to analyze the deformation behavior of low carbon steel during phase transformation. The finite element model was coupled hierarchically with a phase field model that could simulate the kinetics and micro-structural evolution during the austenite-to-ferrite transformation of low carbon steel. Thermo-elastic-plastic constitutive equations for each phase were adopted to confirm the transformation plasticity due to the weaker phase yielding that was proposed by Greenwood and Johnson. From the simulations under various possible plastic properties of each phase, a more quantitative understanding of the origin of transformation plasticity was attempted by a comparison with the experimental observation. PMID:22558295

Finite element concepts in computational aerodynamics

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.

REDBACK: an Open-Source Highly Scalable Simulation Tool for Rock Mechanics with Dissipative Feedbacks

NASA Astrophysics Data System (ADS)

Poulet, T.; Veveakis, M.; Paesold, M.; Regenauer-Lieb, K.

2014-12-01

Multiphysics modelling has become an indispensable tool for geoscientists to simulate the complex behaviours observed in their various fields of study where multiple processes are involved, including thermal, hydraulic, mechanical and chemical (THMC) laws. This modelling activity involves simulations that are computationally expensive and its soaring uptake is tightly linked to the increasing availability of supercomputing power and easy access to powerful nonlinear solvers such as PETSc (http://www.mcs.anl.gov/petsc/). The Multiphysics Object-Oriented Simulation Environment (MOOSE) is a finite-element, multiphysics framework (http://mooseframework.org) that can harness such computational power and allow scientists to develop easily some tightly-coupled fully implicit multiphysics simulations that run automatically in parallel on large clusters. This open-source framework provides a powerful tool to collaborate on numerical modelling activities and we are contributing to its development with REDBACK (https://github.com/pou036/redback), a module for Rock mEchanics with Dissipative feedBACKs. REDBACK builds on the tensor mechanics finite strain implementation available in MOOSE to provide a THMC simulator where the energetic formulation highlights the importance of all dissipative terms in the coupled system of equations. We show first applications of fully coupled dehydration reactions triggering episodic fluid transfer through shear zones (Alevizos et al, 2014). The dimensionless approach used allows focusing on the critical underlying variables which are driving the resulting behaviours observed and this tool is specifically designed to study material instabilities underpinning geological features like faulting, folding, boudinage, shearing, fracturing, etc. REDBACK provides a collaborative and educational tool which captures the physical and mathematical understanding of such material instabilities and provides an easy way to apply this knowledge to realistic scenarios, where the size and complexity of the geometries considered, along with the material parameters distributions, add as many sources of different instabilities. References: Alevizos, S., T. Poulet, and E. Veveakis (2014), J. Geophys. Res., 119, 4558-4582, doi:10.1002/2013JB010070.

A point implicit time integration technique for slow transient flow problems

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

Kadioglu, Samet Y.; Berry, Ray A.; Martineau, Richard C.

2015-05-01

We introduce a point implicit time integration technique for slow transient flow problems. The method treats the solution variables of interest (that can be located at cell centers, cell edges, or cell nodes) implicitly and the rest of the information related to same or other variables are handled explicitly. The method does not require implicit iteration; instead it time advances the solutions in a similar spirit to explicit methods, except it involves a few additional function(s) evaluation steps. Moreover, the method is unconditionally stable, as a fully implicit method would be. This new approach exhibits the simplicity of implementation ofmore » explicit methods and the stability of implicit methods. It is specifically designed for slow transient flow problems of long duration wherein one would like to perform time integrations with very large time steps. Because the method can be time inaccurate for fast transient problems, particularly with larger time steps, an appropriate solution strategy for a problem that evolves from a fast to a slow transient would be to integrate the fast transient with an explicit or semi-implicit technique and then switch to this point implicit method as soon as the time variation slows sufficiently. We have solved several test problems that result from scalar or systems of flow equations. Our findings indicate the new method can integrate slow transient problems very efficiently; and its implementation is very robust.« less

Nonlinear Transient Growth and Boundary Layer Transition

NASA Technical Reports Server (NTRS)

Paredes, Pedro; Choudhari, Meelan M.; Li, Fei

2016-01-01

Parabolized stability equations (PSE) are used in a variational approach to study the optimal, non-modal disturbance growth in a Mach 3 at plate boundary layer and a Mach 6 circular cone boundary layer. As noted in previous works, the optimal initial disturbances correspond to steady counter-rotating streamwise vortices, which subsequently lead to the formation of streamwise-elongated structures, i.e., streaks, via a lift-up effect. The nonlinear evolution of the linearly optimal stationary perturbations is computed using the nonlinear plane-marching PSE for stationary perturbations. A fully implicit marching technique is used to facilitate the computation of nonlinear streaks with large amplitudes. To assess the effect of the finite-amplitude streaks on transition, the linear form of plane- marching PSE is used to investigate the instability of the boundary layer flow modified by spanwise periodic streaks. The onset of bypass transition is estimated by using an N- factor criterion based on the amplification of the streak instabilities. Results show that, for both flow configurations of interest, streaks of sufficiently large amplitude can lead to significantly earlier onset of transition than that in an unperturbed boundary layer without any streaks.

Latent hardening size effect in small-scale plasticity

NASA Astrophysics Data System (ADS)

Bardella, Lorenzo; Segurado, Javier; Panteghini, Andrea; Llorca, Javier

2013-07-01

We aim at understanding the multislip behaviour of metals subject to irreversible deformations at small-scales. By focusing on the simple shear of a constrained single-crystal strip, we show that discrete Dislocation Dynamics (DD) simulations predict a strong latent hardening size effect, with smaller being stronger in the range [1.5 µm, 6 µm] for the strip height. We attempt to represent the DD pseudo-experimental results by developing a flow theory of Strain Gradient Crystal Plasticity (SGCP), involving both energetic and dissipative higher-order terms and, as a main novelty, a strain gradient extension of the conventional latent hardening. In order to discuss the capability of the SGCP theory proposed, we implement it into a Finite Element (FE) code and set its material parameters on the basis of the DD results. The SGCP FE code is specifically developed for the boundary value problem under study so that we can implement a fully implicit (Backward Euler) consistent algorithm. Special emphasis is placed on the discussion of the role of the material length scales involved in the SGCP model, from both the mechanical and numerical points of view.

Multigrid direct numerical simulation of the whole process of flow transition in 3-D boundary layers

NASA Technical Reports Server (NTRS)

Liu, Chaoqun; Liu, Zhining

1993-01-01

A new technology was developed in this study which provides a successful numerical simulation of the whole process of flow transition in 3-D boundary layers, including linear growth, secondary instability, breakdown, and transition at relatively low CPU cost. Most other spatial numerical simulations require high CPU cost and blow up at the stage of flow breakdown. A fourth-order finite difference scheme on stretched and staggered grids, a fully implicit time marching technique, a semi-coarsening multigrid based on the so-called approximate line-box relaxation, and a buffer domain for the outflow boundary conditions were all used for high-order accuracy, good stability, and fast convergence. A new fine-coarse-fine grid mapping technique was developed to keep the code running after the laminar flow breaks down. The computational results are in good agreement with linear stability theory, secondary instability theory, and some experiments. The cost for a typical case with 162 x 34 x 34 grid is around 2 CRAY-YMP CPU hours for 10 T-S periods.

Explicit formulation of second and third order optical nonlinearity in the FDTD framework

NASA Astrophysics Data System (ADS)

Varin, Charles; Emms, Rhys; Bart, Graeme; Fennel, Thomas; Brabec, Thomas

2018-01-01

The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires solving iteratively an implicit form of Maxwell's equations over the entire numerical space and at each time step. Reaching numerical convergence demands significant computational resources and practical implementation often requires major modifications to the core FDTD engine. In this paper, we present an explicit method to include second and third order optical nonlinearity in the FDTD framework based on a nonlinear generalization of the Lorentz dispersion model. A formal derivation of the nonlinear Lorentz dispersion equation is equally provided, starting from the quantum mechanical equations describing nonlinear optics in the two-level approximation. With the proposed approach, numerical integration of optical nonlinearity and dispersion in FDTD is intuitive, transparent, and fully explicit. A strong-field formulation is also proposed, which opens an interesting avenue for FDTD-based modelling of the extreme nonlinear optics phenomena involved in laser filamentation and femtosecond micromachining of dielectrics.

Mathematical modeling of polymer flooding using the unstructured Voronoi grid

NASA Astrophysics Data System (ADS)

Kireev, T. F.; Bulgakova, G. T.; Khatmullin, I. F.

2017-12-01

Effective recovery of unconventional oil reserves necessitates development of enhanced oil recovery techniques such as polymer flooding. The study investigated the model of polymer flooding with effects of adsorption and water salinity. The model takes into account six components that include elements of the classic black oil model. These components are polymer, salt, water, dead oil, dry gas and dissolved gas. Solution of the problem is obtained by finite volume method on unstructured Voronoi grid using fully implicit scheme and the Newton’s method. To compare several different grid configurations numerical simulation of polymer flooding is performed. The oil rates obtained by a hexagonal locally refined Voronoi grid are shown to be more accurate than the oil rates obtained by a rectangular grid with the same number of cells. The latter effect is caused by high solution accuracy near the wells due to the local grid refinement. Minimization of the grid orientation effect caused by the hexagonal pattern is also demonstrated. However, in the inter-well regions with large Voronoi cells flood front tends to flatten and the water breakthrough moment is smoothed.

NASCRIN - NUMERICAL ANALYSIS OF SCRAMJET INLET

NASA Technical Reports Server (NTRS)

Kumar, A.

1994-01-01

The NASCRIN program was developed for analyzing two-dimensional flow fields in supersonic combustion ramjet (scramjet) inlets. NASCRIN solves the two-dimensional Euler or Navier-Stokes equations in conservative form by an unsplit, explicit, two-step finite-difference method. A more recent explicit-implicit, two-step scheme has also been incorporated in the code for viscous flow analysis. An algebraic, two-layer eddy-viscosity model is used for the turbulent flow calculations. NASCRIN can analyze both inviscid and viscous flows with no struts, one strut, or multiple struts embedded in the flow field. NASCRIN can be used in a quasi-three-dimensional sense for some scramjet inlets under certain simplifying assumptions. Although developed for supersonic internal flow, NASCRIN may be adapted to a variety of other flow problems. In particular, it should be readily adaptable to subsonic inflow with supersonic outflow, supersonic inflow with subsonic outflow, or fully subsonic flow. The NASCRIN program is available for batch execution on the CDC CYBER 203. The vectorized FORTRAN version was developed in 1983. NASCRIN has a central memory requirement of approximately 300K words for a grid size of about 3,000 points.

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.

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

An implicit dispersive transport algorithm for the US Geological Survey MOC3D solute-transport model

USGS Publications Warehouse

Kipp, K.L.; Konikow, Leonard F.; Hornberger, G.Z.

1998-01-01

This report documents an extension to the U.S. Geological Survey MOC3D transport model that incorporates an implicit-in-time difference approximation for the dispersive transport equation, including source/sink terms. The original MOC3D transport model (Version 1) uses the method of characteristics to solve the transport equation on the basis of the velocity field. The original MOC3D solution algorithm incorporates particle tracking to represent advective processes and an explicit finite-difference formulation to calculate dispersive fluxes. The new implicit procedure eliminates several stability criteria required for the previous explicit formulation. This allows much larger transport time increments to be used in dispersion-dominated problems. The decoupling of advective and dispersive transport in MOC3D, however, is unchanged. With the implicit extension, the MOC3D model is upgraded to Version 2. A description of the numerical method of the implicit dispersion calculation, the data-input requirements and output options, and the results of simulator testing and evaluation are presented. Version 2 of MOC3D was evaluated for the same set of problems used for verification of Version 1. These test results indicate that the implicit calculation of Version 2 matches the accuracy of Version 1, yet is more efficient than the explicit calculation for transport problems that are characterized by a grid Peclet number less than about 1.0.

Computational simulation of laser heat processing of materials

NASA Astrophysics Data System (ADS)

Shankar, Vijaya; Gnanamuthu, Daniel

1987-04-01

A computational model simulating the laser heat treatment of AISI 4140 steel plates with a CW CO2 laser beam has been developed on the basis of the three-dimensional, time-dependent heat equation (subject to the appropriate boundary conditions). The solution method is based on Newton iteration applied to a triple-approximate factorized form of the equation. The method is implicit and time-accurate; the maintenance of time-accuracy in the numerical formulation is noted to be critical for the simulation of finite length workpieces with a finite laser beam dwell time.

A comparison of two central difference schemes for solving the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Maksymiuk, C. M.; Swanson, R. C.; Pulliam, T. H.

1990-01-01

Five viscous transonic airfoil cases were computed by two significantly different computational fluid dynamics codes: An explicit finite-volume algorithm with multigrid, and an implicit finite-difference approximate-factorization method with Eigenvector diagonalization. Both methods are described in detail, and their performance on the test cases is compared. The codes utilized the same grids, turbulence model, and computer to provide the truest test of the algorithms. The two approaches produce very similar results, which, for attached flows, also agree well with experimental results; however, the explicit code is considerably faster.

The Crank Nicolson Time Integrator for EMPHASIS.

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

McGregor, Duncan Alisdair Odum; Love, Edward; Kramer, Richard Michael Jack

2018-03-01

We investigate the use of implicit time integrators for finite element time domain approxi- mations of Maxwell's equations in vacuum. We discretize Maxwell's equations in time using Crank-Nicolson and in 3D space using compatible finite elements. We solve the system by taking a single step of Newton's method and inverting the Eddy-Current Schur complement allowing for the use of standard preconditioning techniques. This approach also generalizes to more complex material models that can include the Unsplit PML. We present verification results and demonstrate performance at CFL numbers up to 1000.

Application of a lower-upper implicit scheme and an interactive grid generation for turbomachinery flow field simulations

NASA Technical Reports Server (NTRS)

Choo, Yung K.; Soh, Woo-Yung; Yoon, Seokkwan

1989-01-01

A finite-volume lower-upper (LU) implicit scheme is used to simulate an inviscid flow in a tubine cascade. This approximate factorization scheme requires only the inversion of sparse lower and upper triangular matrices, which can be done efficiently without extensive storage. As an implicit scheme it allows a large time step to reach the steady state. An interactive grid generation program (TURBO), which is being developed, is used to generate grids. This program uses the control point form of algebraic grid generation which uses a sparse collection of control points from which the shape and position of coordinate curves can be adjusted. A distinct advantage of TURBO compared with other grid generation programs is that it allows the easy change of local mesh structure without affecting the grid outside the domain of independence. Sample grids are generated by TURBO for a compressor rotor blade and a turbine cascade. The turbine cascade flow is simulated by using the LU implicit scheme on the grid generated by TURBO.

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.

Development and application of the GIM code for the Cyber 203 computer

NASA Technical Reports Server (NTRS)

Stainaker, J. F.; Robinson, M. A.; Rawlinson, E. G.; Anderson, P. G.; Mayne, A. W.; Spradley, L. W.

1982-01-01

The GIM computer code for fluid dynamics research was developed. Enhancement of the computer code, implicit algorithm development, turbulence model implementation, chemistry model development, interactive input module coding and wing/body flowfield computation are described. The GIM quasi-parabolic code development was completed, and the code used to compute a number of example cases. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and implicit finite difference scheme were also added. Development was completed on the interactive module for generating the input data for GIM. Solutions for inviscid hypersonic flow over a wing/body configuration are also presented.

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

Topology optimization of finite strain viscoplastic systems under transient loads

DOE PAGES

Ivarsson, Niklas; Wallin, Mathias; Tortorelli, Daniel

2018-02-08

In this paper, a transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capabilitymore » of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. Finally, the numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.« less

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.

1989-01-01

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

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).

TAIR- TRANSONIC AIRFOIL ANALYSIS COMPUTER CODE

NASA Technical Reports Server (NTRS)

Dougherty, F. C.

1994-01-01

The Transonic Airfoil analysis computer code, TAIR, was developed to employ a fast, fully implicit algorithm to solve the conservative full-potential equation for the steady transonic flow field about an arbitrary airfoil immersed in a subsonic free stream. The full-potential formulation is considered exact under the assumptions of irrotational, isentropic, and inviscid flow. These assumptions are valid for a wide range of practical transonic flows typical of modern aircraft cruise conditions. The primary features of TAIR include: a new fully implicit iteration scheme which is typically many times faster than classical successive line overrelaxation algorithms; a new, reliable artifical density spatial differencing scheme treating the conservative form of the full-potential equation; and a numerical mapping procedure capable of generating curvilinear, body-fitted finite-difference grids about arbitrary airfoil geometries. Three aspects emphasized during the development of the TAIR code were reliability, simplicity, and speed. The reliability of TAIR comes from two sources: the new algorithm employed and the implementation of effective convergence monitoring logic. TAIR achieves ease of use by employing a "default mode" that greatly simplifies code operation, especially by inexperienced users, and many useful options including: several airfoil-geometry input options, flexible user controls over program output, and a multiple solution capability. The speed of the TAIR code is attributed to the new algorithm and the manner in which it has been implemented. Input to the TAIR program consists of airfoil coordinates, aerodynamic and flow-field convergence parameters, and geometric and grid convergence parameters. The airfoil coordinates for many airfoil shapes can be generated in TAIR from just a few input parameters. Most of the other input parameters have default values which allow the user to run an analysis in the default mode by specifing only a few input parameters. Output from TAIR may include aerodynamic coefficients, the airfoil surface solution, convergence histories, and printer plots of Mach number and density contour maps. The TAIR program is written in FORTRAN IV for batch execution and has been implemented on a CDC 7600 computer with a central memory requirement of approximately 155K (octal) of 60 bit words. The TAIR program was developed in 1981.

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

NASA Technical Reports Server (NTRS)

Adelman, H. M.; Haftka, R. T.; Robinson, J. C.

1982-01-01

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame tst article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described.

Studies of implicit and explicit solution techniques in transient thermal analysis of structures

NASA Astrophysics Data System (ADS)

Adelman, H. M.; Haftka, R. T.; Robinson, J. C.

1982-08-01

Studies aimed at an increase in the efficiency of calculating transient temperature fields in complex aerospace vehicle structures are reported. The advantages and disadvantages of explicit and implicit algorithms are discussed and a promising set of implicit algorithms with variable time steps, known as GEARIB, is described. Test problems, used for evaluating and comparing various algorithms, are discussed and finite element models of the configurations are described. These problems include a coarse model of the Space Shuttle wing, an insulated frame tst article, a metallic panel for a thermal protection system, and detailed models of sections of the Space Shuttle wing. Results generally indicate a preference for implicit over explicit algorithms for transient structural heat transfer problems when the governing equations are stiff (typical of many practical problems such as insulated metal structures). The effects on algorithm performance of different models of an insulated cylinder are demonstrated. The stiffness of the problem is highly sensitive to modeling details and careful modeling can reduce the stiffness of the equations to the extent that explicit methods may become the best choice. Preliminary applications of a mixed implicit-explicit algorithm and operator splitting techniques for speeding up the solution of the algebraic equations are also described.

Stability analysis of implicit time discretizations for the Compton-scattering Fokker-Planck equation

NASA Astrophysics Data System (ADS)

Densmore, Jeffery D.; Warsa, James S.; Lowrie, Robert B.; Morel, Jim E.

2009-09-01

The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.

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

IMPLEMENTATION AND VALIDATION OF A FULLY IMPLICIT ACCUMULATOR MODEL IN RELAP-7

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

Zhao, Haihua; Zou, Ling; Zhang, Hongbin

2016-01-01

This paper presents the implementation and validation of an accumulator model in RELAP-7 under the framework of preconditioned Jacobian free Newton Krylov (JFNK) method, based on the similar model used in RELAP5. RELAP-7 is a new nuclear reactor system safety analysis code being developed at the Idaho National Laboratory (INL). RELAP-7 is a fully implicit system code. The JFNK and preconditioning methods used in RELAP-7 is briefly discussed. The slightly modified accumulator model is summarized for completeness. The implemented model was validated with LOFT L3-1 test and benchmarked with RELAP5 results. RELAP-7 and RELAP5 had almost identical results for themore » accumulator gas pressure and water level, although there were some minor difference in other parameters such as accumulator gas temperature and tank wall temperature. One advantage of the JFNK method is its easiness to maintain and modify models due to fully separation of numerical methods from physical models. It would be straightforward to extend the current RELAP-7 accumulator model to simulate the advanced accumulator design.« less

Second order accurate finite difference approximations for the transonic small disturbance equation and the full potential equation

NASA Technical Reports Server (NTRS)

Mostrel, M. M.

1988-01-01

New shock-capturing finite difference approximations for solving two scalar conservation law nonlinear partial differential equations describing inviscid, isentropic, compressible flows of aerodynamics at transonic speeds are presented. A global linear stability theorem is applied to these schemes in order to derive a necessary and sufficient condition for the finite element method. A technique is proposed to render the described approximations total variation-stable by applying the flux limiters to the nonlinear terms of the difference equation dimension by dimension. An entropy theorem applying to the approximations is proved, and an implicit, forward Euler-type time discretization of the approximation is presented. Results of some numerical experiments using the approximations are reported.

Benchmark solution of the dynamic response of a spherical shell at finite strain

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

Versino, Daniele; Brock, Jerry S.

2016-09-28

Our paper describes the development of high fidelity solutions for the study of homogeneous (elastic and inelastic) spherical shells subject to dynamic loading and undergoing finite deformations. The goal of the activity is to provide high accuracy results that can be used as benchmark solutions for the verification of computational physics codes. Furthermore, the equilibrium equations for the geometrically non-linear problem are solved through mode expansion of the displacement field and the boundary conditions are enforced in a strong form. Time integration is performed through high-order implicit Runge–Kutta schemes. Finally, we evaluate accuracy and convergence of the proposed method bymore » means of numerical examples with finite deformations and material non-linearities and inelasticity.« less

Nonlinear truncation error analysis of finite difference schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Klopfer, G. H.; Mcrae, D. S.

1983-01-01

It is pointed out that, in general, dissipative finite difference integration schemes have been found to be quite robust when applied to the Euler equations of gas dynamics. The present investigation considers a modified equation analysis of both implicit and explicit finite difference techniques as applied to the Euler equations. The analysis is used to identify those error terms which contribute most to the observed solution errors. A technique for analytically removing the dominant error terms is demonstrated, resulting in a greatly improved solution for the explicit Lax-Wendroff schemes. It is shown that the nonlinear truncation errors are quite large and distributed quite differently for each of the three conservation equations as applied to a one-dimensional shock tube problem.

Finite element dynamic analysis on CDC STAR-100 computer

NASA Technical Reports Server (NTRS)

Noor, A. K.; Lambiotte, J. J., Jr.

1978-01-01

Computational algorithms are presented for the finite element dynamic analysis of structures on the CDC STAR-100 computer. The spatial behavior is described using higher-order finite elements. The temporal behavior is approximated by using either the central difference explicit scheme or Newmark's implicit scheme. In each case the analysis is broken up into a number of basic macro-operations. Discussion is focused on the organization of the computation and the mode of storage of different arrays to take advantage of the STAR pipeline capability. The potential of the proposed algorithms is discussed and CPU times are given for performing the different macro-operations for a shell modeled by higher order composite shallow shell elements having 80 degrees of freedom.

Assessing a mini-application as a performance proxy for a finite element method engineering application

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

Lin, Paul T.; Heroux, Michael A.; Barrett, Richard F.

The performance of a large-scale, production-quality science and engineering application (‘app’) is often dominated by a small subset of the code. Even within that subset, computational and data access patterns are often repeated, so that an even smaller portion can represent the performance-impacting features. If application developers, parallel computing experts, and computer architects can together identify this representative subset and then develop a small mini-application (‘miniapp’) that can capture these primary performance characteristics, then this miniapp can be used to both improve the performance of the app as well as provide a tool for co-design for the high-performance computing community.more » However, a critical question is whether a miniapp can effectively capture key performance behavior of an app. This study provides a comparison of an implicit finite element semiconductor device modeling app on unstructured meshes with an implicit finite element miniapp on unstructured meshes. The goal is to assess whether the miniapp is predictive of the performance of the app. Finally, single compute node performance will be compared, as well as scaling up to 16,000 cores. Results indicate that the miniapp can be reasonably predictive of the performance characteristics of the app for a single iteration of the solver on a single compute node.« less

Assessing a mini-application as a performance proxy for a finite element method engineering application

DOE PAGES

Lin, Paul T.; Heroux, Michael A.; Barrett, Richard F.; ...

2015-07-30

The performance of a large-scale, production-quality science and engineering application (‘app’) is often dominated by a small subset of the code. Even within that subset, computational and data access patterns are often repeated, so that an even smaller portion can represent the performance-impacting features. If application developers, parallel computing experts, and computer architects can together identify this representative subset and then develop a small mini-application (‘miniapp’) that can capture these primary performance characteristics, then this miniapp can be used to both improve the performance of the app as well as provide a tool for co-design for the high-performance computing community.more » However, a critical question is whether a miniapp can effectively capture key performance behavior of an app. This study provides a comparison of an implicit finite element semiconductor device modeling app on unstructured meshes with an implicit finite element miniapp on unstructured meshes. The goal is to assess whether the miniapp is predictive of the performance of the app. Finally, single compute node performance will be compared, as well as scaling up to 16,000 cores. Results indicate that the miniapp can be reasonably predictive of the performance characteristics of the app for a single iteration of the solver on a single compute node.« less

Simulation of separated flow past a bluff body using Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Ghia, K. N.; Ghia, U.; Osswald, G. A.; Liu, C. A.

1987-01-01

Two-dimensional flow past a bluff body is presently simulated on the basis of an analysis that employs the incompressible, unsteady Navier-Stokes equations in terms of vorticity and stream function. The fully implicit, time-marching, alternating-direction, implicit-block Gaussian elimination used is a direct method with second-order spatial accuracy; this allows it to avoid the introduction of any artificial viscosity. Attention is given to the simulation of flow past a circular cylinder with and without symmetry, requiring the use of either the half or the full cylinder, respectively.

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

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

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Development of cost-effective surfactant flooding technology. First annual report for the period, September 30, 1992--September 29, 1993

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

Pope, G.A.; Sepehrnoori, K.

1994-08-01

This research consists of the parallel development of a new chemical flooding simulator and the application of existing UTCHEM simulation code to model surfactant flooding. The new code is based upon a completely new numerical method that combines for the first time higher order finite difference methods, flux limiters, and implicit algorithms. Early results indicate that this approach has significant advantages in some problems and will likely enable simulation of much larger and more realistic chemical floods once it is fully developed. Additional improvements have also been made to the UTCHEM code and it has been applied for the firstmore » time to the study of stochastic reservoirs with and without horizontal wells to evaluate methods to reduce the cost and risk of surfactant flooding. During the first year of this contract, significant progress has been made on both of these tasks. The authors have found that there are indeed significant differences between the performance predictions based upon the traditional layered reservoir description and the more realistic and flexible descriptions using geostatistics. These preliminary studies of surfactant flooding using horizontal wells shows that although they have significant potential to greatly reduce project life and thus improve the economics of the process, their use requires accurate reservoir descriptions and simulations to be effective. Much more needs to be done to fully understand and optimize their use and develop reliable design criteria.« less

Processing implicit control: evidence from reading times

PubMed Central

McCourt, Michael; Green, Jeffrey J.; Lau, Ellen; Williams, Alexander

2015-01-01

Sentences such as “The ship was sunk to collect the insurance” exhibit an unusual form of anaphora, implicit control, where neither anaphor nor antecedent is audible. The non-finite reason clause has an understood subject, PRO, that is anaphoric; here it may be understood as naming the agent of the event of the host clause. Yet since the host is a short passive, this agent is realized by no audible dependent. The putative antecedent to PRO is therefore implicit, which it normally cannot be. What sorts of representations subserve the comprehension of this dependency? Here we present four self-paced reading time studies directed at this question. Previous work showed no processing cost for implicit vs. explicit control, and took this to support the view that PRO is linked syntactically to a silent argument in the passive. We challenge this conclusion by reporting that we also find no processing cost for remote implicit control, as in: “The ship was sunk. The reason was to collect the insurance.” Here the dependency crosses two independent sentences, and so cannot, we argue, be mediated by syntax. Our Experiments 1–4 examined the processing of both implicit (short passive) and explicit (active or long passive) control in both local and remote configurations. Experiments 3 and 4 added either “3 days ago” or “just in order” to the local conditions, to control for the distance between the passive and infinitival verbs, and for the predictability of the reason clause, respectively. We replicate the finding that implicit control does not impose an additional processing cost. But critically we show that remote control does not impose a processing cost either. Reading times at the reason clause were never slower when control was remote. In fact they were always faster. Thus, efficient processing of local implicit control cannot show that implicit control is mediated by syntax; nor, in turn, that there is a silent but grammatically active argument in passives. PMID:26579016

Flow adjustment inside large finite-size wind farms approaching the infinite wind farm regime

NASA Astrophysics Data System (ADS)

Wu, Ka Ling; Porté-Agel, Fernando

2017-04-01

Due to the increasing number and the growing size of wind farms, the distance among them continues to decrease. Thus, it is necessary to understand how these large finite-size wind farms and their wakes could interfere the atmospheric boundary layer (ABL) dynamics and adjacent wind farms. Fully-developed flow inside wind farms has been extensively studied through numerical simulations of infinite wind farms. The transportation of momentum and energy is only vertical and the advection of them is neglected in these infinite wind farms. However, less attention has been paid to examine the length of wind farms required to reach such asymptotic regime and the ABL dynamics in the leading and trailing edges of the large finite-size wind farms. Large eddy simulations are performed in this study to investigate the flow adjustment inside large finite-size wind farms in conventionally-neutral boundary layer with the effect of Coriolis force and free-atmosphere stratification from 1 to 5 K/km. For the large finite-size wind farms considered in the present work, when the potential temperature lapse rate is 5 K/km, the wind farms exceed the height of the ABL by two orders of magnitude for the incoming flow inside the farms to approach the fully-developed regime. An entrance fetch of approximately 40 times of the ABL height is also required for such flow adjustment. At the fully-developed flow regime of the large finite-size wind farms, the flow characteristics match those of infinite wind farms even though they have different adjustment length scales. The role of advection at the entrance and exit regions of the large finite-size wind farms is also examined. The interaction between the internal boundary layer developed above the large finite-size wind farms and the ABL under different potential temperature lapse rates are compared. It is shown that the potential temperature lapse rate plays a role in whether the flow inside the large finite-size wind farms adjusts to the fully-developed flow regime. The flow characteristics of the wake of these large finite-size wind farms are reported to forecast the effect of large finite-size wind farms on adjacent wind farms. A power deficit as large as 8% is found at a distance of 10 km downwind from the large finite-size wind farms.

Convergence Acceleration of Runge-Kutta Schemes for Solving the Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Swanson, Roy C., Jr.; Turkel, Eli; Rossow, C.-C.

2007-01-01

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 can be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. This RK/implicit scheme is used as a smoother for multigrid. Fourier analysis is applied to determine damping properties. Numerical dissipation operators based on the Roe scheme, a matrix dissipation, and the CUSP scheme are considered in evaluating the RK/implicit scheme. In addition, the effect of the number of RK stages is examined. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. Turbulent flows over an airfoil and wing at subsonic and transonic conditions are computed. The effects of the cell aspect ratio on convergence are investigated for Reynolds numbers between 5:7 x 10(exp 6) and 100 x 10(exp 6). It is demonstrated that the implicit preconditioner can reduce the computational time of a well-tuned standard RK scheme by a factor between four and ten.

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.

Vectorization on the star computer of several numerical methods for a fluid flow problem

NASA Technical Reports Server (NTRS)

Lambiotte, J. J., Jr.; Howser, L. M.

1974-01-01

A reexamination of some numerical methods is considered in light of the new class of computers which use vector streaming to achieve high computation rates. A study has been made of the effect on the relative efficiency of several numerical methods applied to a particular fluid flow problem when they are implemented on a vector computer. The method of Brailovskaya, the alternating direction implicit method, a fully implicit method, and a new method called partial implicitization have been applied to the problem of determining the steady state solution of the two-dimensional flow of a viscous imcompressible fluid in a square cavity driven by a sliding wall. Results are obtained for three mesh sizes and a comparison is made of the methods for serial computation.

An Implicit Solver on A Parallel Block-Structured Adaptive Mesh Grid for FLASH

NASA Astrophysics Data System (ADS)

Lee, D.; Gopal, S.; Mohapatra, P.

2012-07-01

We introduce a fully implicit solver for FLASH based on a Jacobian-Free Newton-Krylov (JFNK) approach with an appropriate preconditioner. The main goal of developing this JFNK-type implicit solver is to provide efficient high-order numerical algorithms and methodology for simulating stiff systems of differential equations on large-scale parallel computer architectures. A large number of natural problems in nonlinear physics involve a wide range of spatial and time scales of interest. A system that encompasses such a wide magnitude of scales is described as "stiff." A stiff system can arise in many different fields of physics, including fluid dynamics/aerodynamics, laboratory/space plasma physics, low Mach number flows, reactive flows, radiation hydrodynamics, and geophysical flows. One of the big challenges in solving such a stiff system using current-day computational resources lies in resolving time and length scales varying by several orders of magnitude. We introduce FLASH's preliminary implementation of a time-accurate JFNK-based implicit solver in the framework of FLASH's unsplit hydro solver.

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

A Semi-implicit Treatment of Porous Media in Steady-State CFD.

PubMed

Domaingo, Andreas; Langmayr, Daniel; Somogyi, Bence; Almbauer, Raimund

There are many situations in computational fluid dynamics which require the definition of source terms in the Navier-Stokes equations. These source terms not only allow to model the physics of interest but also have a strong impact on the reliability, stability, and convergence of the numerics involved. Therefore, sophisticated numerical approaches exist for the description of such source terms. In this paper, we focus on the source terms present in the Navier-Stokes or Euler equations due to porous media-in particular the Darcy-Forchheimer equation. We introduce a method for the numerical treatment of the source term which is independent of the spatial discretization and based on linearization. In this description, the source term is treated in a fully implicit way whereas the other flow variables can be computed in an implicit or explicit manner. This leads to a more robust description in comparison with a fully explicit approach. The method is well suited to be combined with coarse-grid-CFD on Cartesian grids, which makes it especially favorable for accelerated solution of coupled 1D-3D problems. To demonstrate the applicability and robustness of the proposed method, a proof-of-concept example in 1D, as well as more complex examples in 2D and 3D, is presented.

Fully implicit adaptive mesh refinement algorithm for reduced MHD

NASA Astrophysics Data System (ADS)

Philip, Bobby; Pernice, Michael; Chacon, Luis

2006-10-01

In the macroscopic simulation of plasmas, the numerical modeler is faced with the challenge of dealing with multiple time and length scales. Traditional approaches based on explicit time integration techniques and fixed meshes are not suitable for this challenge, as such approaches prevent the modeler from using realistic plasma parameters to keep the computation feasible. We propose here a novel approach, based on implicit methods and structured adaptive mesh refinement (SAMR). Our emphasis is on both accuracy and scalability with the number of degrees of freedom. As a proof-of-principle, we focus on the reduced resistive MHD model as a basic MHD model paradigm, which is truly multiscale. The approach taken here is to adapt mature physics-based technology to AMR grids, and employ AMR-aware multilevel techniques (such as fast adaptive composite grid --FAC-- algorithms) for scalability. We demonstrate that the concept is indeed feasible, featuring near-optimal scalability under grid refinement. Results of fully-implicit, dynamically-adaptive AMR simulations in challenging dissipation regimes will be presented on a variety of problems that benefit from this capability, including tearing modes, the island coalescence instability, and the tilt mode instability. L. Chac'on et al., J. Comput. Phys. 178 (1), 15- 36 (2002) B. Philip, M. Pernice, and L. Chac'on, Lecture Notes in Computational Science and Engineering, accepted (2006)

Emotion effects on implicit and explicit musical memory in normal aging.

PubMed

Narme, Pauline; Peretz, Isabelle; Strub, Marie-Laure; Ergis, Anne-Marie

2016-12-01

Normal aging affects explicit memory while leaving implicit memory relatively spared. Normal aging also modifies how emotions are processed and experienced, with increasing evidence that older adults (OAs) focus more on positive information than younger adults (YAs). The aim of the present study was to investigate how age-related changes in emotion processing influence explicit and implicit memory. We used emotional melodies that differed in terms of valence (positive or negative) and arousal (high or low). Implicit memory was assessed with a preference task exploiting exposure effects, and explicit memory with a recognition task. Results indicated that effects of valence and arousal interacted to modulate both implicit and explicit memory in YAs. In OAs, recognition was poorer than in YAs; however, recognition of positive and high-arousal (happy) studied melodies was comparable. Insofar as socioemotional selectivity theory (SST) predicts a preservation of the recognition of positive information, our findings are not fully consistent with the extension of this theory to positive melodies since recognition of low-arousal (peaceful) studied melodies was poorer in OAs. In the preference task, YAs showed stronger exposure effects than OAs, suggesting an age-related decline of implicit memory. This impairment is smaller than the one observed for explicit memory (recognition), extending to the musical domain the dissociation between explicit memory decline and implicit memory relative preservation in aging. Finally, the disproportionate preference for positive material seen in OAs did not translate into stronger exposure effects for positive material suggesting no age-related emotional bias in implicit memory. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Practical aspects of prestack depth migration with finite differences

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

Ober, C.C.; Oldfield, R.A.; Womble, D.E.

1997-07-01

Finite-difference, prestack, depth migrations offers significant improvements over Kirchhoff methods in imaging near or under salt structures. The authors have implemented a finite-difference prestack depth migration algorithm for use on massively parallel computers which is discussed. The image quality of the finite-difference scheme has been investigated and suggested improvements are discussed. In this presentation, the authors discuss an implicit finite difference migration code, called Salvo, that has been developed through an ACTI (Advanced Computational Technology Initiative) joint project. This code is designed to be efficient on a variety of massively parallel computers. It takes advantage of both frequency and spatialmore » parallelism as well as the use of nodes dedicated to data input/output (I/O). Besides giving an overview of the finite-difference algorithm and some of the parallelism techniques used, migration results using both Kirchhoff and finite-difference migration will be presented and compared. The authors start out with a very simple Cartoon model where one can intuitively see the multiple travel paths and some of the potential problems that will be encountered with Kirchhoff migration. More complex synthetic models as well as results from actual seismic data from the Gulf of Mexico will be shown.« less

Numerical solution of the Saint-Venant equations by an efficient hybrid finite-volume/finite-difference method

NASA Astrophysics Data System (ADS)

Lai, Wencong; Khan, Abdul A.

2018-04-01

A computationally efficient hybrid finite-volume/finite-difference method is proposed for the numerical solution of Saint-Venant equations in one-dimensional open channel flows. The method adopts a mass-conservative finite volume discretization for the continuity equation and a semi-implicit finite difference discretization for the dynamic-wave momentum equation. The spatial discretization of the convective flux term in the momentum equation employs an upwind scheme and the water-surface gradient term is discretized using three different schemes. The performance of the numerical method is investigated in terms of efficiency and accuracy using various examples, including steady flow over a bump, dam-break flow over wet and dry downstream channels, wetting and drying in a parabolic bowl, and dam-break floods in laboratory physical models. Numerical solutions from the hybrid method are compared with solutions from a finite volume method along with analytic solutions or experimental measurements. Comparisons demonstrates that the hybrid method is efficient, accurate, and robust in modeling various flow scenarios, including subcritical, supercritical, and transcritical flows. In this method, the QUICK scheme for the surface slope discretization is more accurate and less diffusive than the center difference and the weighted average schemes.

A Modular Three-Dimensional Finite-Difference Ground-Water Flow Model

USGS Publications Warehouse

McDonald, Michael G.; Harbaugh, Arlen W.; Guo, Weixing; Lu, Guoping

1988-01-01

This report presents a finite-difference model and its associated modular computer program. The model simulates flow in three dimensions. The report includes detailed explanations of physical and mathematical concepts on which the model is based and an explanation of how those concepts are incorporated in the modular structure of the computer program. The modular structure consists of a Main Program and a series of highly independent subroutines called 'modules.' The modules are grouped into 'packages.' Each package deals with a specific feature of the hydrologic system which is to be simulated, such as flow from rivers or flow into drains, or with a specific method of solving linear equations which describe the flow system, such as the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The division of the program into modules permits the user to examine specific hydrologic features of the model independently. This also facilita development of additional capabilities because new packages can be added to the program without modifying the existing packages. The input and output systems of the computer program are also designed to permit maximum flexibility. Ground-water flow within the aquifer is simulated using a block-centered finite-difference approach. Layers can be simulated as confined, unconfined, or a combination of confined and unconfined. Flow associated with external stresses, such as wells, areal recharge, evapotranspiration, drains, and streams, can also be simulated. The finite-difference equations can be solved using either the Strongly Implicit Procedure or Slice-Successive Overrelaxation. The program is written in FORTRAN 77 and will run without modification on most computers that have a FORTRAN 77 compiler. For each program ,module, this report includes a narrative description, a flow chart, a list of variables, and a module listing.

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.

A new solution method for wheel/rail rolling contact.

PubMed

Yang, Jian; Song, Hua; Fu, Lihua; Wang, Meng; Li, Wei

2016-01-01

To solve the problem of wheel/rail rolling contact of nonlinear steady-state curving, a three-dimensional transient finite element (FE) model is developed by the explicit software ANSYS/LS-DYNA. To improve the solving speed and efficiency, an explicit-explicit order solution method is put forward based on analysis of the features of implicit and explicit algorithm. The solution method was first applied to calculate the pre-loading of wheel/rail rolling contact with explicit algorithm, and then the results became the initial conditions in solving the dynamic process of wheel/rail rolling contact with explicit algorithm as well. Simultaneously, the common implicit-explicit order solution method is used to solve the FE model. Results show that the explicit-explicit order solution method has faster operation speed and higher efficiency than the implicit-explicit order solution method while the solution accuracy is almost the same. Hence, the explicit-explicit order solution method is more suitable for the wheel/rail rolling contact model with large scale and high nonlinearity.

Higher-order compositional modeling of three-phase flow in 3D fractured porous media based on cross-flow equilibrium

NASA Astrophysics Data System (ADS)

Moortgat, Joachim; Firoozabadi, Abbas

2013-10-01

Numerical simulation of multiphase compositional flow in fractured porous media, when all the species can transfer between the phases, is a real challenge. Despite the broad applications in hydrocarbon reservoir engineering and hydrology, a compositional numerical simulator for three-phase flow in fractured media has not appeared in the literature, to the best of our knowledge. In this work, we present a three-phase fully compositional simulator for fractured media, based on higher-order finite element methods. To achieve computational efficiency, we invoke the cross-flow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks. We adopt the mixed hybrid finite element (MHFE) method to approximate convective Darcy fluxes and the pressure equation. This approach is the most natural choice for flow in fractured media. The mass balance equations are discretized by the discontinuous Galerkin (DG) method, which is perhaps the most efficient approach to capture physical discontinuities in phase properties at the matrix-fracture interfaces and at phase boundaries. In this work, we account for gravity and Fickian diffusion. The modeling of capillary effects is discussed in a separate paper. We present the mathematical framework, using the implicit-pressure-explicit-composition (IMPEC) scheme, which facilitates rigorous thermodynamic stability analyses and the computation of phase behavior effects to account for transfer of species between the phases. A deceptively simple CFL condition is implemented to improve numerical stability and accuracy. We provide six numerical examples at both small and larger scales and in two and three dimensions, to demonstrate powerful features of the formulation.

Multi-dimensional multi-species modeling of transient electrodeposition in LIGA microfabrication.

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

Evans, Gregory Herbert; Chen, Ken Shuang

2004-06-01

This report documents the efforts and accomplishments of the LIGA electrodeposition modeling project which was headed by the ASCI Materials and Physics Modeling Program. A multi-dimensional framework based on GOMA was developed for modeling time-dependent diffusion and migration of multiple charged species in a dilute electrolyte solution with reduction electro-chemical reactions on moving deposition surfaces. By combining the species mass conservation equations with the electroneutrality constraint, a Poisson equation that explicitly describes the electrolyte potential was derived. The set of coupled, nonlinear equations governing species transport, electric potential, velocity, hydrodynamic pressure, and mesh motion were solved in GOMA, using themore » finite-element method and a fully-coupled implicit solution scheme via Newton's method. By treating the finite-element mesh as a pseudo solid with an arbitrary Lagrangian-Eulerian formulation and by repeatedly performing re-meshing with CUBIT and re-mapping with MAPVAR, the moving deposition surfaces were tracked explicitly from start of deposition until the trenches were filled with metal, thus enabling the computation of local current densities that potentially influence the microstructure and frictional/mechanical properties of the deposit. The multi-dimensional, multi-species, transient computational framework was demonstrated in case studies of two-dimensional nickel electrodeposition in single and multiple trenches, without and with bath stirring or forced flow. Effects of buoyancy-induced convection on deposition were also investigated. To further illustrate its utility, the framework was employed to simulate deposition in microscreen-based LIGA molds. Lastly, future needs for modeling LIGA electrodeposition are discussed.« less

Application of CHAD hydrodynamics to shock-wave problems

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

Trease, H.E.; O`Rourke, P.J.; Sahota, M.S.

1997-12-31

CHAD is the latest in a sequence of continually evolving computer codes written to effectively utilize massively parallel computer architectures and the latest grid generators for unstructured meshes. Its applications range from automotive design issues such as in-cylinder and manifold flows of internal combustion engines, vehicle aerodynamics, underhood cooling and passenger compartment heating, ventilation, and air conditioning to shock hydrodynamics and materials modeling. CHAD solves the full unsteady Navier-Stoke equations with the k-epsilon turbulence model in three space dimensions. The code has four major features that distinguish it from the earlier KIVA code, also developed at Los Alamos. First, itmore » is based on a node-centered, finite-volume method in which, like finite element methods, all fluid variables are located at computational nodes. The computational mesh efficiently and accurately handles all element shapes ranging from tetrahedra to hexahedra. Second, it is written in standard Fortran 90 and relies on automatic domain decomposition and a universal communication library written in standard C and MPI for unstructured grids to effectively exploit distributed-memory parallel architectures. Thus the code is fully portable to a variety of computing platforms such as uniprocessor workstations, symmetric multiprocessors, clusters of workstations, and massively parallel platforms. Third, CHAD utilizes a variable explicit/implicit upwind method for convection that improves computational efficiency in flows that have large velocity Courant number variations due to velocity of mesh size variations. Fourth, CHAD is designed to also simulate shock hydrodynamics involving multimaterial anisotropic behavior under high shear. The authors will discuss CHAD capabilities and show several sample calculations showing the strengths and weaknesses of CHAD.« less

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

PubMed

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

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

On the velocity space discretization for the Vlasov-Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods

NASA Astrophysics Data System (ADS)

Camporeale, E.; Delzanno, G. L.; Bergen, B. K.; Moulton, J. D.

2016-01-01

We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier-Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC.

Combustion of liquid-fuel droplets in supercritical conditions

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Yang, Vigor; Hsaio, C. C.

1992-01-01

A comprehensive analysis of liquid-fuel droplet combustion in both subcritical and supercritical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates variable thermophysical properties, finite-rate chemical kinetics, and a full treatment of liquid-vapor phase equilibrium at the drop surface. The governing equations and associated interfacial boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures in the range of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influence on fluid transport, gas-liquid interfacial thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibit a considerable change in the combustion mechanism at the critical pressure, mainly as a result of reduced mass diffusivity and latent heat of vaporization with increased pressure.

Multigrid methods for flow transition in three-dimensional boundary layers with surface roughness

NASA Technical Reports Server (NTRS)

Liu, Chaoqun; Liu, Zhining; Mccormick, Steve

1993-01-01

The efficient multilevel adaptive method has been successfully applied to perform direct numerical simulations (DNS) of flow transition in 3-D channels and 3-D boundary layers with 2-D and 3-D isolated and distributed roughness in a curvilinear coordinate system. A fourth-order finite difference technique on stretched and staggered grids, a fully-implicit time marching scheme, a semi-coarsening multigrid method associated with line distributive relaxation scheme, and an improved outflow boundary-condition treatment, which needs only a very short buffer domain to damp all order-one wave reflections, are developed. These approaches make the multigrid DNS code very accurate and efficient. This allows us not only to be able to do spatial DNS for the 3-D channel and flat plate at low computational costs, but also to do spatial DNS for transition in the 3-D boundary layer with 3-D single and multiple roughness elements, which would have extremely high computational costs with conventional methods. Numerical results show good agreement with the linear stability theory, the secondary instability theory, and a number of laboratory experiments. The contribution of isolated and distributed roughness to transition is analyzed.

Data driven modeling of plastic deformation

DOE PAGES

Versino, Daniele; Tonda, Alberto; Bronkhorst, Curt A.

2017-05-01

In this paper the application of machine learning techniques for the development of constitutive material models is being investigated. A flow stress model, for strain rates ranging from 10 –4 to 10 12 (quasi-static to highly dynamic), and temperatures ranging from room temperature to over 1000 K, is obtained by beginning directly with experimental stress-strain data for Copper. An incrementally objective and fully implicit time integration scheme is employed to integrate the hypo-elastic constitutive model, which is then implemented into a finite element code for evaluation. Accuracy and performance of the flow stress models derived from symbolic regression are assessedmore » by comparison to Taylor anvil impact data. The results obtained with the free-form constitutive material model are compared to well-established strength models such as the Preston-Tonks-Wallace (PTW) model and the Mechanical Threshold Stress (MTS) model. Here, preliminary results show candidate free-form models comparing well with data in regions of stress-strain space with sufficient experimental data, pointing to a potential means for both rapid prototyping in future model development, as well as the use of machine learning in capturing more data as a guide for more advanced model development.« less

Analytical and computational studies on the vacuum performance of a chevron ejector

NASA Astrophysics Data System (ADS)

Kong, F. S.; Jin, Y. Z.; Kim, H. D.

2016-11-01

The effects of chevrons on the performance of a supersonic vacuum ejector-diffuser system are investigated numerically and evaluated theoretically in this work. A three-dimensional geometrical domain is numerically solved using a fully implicit finite volume scheme based on the unsteady Reynolds stress model. A one-dimensional mathematical model provides a useful tool to reveal the steady flow physics inside the vacuum ejector-diffuser system. The effects of the chevron nozzle on the generation of recirculation regions and Reynolds stress behaviors are studied and compared with those of a conventional convergent nozzle. The present performance parameters obtained from the simulated results and the mathematical results are validated with existing experimental data and show good agreement. Primary results show that the duration of the transient period and the secondary chamber pressure at a dynamic equilibrium state depend strongly on the primary jet conditions, such as inlet pressure and primary nozzle shape. Complicated oscillatory flow, generated by the unsteady movement of recirculation, finally settles into a dynamic equilibrium state. As a vortex generator, the chevron demonstrated its strong entrainment capacity to accelerate the starting transient flows to a certain extent and reduce the dynamic equilibrium pressure of the secondary chamber significantly.

Numerical study of the flow in a three-dimensional thermally driven cavity

NASA Astrophysics Data System (ADS)

Rauwoens, Pieter; Vierendeels, Jan; Merci, Bart

2008-06-01

Solutions for the fully compressible Navier-Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied. Results are computed using a finite volume method on a structured, collocated grid. An explicit third-order discretization for the convective part and an implicit central discretization for the acoustic part and for the diffusive part are used. To stabilize the scheme an artificial dissipation term for the pressure and the temperature is introduced. The discrete equations are solved using a time-marching method with restrictions on the timestep corresponding to the explicit parts of the solver. Multigrid is used as acceleration technique.

Combustion of liquid fuel droplets in supercritical conditions

NASA Technical Reports Server (NTRS)

Shuen, J. S.; Yang, Vigor

1991-01-01

A comprehensive analysis of liquid-fuel droplet combustion in both sub- and super-critical environments has been conducted. The formulation is based on the complete conservation equations for both gas and liquid phases, and accommodates finite-rate chemical kinetics and a full treatment of liquid-vapor phase equilibrium at the droplet surface. The governing equations and the associated interface boundary conditions are solved numerically using a fully coupled, implicit scheme with the dual time-stepping integration technique. The model is capable of treating the entire droplet history, including the transition from the subcritical to the supercritical state. As a specific example, the combustion of n-pentane fuel droplets in air is studied for pressures of 5-140 atm. Results indicate that the ambient gas pressure exerts significant control of droplet gasification and burning processes through its influences on the fluid transport, gas/liquid interface thermodynamics, and chemical reactions. The droplet gasification rate increases progressively with pressure. However, the data for the overall burnout time exhibits a significant variation near the critical burning pressure, mainly as a result of reduced mass-diffusion rate and latent heat of vaporization with increased pressure. The influence of droplet size on the burning characteristics is also noted.

Integrated Thermal Response Tool for Earth Entry Vehicles

NASA Technical Reports Server (NTRS)

Chen, Y.-K.; Milos, F. S.; Partridge, Harry (Technical Monitor)

2001-01-01

A system is presented for multi-dimensional, fully-coupled thermal response modeling of hypersonic entry vehicles. The system consists of a two-dimensional implicit thermal response, pyrolysis and ablation program (TITAN), a commercial finite-element thermal and mechanical analysis code (MARC), and a high fidelity Navier-Stokes equation solver (GIANTS). The simulations performed by this integrated system include hypersonic flow-field, fluid and solid interaction, ablation, shape change, pyrolysis gas generation and flow, and thermal response of heatshield and structure. The thermal response of the ablating and charring heatshield material is simulated using TITAN, and that of the underlying structural is simulated using MARC. The ablating heatshield is treated as an outer boundary condition of the structure, and continuity conditions of temperature and heat flux are imposed at the interface between TITAN and MARC. Aerothermal environments with fluid and solid interaction are predicted by coupling TITAN and GIANTS through surface energy balance equations. With this integrated system, the aerothermal environments for an entry vehicle and the thermal response of both the heatshield and the structure can be obtained simultaneously. Representative computations for a proposed blunt body earth entry vehicle are presented and discussed in detail.

A scalable nonlinear fluid-structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

NASA Astrophysics Data System (ADS)

Kong, Fande; Cai, Xiao-Chuan

2017-07-01

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear in many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexact Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here "geometry" includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.

A scalable nonlinear fluid–structure interaction solver based on a Schwarz preconditioner with isogeometric unstructured coarse spaces in 3D

DOE PAGES

Kong, Fande; Cai, Xiao-Chuan

2017-03-24

Nonlinear fluid-structure interaction (FSI) problems on unstructured meshes in 3D appear many applications in science and engineering, such as vibration analysis of aircrafts and patient-specific diagnosis of cardiovascular diseases. In this work, we develop a highly scalable, parallel algorithmic and software framework for FSI problems consisting of a nonlinear fluid system and a nonlinear solid system, that are coupled monolithically. The FSI system is discretized by a stabilized finite element method in space and a fully implicit backward difference scheme in time. To solve the large, sparse system of nonlinear algebraic equations at each time step, we propose an inexactmore » Newton-Krylov method together with a multilevel, smoothed Schwarz preconditioner with isogeometric coarse meshes generated by a geometry preserving coarsening algorithm. Here ''geometry'' includes the boundary of the computational domain and the wet interface between the fluid and the solid. We show numerically that the proposed algorithm and implementation are highly scalable in terms of the number of linear and nonlinear iterations and the total compute time on a supercomputer with more than 10,000 processor cores for several problems with hundreds of millions of unknowns.« less

Data driven modeling of plastic deformation

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

Versino, Daniele; Tonda, Alberto; Bronkhorst, Curt A.

In this paper the application of machine learning techniques for the development of constitutive material models is being investigated. A flow stress model, for strain rates ranging from 10 –4 to 10 12 (quasi-static to highly dynamic), and temperatures ranging from room temperature to over 1000 K, is obtained by beginning directly with experimental stress-strain data for Copper. An incrementally objective and fully implicit time integration scheme is employed to integrate the hypo-elastic constitutive model, which is then implemented into a finite element code for evaluation. Accuracy and performance of the flow stress models derived from symbolic regression are assessedmore » by comparison to Taylor anvil impact data. The results obtained with the free-form constitutive material model are compared to well-established strength models such as the Preston-Tonks-Wallace (PTW) model and the Mechanical Threshold Stress (MTS) model. Here, preliminary results show candidate free-form models comparing well with data in regions of stress-strain space with sufficient experimental data, pointing to a potential means for both rapid prototyping in future model development, as well as the use of machine learning in capturing more data as a guide for more advanced model development.« less

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

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.

A cubic spline approximation for problems in fluid mechanics

NASA Technical Reports Server (NTRS)

Rubin, S. G.; Graves, R. A., Jr.

1975-01-01

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

An advanced probabilistic structural analysis method for implicit performance functions

NASA Technical Reports Server (NTRS)

Wu, Y.-T.; Millwater, H. R.; Cruse, T. A.

1989-01-01

In probabilistic structural analysis, the performance or response functions usually are implicitly defined and must be solved by numerical analysis methods such as finite element methods. In such cases, the most commonly used probabilistic analysis tool is the mean-based, second-moment method which provides only the first two statistical moments. This paper presents a generalized advanced mean value (AMV) method which is capable of establishing the distributions to provide additional information for reliability design. The method requires slightly more computations than the second-moment method but is highly efficient relative to the other alternative methods. In particular, the examples show that the AMV method can be used to solve problems involving non-monotonic functions that result in truncated distributions.

A conservative finite difference algorithm for the unsteady transonic potential equation in generalized coordinates

NASA Technical Reports Server (NTRS)

Bridgeman, J. O.; Steger, J. L.; Caradonna, F. X.

1982-01-01

An implicit, approximate-factorization, finite-difference algorithm has been developed for the computation of unsteady, inviscid transonic flows in two and three dimensions. The computer program solves the full-potential equation in generalized coordinates in conservation-law form in order to properly capture shock-wave position and speed. A body-fitted coordinate system is employed for the simple and accurate treatment of boundary conditions on the body surface. The time-accurate algorithm is modified to a conventional ADI relaxation scheme for steady-state computations. Results from two- and three-dimensional steady and two-dimensional unsteady calculations are compared with existing methods.

Co-simulation coupling spectral/finite elements for 3D soil/structure interaction problems

NASA Astrophysics Data System (ADS)

Zuchowski, Loïc; Brun, Michael; De Martin, Florent

2018-05-01

The coupling between an implicit finite elements (FE) code and an explicit spectral elements (SE) code has been explored for solving the elastic wave propagation in the case of soil/structure interaction problem. The coupling approach is based on domain decomposition methods in transient dynamics. The spatial coupling at the interface is managed by a standard coupling mortar approach, whereas the time integration is dealt with an hybrid asynchronous time integrator. An external coupling software, handling the interface problem, has been set up in order to couple the FE software Code_Aster with the SE software EFISPEC3D.

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.

The SPAR thermal analyzer: Present and future

NASA Astrophysics Data System (ADS)

Marlowe, M. B.; Whetstone, W. D.; Robinson, J. C.

The SPAR thermal analyzer, a system of finite-element processors for performing steady-state and transient thermal analyses, is described. The processors communicate with each other through the SPAR random access data base. As each processor is executed, all pertinent source data is extracted from the data base and results are stored in the data base. Steady state temperature distributions are determined by a direct solution method for linear problems and a modified Newton-Raphson method for nonlinear problems. An explicit and several implicit methods are available for the solution of transient heat transfer problems. Finite element plotting capability is available for model checkout and verification.

The SPAR thermal analyzer: Present and future

NASA Technical Reports Server (NTRS)

Marlowe, M. B.; Whetstone, W. D.; Robinson, J. C.

1982-01-01

The SPAR thermal analyzer, a system of finite-element processors for performing steady-state and transient thermal analyses, is described. The processors communicate with each other through the SPAR random access data base. As each processor is executed, all pertinent source data is extracted from the data base and results are stored in the data base. Steady state temperature distributions are determined by a direct solution method for linear problems and a modified Newton-Raphson method for nonlinear problems. An explicit and several implicit methods are available for the solution of transient heat transfer problems. Finite element plotting capability is available for model checkout and verification.

Flux vector splitting of the inviscid equations with application to finite difference methods

NASA Technical Reports Server (NTRS)

Steger, J. L.; Warming, R. F.

1979-01-01

The conservation-law form of the inviscid gasdynamic equations has the remarkable property that the nonlinear flux vectors are homogeneous functions of degree one. This property readily permits the splitting of flux vectors into subvectors by similarity transformations so that each subvector has associated with it a specified eigenvalue spectrum. As a consequence of flux vector splitting, new explicit and implicit dissipative finite-difference schemes are developed for first-order hyperbolic systems of equations. Appropriate one-sided spatial differences for each split flux vector are used throughout the computational field even if the flow is locally subsonic. The results of some preliminary numerical computations are included.

Implicit Acquisition of Grammars with Crossed and Nested Non-Adjacent Dependencies: Investigating the Push-Down Stack Model

ERIC Educational Resources Information Center

Udden, Julia; Ingvar, Martin; Hagoort, Peter; Petersson, Karl M.

2012-01-01

A recent hypothesis in empirical brain research on language is that the fundamental difference between animal and human communication systems is captured by the distinction between finite-state and more complex phrase-structure grammars, such as context-free and context-sensitive grammars. However, the relevance of this distinction for the study…

Coastal Modeling System: Mathematical Formulations and Numerical Methods

DTIC Science & Technology

2014-03-01

sediment transport , and morphology change. The CMS was designed and developed for coastal inlets and navigation applications, including channel...numerical methods of hydrodynamic, salinity and sediment transport , and morphology change model CMS-Flow. The CMS- Flow uses the Finite Volume...and the influence of coastal structures. The implicit hydrodynamic model is coupled to a nonequilibrium transport model of multiple-sized total

Finite element solution to passive scalar transport behind line sources under neutral and unstable stratification

NASA Astrophysics Data System (ADS)

Liu, Chun-Ho; Leung, Dennis Y. C.

2006-02-01

This study employed a direct numerical simulation (DNS) technique to contrast the plume behaviours and mixing of passive scalar emitted from line sources (aligned with the spanwise direction) in neutrally and unstably stratified open-channel flows. The DNS model was developed using the Galerkin finite element method (FEM) employing trilinear brick elements with equal-order interpolating polynomials that solved the momentum and continuity equations, together with conservation of energy and mass equations in incompressible flow. The second-order accurate fractional-step method was used to handle the implicit velocity-pressure coupling in incompressible flow. It also segregated the solution to the advection and diffusion terms, which were then integrated in time, respectively, by the explicit third-order accurate Runge-Kutta method and the implicit second-order accurate Crank-Nicolson method. The buoyancy term under unstable stratification was integrated in time explicitly by the first-order accurate Euler method. The DNS FEM model calculated the scalar-plume development and the mean plume path. In particular, it calculated the plume meandering in the wall-normal direction under unstable stratification that agreed well with the laboratory and field measurements, as well as previous modelling results available in literature.

Dynamic Relaxation: A Technique for Detailed Thermo-Elastic Structural Analysis of Transportation Structures

NASA Astrophysics Data System (ADS)

Shoukry, Samir N.; William, Gergis W.; Riad, Mourad Y.; McBride, Kevyn C.

2006-08-01

Dynamic relaxation is a technique developed to solve static problems through an explicit integration in finite element. The main advantage of such a technique is the ability to solve a large problem in a relatively short time compared with the traditional implicit techniques, especially when using nonlinear material models. This paper describes the use of such a technique in analyzing large transportation structures as dowel jointed concrete pavements and 306-m-long, reinforced concrete bridge superstructure under the effect of temperature variations. The main feature of the pavement model is the detailed modeling of dowel bars and their interfaces with the surrounding concrete using extremely fine mesh of solid elements, while in the bridge structure it is the detailed modeling of the girder-deck interface as well as the bracing members between the girders. The 3DFE results were found to be in a good agreement with experimentally measured data obtained from an instrumented pavements sections and a highway bridge constructed in West Virginia. Thus, such a technique provides a good tool for analyzing the response of large structures to static loads in a fraction of the time required by traditional, implicit finite element methods.

An efficient numerical model for multicomponent compressible flow in fractured porous media

NASA Astrophysics Data System (ADS)

Zidane, Ali; Firoozabadi, Abbas

2014-12-01

An efficient and accurate numerical model for multicomponent compressible single-phase flow in fractured media is presented. The discrete-fracture approach is used to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross flow equilibrium in the fractures. This will allow large matrix elements in the neighborhood of the fractures and considerable speed up of the algorithm. We use an implicit finite volume (FV) scheme to solve the species mass balance equation in the fractures. This step avoids the use of Courant-Freidricks-Levy (CFL) condition and contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix. Four numerical examples are presented to demonstrate the robustness and efficiency of the proposed model. We show that the combination of the fracture cross-flow equilibrium and the implicit composition calculation in the fractures increase the computational speed 20-130 times in 2D. In 3D, one may expect even a higher computational efficiency.

Application of adaptive gridding to magnetohydrodynamic flows

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

Schnack, D.D.; Lotatti, I.; Satyanarayana, P.

1996-12-31

The numerical simulation of the primitive, three-dimensional, time-dependent, resistive MHD equations on an unstructured, adaptive poloidal mesh using the TRIM code has been reported previously. The toroidal coordinate is approximated pseudo-spectrally with finite Fourier series and Fast-Fourier Transforms. The finite-volume algorithm preserves the magnetic field as solenoidal to round-off error, and also conserves mass, energy, and magnetic flux exactly. A semi-implicit method is used to allow for large time steps on the unstructured mesh. This is important for tokamak calculations where the relevant time scale is determined by the poloidal Alfven time. This also allows the viscosity to be treatedmore » implicitly. A conjugate-gradient method with pre-conditioning is used for matrix inversion. Applications to the growth and saturation of ideal instabilities in several toroidal fusion systems has been demonstrated. Recently we have concentrated on the details of the mesh adaption algorithm used in TRIM. We present several two-dimensional results relating to the use of grid adaptivity to track the evolution of hydrodynamic and MHD structures. Examples of plasma guns, opening switches, and supersonic flow over a magnetized sphere are presented. Issues relating to mesh adaption criteria are discussed.« less

An efficient, explicit finite-rate algorithm to compute flows in chemical nonequilibrium

NASA Technical Reports Server (NTRS)

Palmer, Grant

1989-01-01

An explicit finite-rate code was developed to compute hypersonic viscous chemically reacting flows about three-dimensional bodies. Equations describing the finite-rate chemical reactions were fully coupled to the gas dynamic equations using a new coupling technique. The new technique maintains stability in the explicit finite-rate formulation while permitting relatively large global time steps.

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.

Reactive Transport Modeling of Induced Calcite Precipitation Reaction Fronts in Porous Media Using A Parallel, Fully Coupled, Fully Implicit Approach

NASA Astrophysics Data System (ADS)

Guo, L.; Huang, H.; Gaston, D.; Redden, G. D.; Fox, D. T.; Fujita, Y.

2010-12-01

Inducing mineral precipitation in the subsurface is one potential strategy for immobilizing trace metal and radionuclide contaminants. Generating mineral precipitates in situ can be achieved by manipulating chemical conditions, typically through injection or in situ generation of reactants. How these reactants transport, mix and react within the medium controls the spatial distribution and composition of the resulting mineral phases. Multiple processes, including fluid flow, dispersive/diffusive transport of reactants, biogeochemical reactions and changes in porosity-permeability, are tightly coupled over a number of scales. Numerical modeling can be used to investigate the nonlinear coupling effects of these processes which are quite challenging to explore experimentally. Many subsurface reactive transport simulators employ a de-coupled or operator-splitting approach where transport equations and batch chemistry reactions are solved sequentially. However, such an approach has limited applicability for biogeochemical systems with fast kinetics and strong coupling between chemical reactions and medium properties. A massively parallel, fully coupled, fully implicit Reactive Transport simulator (referred to as “RAT”) based on a parallel multi-physics object-oriented simulation framework (MOOSE) has been developed at the Idaho National Laboratory. Within this simulator, systems of transport and reaction equations can be solved simultaneously in a fully coupled, fully implicit manner using the Jacobian Free Newton-Krylov (JFNK) method with additional advanced computing capabilities such as (1) physics-based preconditioning for solution convergence acceleration, (2) massively parallel computing and scalability, and (3) adaptive mesh refinements for 2D and 3D structured and unstructured mesh. The simulator was first tested against analytical solutions, then applied to simulating induced calcium carbonate mineral precipitation in 1D columns and 2D flow cells as analogs to homogeneous and heterogeneous porous media, respectively. In 1D columns, calcium carbonate mineral precipitation was driven by urea hydrolysis catalyzed by urease enzyme, and in 2D flow cells, calcium carbonate mineral forming reactants were injected sequentially, forming migrating reaction fronts that are typically highly nonuniform. The RAT simulation results for the spatial and temporal distributions of precipitates, reaction rates and major species in the system, and also for changes in porosity and permeability, were compared to both laboratory experimental data and computational results obtained using other reactive transport simulators. The comparisons demonstrate the ability of RAT to simulate complex nonlinear systems and the advantages of fully coupled approaches, over de-coupled methods, for accurate simulation of complex, dynamic processes such as engineered mineral precipitation in subsurface environments.

Automatic abdominal multi-organ segmentation using deep convolutional neural network and time-implicit level sets.

PubMed

Hu, Peijun; Wu, Fa; Peng, Jialin; Bao, Yuanyuan; Chen, Feng; Kong, Dexing

2017-03-01

Multi-organ segmentation from CT images is an essential step for computer-aided diagnosis and surgery planning. However, manual delineation of the organs by radiologists is tedious, time-consuming and poorly reproducible. Therefore, we propose a fully automatic method for the segmentation of multiple organs from three-dimensional abdominal CT images. The proposed method employs deep fully convolutional neural networks (CNNs) for organ detection and segmentation, which is further refined by a time-implicit multi-phase evolution method. Firstly, a 3D CNN is trained to automatically localize and delineate the organs of interest with a probability prediction map. The learned probability map provides both subject-specific spatial priors and initialization for subsequent fine segmentation. Then, for the refinement of the multi-organ segmentation, image intensity models, probability priors as well as a disjoint region constraint are incorporated into an unified energy functional. Finally, a novel time-implicit multi-phase level-set algorithm is utilized to efficiently optimize the proposed energy functional model. Our method has been evaluated on 140 abdominal CT scans for the segmentation of four organs (liver, spleen and both kidneys). With respect to the ground truth, average Dice overlap ratios for the liver, spleen and both kidneys are 96.0, 94.2 and 95.4%, respectively, and average symmetric surface distance is less than 1.3 mm for all the segmented organs. The computation time for a CT volume is 125 s in average. The achieved accuracy compares well to state-of-the-art methods with much higher efficiency. A fully automatic method for multi-organ segmentation from abdominal CT images was developed and evaluated. The results demonstrated its potential in clinical usage with high effectiveness, robustness and efficiency.

Implicit unified gas-kinetic scheme for steady state solutions in all flow regimes

NASA Astrophysics Data System (ADS)

Zhu, Yajun; Zhong, Chengwen; Xu, Kun

2016-06-01

This paper presents an implicit unified gas-kinetic scheme (UGKS) for non-equilibrium steady state flow computation. The UGKS is a direct modeling method for flow simulation in all regimes with the updates of both macroscopic flow variables and microscopic gas distribution function. By solving the macroscopic equations implicitly, a predicted equilibrium state can be obtained first through iterations. With the newly predicted equilibrium state, the evolution equation of the gas distribution function and the corresponding collision term can be discretized in a fully implicit way for fast convergence through iterations as well. The lower-upper symmetric Gauss-Seidel (LU-SGS) factorization method is implemented to solve both macroscopic and microscopic equations, which improves the efficiency of the scheme. Since the UGKS is a direct modeling method and its physical solution depends on the mesh resolution and the local time step, a physical time step needs to be fixed before using an implicit iterative technique with a pseudo-time marching step. Therefore, the physical time step in the current implicit scheme is determined by the same way as that in the explicit UGKS for capturing the physical solution in all flow regimes, but the convergence to a steady state speeds up through the adoption of a numerical time step with large CFL number. Many numerical test cases in different flow regimes from low speed to hypersonic ones, such as the Couette flow, cavity flow, and the flow passing over a cylinder, are computed to validate the current implicit method. The overall efficiency of the implicit UGKS can be improved by one or two orders of magnitude in comparison with the explicit one.

Studying Different Tasks of Implicit Learning across Multiple Test Sessions Conducted on the Web

PubMed Central

Sævland, Werner; Norman, Elisabeth

2016-01-01

Implicit learning is usually studied through individual performance on a single task, with the most common tasks being the Serial Reaction Time (SRT) task, the Dynamic System Control (DSC) task, and Artificial Grammar Learning (AGL). Few attempts have been made to compare performance across different implicit learning tasks within the same study. The current study was designed to explore the relationship between performance on the DSC Sugar factory task and the Alternating Serial Reaction Time (ASRT) task. We also addressed another limitation of traditional implicit learning experiments, namely that implicit learning is usually studied in laboratory settings over a restricted time span lasting for less than an hour. In everyday situations, implicit learning is assumed to involve a gradual accumulation of knowledge across several learning episodes over a longer time span. One way to increase the ecological validity of implicit learning experiments could be to present the learning material repeatedly across shorter test sessions. This can most easily be done by using a web-based setup in which participants can access the material from home. We therefore created an online web-based system for measuring implicit learning that could be administered in either single or multiple sessions. Participants (n = 66) were assigned to either a single session or a multiple session condition. Learning occurred on both tasks, and awareness measures suggested that acquired knowledge was not fully conscious on either of the tasks. Learning and the degree of conscious awareness of the learned regularities were compared across conditions and tasks. On the DSC task, performance was not affected by whether learning had taken place in one or over multiple sessions. On the ASRT task, RT improvement across blocks was larger in the multiple-session condition. Learning in the two tasks was not related. PMID:27375512

An efficient nonlinear finite-difference approach in the computational modeling of the dynamics of a nonlinear diffusion-reaction equation in microbial ecology.

PubMed

Macías-Díaz, J E; Macías, Siegfried; Medina-Ramírez, I E

2013-12-01

In this manuscript, we present a computational model to approximate the solutions of a partial differential equation which describes the growth dynamics of microbial films. The numerical technique reported in this work is an explicit, nonlinear finite-difference methodology which is computationally implemented using Newton's method. Our scheme is compared numerically against an implicit, linear finite-difference discretization of the same partial differential equation, whose computer coding requires an implementation of the stabilized bi-conjugate gradient method. Our numerical results evince that the nonlinear approach results in a more efficient approximation to the solutions of the biofilm model considered, and demands less computer memory. Moreover, the positivity of initial profiles is preserved in the practice by the nonlinear scheme proposed. Copyright © 2013 Elsevier Ltd. All rights reserved.

TAP 2: A finite element program for thermal analysis of convectively cooled structures

NASA Technical Reports Server (NTRS)

Thornton, E. A.

1980-01-01

A finite element computer program (TAP 2) for steady-state and transient thermal analyses of convectively cooled structures is presented. The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature-dependent thermal parameters is performed using the Newton-Raphson iteration method. Transient analyses are performed using an implicit Crank-Nicolson time integration scheme with consistent or lumped capacitance matrices as an option. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. User instructions and sample problems are presented in appendixes.

A split finite element algorithm for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Baker, A. J.

1979-01-01

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Analysis of composite ablators using massively parallel computation

NASA Technical Reports Server (NTRS)

Shia, David

1995-01-01

In this work, the feasibility of using massively parallel computation to study the response of ablative materials is investigated. Explicit and implicit finite difference methods are used on a massively parallel computer, the Thinking Machines CM-5. The governing equations are a set of nonlinear partial differential equations. The governing equations are developed for three sample problems: (1) transpiration cooling, (2) ablative composite plate, and (3) restrained thermal growth testing. The transpiration cooling problem is solved using a solution scheme based solely on the explicit finite difference method. The results are compared with available analytical steady-state through-thickness temperature and pressure distributions and good agreement between the numerical and analytical solutions is found. It is also found that a solution scheme based on the explicit finite difference method has the following advantages: incorporates complex physics easily, results in a simple algorithm, and is easily parallelizable. However, a solution scheme of this kind needs very small time steps to maintain stability. A solution scheme based on the implicit finite difference method has the advantage that it does not require very small times steps to maintain stability. However, this kind of solution scheme has the disadvantages that complex physics cannot be easily incorporated into the algorithm and that the solution scheme is difficult to parallelize. A hybrid solution scheme is then developed to combine the strengths of the explicit and implicit finite difference methods and minimize their weaknesses. This is achieved by identifying the critical time scale associated with the governing equations and applying the appropriate finite difference method according to this critical time scale. The hybrid solution scheme is then applied to the ablative composite plate and restrained thermal growth problems. The gas storage term is included in the explicit pressure calculation of both problems. Results from ablative composite plate problems are compared with previous numerical results which did not include the gas storage term. It is found that the through-thickness temperature distribution is not affected much by the gas storage term. However, the through-thickness pressure and stress distributions, and the extent of chemical reactions are different from the previous numerical results. Two types of chemical reaction models are used in the restrained thermal growth testing problem: (1) pressure-independent Arrhenius type rate equations and (2) pressure-dependent Arrhenius type rate equations. The numerical results are compared to experimental results and the pressure-dependent model is able to capture the trend better than the pressure-independent one. Finally, a performance study is done on the hybrid algorithm using the ablative composite plate problem. It is found that there is a good speedup of performance on the CM-5. For 32 CPU's, the speedup of performance is 20. The efficiency of the algorithm is found to be a function of the size and execution time of a given problem and the effective parallelization of the algorithm. It also seems that there is an optimum number of CPU's to use for a given problem.

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.

A fully-implicit Particle-In-Cell Monte Carlo Collision code for the simulation of inductively coupled plasmas

NASA Astrophysics Data System (ADS)

Mattei, S.; Nishida, K.; Onai, M.; Lettry, J.; Tran, M. Q.; Hatayama, A.

2017-12-01

We present a fully-implicit electromagnetic Particle-In-Cell Monte Carlo collision code, called NINJA, written for the simulation of inductively coupled plasmas. NINJA employs a kinetic enslaved Jacobian-Free Newton Krylov method to solve self-consistently the interaction between the electromagnetic field generated by the radio-frequency coil and the plasma response. The simulated plasma includes a kinetic description of charged and neutral species as well as the collision processes between them. The algorithm allows simulations with cell sizes much larger than the Debye length and time steps in excess of the Courant-Friedrichs-Lewy condition whilst preserving the conservation of the total energy. The code is applied to the simulation of the plasma discharge of the Linac4 H- ion source at CERN. Simulation results of plasma density, temperature and EEDF are discussed and compared with optical emission spectroscopy measurements. A systematic study of the energy conservation as a function of the numerical parameters is presented.

A comparison between implicit and hybrid methods for the calculation of steady and unsteady inlet flows

NASA Technical Reports Server (NTRS)

Coakley, T. J.; Hsieh, T.

1985-01-01

Numerical simulation of steady and unsteady transonic diffuser flows using two different computer codes are discussed and compared with experimental data. The codes solve the Reynolds-averaged, compressible, Navier-Stokes equations using various turbulence models. One of the codes has been applied extensively to diffuser flows and uses the hybrid method of MacCormack. This code is relatively inefficient numerically. The second code, which was developed more recently, is fully implicit and is relatively efficient numerically. Simulations of steady flows using the implicit code are shown to be in good agreement with simulations using the hybrid code. Both simulations are in good agreement with experimental results. Simulations of unsteady flows using the two codes are in good qualitative agreement with each other, although the quantitative agreement is not as good as in the steady flow cases. The implicit code is shown to be eight times faster than the hybrid code for unsteady flow calculations and up to 32 times faster for steady flow calculations. Results of calculations using alternative turbulence models are also discussed.

An efficicient data structure for three-dimensional vertex based finite volume method

NASA Astrophysics Data System (ADS)

Akkurt, Semih; Sahin, Mehmet

2017-11-01

A vertex based three-dimensional finite volume algorithm has been developed using an edge based data structure.The mesh data structure of the given algorithm is similar to ones that exist in the literature. However, the data structures are redesigned and simplied in order to fit requirements of the vertex based finite volume method. In order to increase the cache efficiency, the data access patterns for the vertex based finite volume method are investigated and these datas are packed/allocated in a way that they are close to each other in the memory. The present data structure is not limited with tetrahedrons, arbitrary polyhedrons are also supported in the mesh without putting any additional effort. Furthermore, the present data structure also supports adaptive refinement and coarsening. For the implicit and parallel implementation of the FVM algorithm, PETSc and MPI libraries are employed. The performance and accuracy of the present algorithm are tested for the classical benchmark problems by comparing the CPU time for the open source algorithms.

Implicit perceptual-motor skill learning in mild cognitive impairment and Parkinson's disease.

PubMed

Gobel, Eric W; Blomeke, Kelsey; Zadikoff, Cindy; Simuni, Tanya; Weintraub, Sandra; Reber, Paul J

2013-05-01

Implicit skill learning is hypothesized to depend on nondeclarative memory that operates independent of the medial temporal lobe (MTL) memory system and instead depends on cortico striatal circuits between the basal ganglia and cortical areas supporting motor function and planning. Research with the Serial Reaction Time (SRT) task suggests that patients with memory disorders due to MTL damage exhibit normal implicit sequence learning. However, reports of intact learning rely on observations of no group differences, leading to speculation as to whether implicit sequence learning is fully intact in these patients. Patients with Parkinson's disease (PD) often exhibit impaired sequence learning, but this impairment is not universally observed. Implicit perceptual-motor sequence learning was examined using the Serial Interception Sequence Learning (SISL) task in patients with amnestic Mild Cognitive Impairment (MCI; n = 11) and patients with PD (n = 15). Sequence learning in SISL is resistant to explicit learning and individually adapted task difficulty controls for baseline performance differences. Patients with MCI exhibited robust sequence learning, equivalent to healthy older adults (n = 20), supporting the hypothesis that the MTL does not contribute to learning in this task. In contrast, the majority of patients with PD exhibited no sequence-specific learning in spite of matched overall task performance. Two patients with PD exhibited performance indicative of an explicit compensatory strategy suggesting that impaired implicit learning may lead to greater reliance on explicit memory in some individuals. The differences in learning between patient groups provides strong evidence in favor of implicit sequence learning depending solely on intact basal ganglia function with no contribution from the MTL memory system.

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

DOE PAGES

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.; ...

2016-09-18

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

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

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

Hyperbolic/parabolic development for the GIM-STAR code. [flow fields in supersonic inlets

NASA Technical Reports Server (NTRS)

Spradley, L. W.; Stalnaker, J. F.; Ratliff, A. W.

1980-01-01

Flow fields in supersonic inlet configurations were computed using the eliptic GIM code on the STAR computer. Spillage flow under the lower cowl was calculated to be 33% of the incoming stream. The shock/boundary layer interaction on the upper propulsive surface was computed including separation. All shocks produced by the flow system were captured. Linearized block implicit (LBI) schemes were examined to determine their application to the GIM code. Pure explicit methods have stability limitations and fully implicit schemes are inherently inefficient; however, LBI schemes show promise as an effective compromise. A quasiparabolic version of the GIM code was developed using elastical parabolized Navier-Stokes methods combined with quasitime relaxation. This scheme is referred to as quasiparabolic although it applies equally well to hyperbolic supersonic inviscid flows. Second order windward differences are used in the marching coordinate and either explicit or linear block implicit time relaxation can be incorporated.

Investigation of pitchfork bifurcation phenomena effects on heat transfer of viscoelastic flow inside a symmetric sudden expansion

NASA Astrophysics Data System (ADS)

Shahbani-Zahiri, A.; Hassanzadeh, H.; Shahmardan, M. M.; Norouzi, M.

2017-11-01

In this paper, the inertial and non-isothermal flows of the viscoelastic fluid through a planar channel with symmetric sudden expansion are numerically simulated. Effects of pitchfork bifurcation phenomena on the heat transfer rate are examined for the thermally developing and fully developed flow of the viscoelastic fluid inside the expanded part of the planar channel with an expansion ratio of 1:3. The rheological model of exponential Phan Thien-Tanner is used to include both the effects of shear-thinning and elasticity in fluid viscosity. The properties of fluids are temperature-dependent, and the viscous dissipation and heat stored by fluid elasticity are considered in the heat transfer equation. For coupling the governing equations, the PISO algorithm (Pressure Implicit with Splitting of Operator) is applied and the system of equations is linearized using the finite volume method on the collocated grids. The main purpose of this study is to examine the pitchfork bifurcation phenomena and its influences on the temperature distribution, the local and mean Nusselt numbers, and the first and second normal stress differences at different Reynolds, elasticity, and Brinkman numbers. The results show that by increasing the Brinkman number for the heated flow of the viscoelastic fluid inside the expanded part of the channel, the value of the mean Nusselt number is almost linearly decreased. Also, the maximum values of the local Nusselt number for the thermally developing flow and the local Nusselt number of the thermally fully developed flow are decremented by enhancing the Brinkman number.

Numerical solution of fractured horizontal wells in shale gas reservoirs considering multiple transport mechanisms

NASA Astrophysics Data System (ADS)

Zhao, Yu-long; Tang, Xu-chuan; Zhang, Lie-hui; Tang, Hong-ming; Tao, Zheng-Wu

2018-06-01

The multiscale pore size and specific gas storage mechanism in organic-rich shale gas reservoirs make gas transport in such reservoirs complicated. Therefore, a model that fully incorporates all transport mechanisms and employs an accurate numerical method is urgently needed to simulate the gas production process. In this paper, a unified model of apparent permeability was first developed, which took into account multiple influential factors including slip flow, Knudsen diffusion (KD), surface diffusion, effects of the adsorbed layer, permeability stress sensitivity, and ad-/desorption phenomena. Subsequently, a comprehensive mathematical model, which included the model of apparent permeability, was derived to describe gas production behaviors. Thereafter, on the basis of unstructured perpendicular bisection grids and finite volume method, a fully implicit numerical simulator was developed using Matlab software. The validation and application of the new model were confirmed using a field case reported in the literature. Finally, the impacts of related influencing factors on gas production were analyzed. The results showed that KD resulted in a negligible impact on gas production in the proposed model. The smaller the pore size was, the more obvious the effects of the adsorbed layer on the well production rate would be. Permeability stress sensitivity had a slight effect on well cumulative production in shale gas reservoirs. Adsorbed gas made a major contribution to the later flow period of the well; the greater the adsorbed gas content, the greater the well production rate would be. This paper can improve the understanding of gas production in shale gas reservoirs for petroleum engineers.

FY07 NRL DoD High Performance Computing Modernization Program Annual Reports

DTIC Science & Technology

2008-09-05

performed. Implicit and explicit solutions methods are used as appropriate. The primary finite element codes used are ABAQUS and ANSYS. User subroutines ...geometric complexities, loading path dependence, rate dependence, and interaction between loading types (electrical, thermal and mechanical). Work is not...are used for specialized material constitutive response. Coupled material responses, such as electrical- thermal for capacitor materials or electrical

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

Social intuition as a form of implicit learning: Sequences of body movements are learned less explicitly than letter sequences

PubMed Central

Norman, Elisabeth; Price, Mark C.

2012-01-01

In the current paper, we first evaluate the suitability of traditional serial reaction time (SRT) and artificial grammar learning (AGL) experiments for measuring implicit learning of social signals. We then report the results of a novel sequence learning task which combines aspects of the SRT and AGL paradigms to meet our suggested criteria for how implicit learning experiments can be adapted to increase their relevance to situations of social intuition. The sequences followed standard finite-state grammars. Sequence learning and consciousness of acquired knowledge were compared between 2 groups of 24 participants viewing either sequences of individually presented letters or sequences of body-posture pictures, which were described as series of yoga movements. Participants in both conditions showed above-chance classification accuracy, indicating that sequence learning had occurred in both stimulus conditions. This shows that sequence learning can still be found when learning procedures reflect the characteristics of social intuition. Rule awareness was measured using trial-by-trial evaluation of decision strategy (Dienes & Scott, 2005; Scott & Dienes, 2008). For letters, sequence classification was best on trials where participants reported responding on the basis of explicit rules or memory, indicating some explicit learning in this condition. For body-posture, classification was not above chance on these types of trial, but instead showed a trend to be best on those trials where participants reported that their responses were based on intuition, familiarity, or random choice, suggesting that learning was more implicit. Results therefore indicate that the use of traditional stimuli in research on sequence learning might underestimate the extent to which learning is implicit in domains such as social learning, contributing to ongoing debate about levels of conscious awareness in implicit learning. PMID:22679467

Implicit time-marching solution of the Navier-Stokes equations for thrust reversing and thrust vectoring nozzle flows

NASA Technical Reports Server (NTRS)

Imlay, S. T.

1986-01-01

An implicit finite volume method is investigated for the solution of the compressible Navier-Stokes equations for flows within thrust reversing and thrust vectoring nozzles. Thrust reversing nozzles typically have sharp corners, and the rapid expansion and large turning angles near these corners are shown to cause unacceptable time step restrictions when conventional approximate factorization methods are used. In this investigation these limitations are overcome by using second-order upwind differencing and line Gauss-Siedel relaxation. This method is implemented with a zonal mesh so that flows through complex nozzle geometries may be efficiently calculated. Results are presented for five nozzle configurations including two with time varying geometries. Three cases are compared with available experimental data and the results are generally acceptable.

Penalty methods for the numerical solution of American multi-asset option problems

NASA Astrophysics Data System (ADS)

Nielsen, Bjørn Fredrik; Skavhaug, Ola; Tveito, Aslak

2008-12-01

We derive and analyze a penalty method for solving American multi-asset option problems. A small, non-linear penalty term is added to the Black-Scholes equation. This approach gives a fixed solution domain, removing the free and moving boundary imposed by the early exercise feature of the contract. Explicit, implicit and semi-implicit finite difference schemes are derived, and in the case of independent assets, we prove that the approximate option prices satisfy some basic properties of the American option problem. Several numerical experiments are carried out in order to investigate the performance of the schemes. We give examples indicating that our results are sharp. Finally, the experiments indicate that in the case of correlated underlying assets, the same properties are valid as in the independent case.

Implicit approximate-factorization schemes for the low-frequency transonic equation

NASA Technical Reports Server (NTRS)

Ballhaus, W. F.; Steger, J. L.

1975-01-01

Two- and three-level implicit finite-difference algorithms for the low-frequency transonic small disturbance-equation are constructed using approximate factorization techniques. The schemes are unconditionally stable for the model linear problem. For nonlinear mixed flows, the schemes maintain stability by the use of conservatively switched difference operators for which stability is maintained only if shock propagation is restricted to be less than one spatial grid point per time step. The shock-capturing properties of the schemes were studied for various shock motions that might be encountered in problems of engineering interest. Computed results for a model airfoil problem that produces a flow field similar to that about a helicopter rotor in forward flight show the development of a shock wave and its subsequent propagation upstream off the front of the airfoil.

A fast efficient implicit scheme for the gasdynamic equations using a matrix reduction technique

NASA Technical Reports Server (NTRS)

Barth, T. J.; Steger, J. L.

1985-01-01

An efficient implicit finite-difference algorithm for the gasdynamic equations utilizing matrix reduction techniques is presented. A significant reduction in arithmetic operations is achieved without loss of the stability characteristics generality found in the Beam and Warming approximate factorization algorithm. Steady-state solutions to the conservative Euler equations in generalized coordinates are obtained for transonic flows and used to show that the method offers computational advantages over the conventional Beam and Warming scheme. Existing Beam and Warming codes can be retrofit with minimal effort. The theoretical extension of the matrix reduction technique to the full Navier-Stokes equations in Cartesian coordinates is presented in detail. Linear stability, using a Fourier stability analysis, is demonstrated and discussed for the one-dimensional Euler equations.

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.

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.

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Freels, J. D.

1989-01-01

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Finite-Difference Solution for Laminar or Turbulent Boundary Layer Flow over Axisymmetric Bodies with Ideal Gas, CF4, or Equilibrium Air Chemistry

NASA Technical Reports Server (NTRS)

Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.

1992-01-01

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

Finite-difference solution for laminar or turbulent boundary layer flow over axisymmetric bodies with ideal gas, CF4, or equilibrium air chemistry

NASA Astrophysics Data System (ADS)

Hamilton, H. Harris, II; Millman, Daniel R.; Greendyke, Robert B.

1992-12-01

A computer code was developed that uses an implicit finite-difference technique to solve nonsimilar, axisymmetric boundary layer equations for both laminar and turbulent flow. The code can treat ideal gases, air in chemical equilibrium, and carbon tetrafluoride (CF4), which is a useful gas for hypersonic blunt-body simulations. This is the only known boundary layer code that can treat CF4. Comparisons with experimental data have demonstrated that accurate solutions are obtained. The method should prove useful as an analysis tool for comparing calculations with wind tunnel experiments and for making calculations about flight vehicles where equilibrium air chemistry assumptions are valid.

Accuracy of a class of concurrent algorithms for transient finite element analysis

NASA Technical Reports Server (NTRS)

Ortiz, Michael; Sotelino, Elisa D.; Nour-Omid, Bahram

1988-01-01

The accuracy of a new class of concurrent procedures for transient finite element analysis is examined. A phase error analysis is carried out which shows that wave retardation leading to unacceptable loss of accuracy may occur if a Courant condition based on the dimensions of the subdomains is violated. Numerical tests suggest that this Courant condition is conservative for typical structural applications and may lead to a marked increase in accuracy as the number of subdomains is increased. Theoretical speed-up ratios are derived which suggest that the algorithms under consideration can be expected to exhibit a performance superior to that of globally implicit methods when implemented on parallel machines.

Two-level schemes for the advection equation

NASA Astrophysics Data System (ADS)

Vabishchevich, Petr N.

2018-06-01

The advection equation is the basis for mathematical models of continuum mechanics. In the approximate solution of nonstationary problems it is necessary to inherit main properties of the conservatism and monotonicity of the solution. In this paper, the advection equation is written in the symmetric form, where the advection operator is the half-sum of advection operators in conservative (divergent) and non-conservative (characteristic) forms. The advection operator is skew-symmetric. Standard finite element approximations in space are used. The standard explicit two-level scheme for the advection equation is absolutely unstable. New conditionally stable regularized schemes are constructed, on the basis of the general theory of stability (well-posedness) of operator-difference schemes, the stability conditions of the explicit Lax-Wendroff scheme are established. Unconditionally stable and conservative schemes are implicit schemes of the second (Crank-Nicolson scheme) and fourth order. The conditionally stable implicit Lax-Wendroff scheme is constructed. The accuracy of the investigated explicit and implicit two-level schemes for an approximate solution of the advection equation is illustrated by the numerical results of a model two-dimensional problem.

Comparison of Gunshot Entrance Morphologies Caused by .40-Caliber Smith & Wesson, .380-Caliber, and 9-mm Luger Bullets: A Finite Element Analysis Study

PubMed Central

Matoso, Rodrigo Ivo; Freire, Alexandre Rodrigues; Santos, Leonardo Soriano de Mello; Daruge Junior, Eduardo; Rossi, Ana Claudia; Prado, Felippe Bevilacqua

2014-01-01

Firearms can cause fatal wounds, which can be identified by traces on or around the body. However, there are cases where neither the bullet nor gun is found at the crime scene. Ballistic research involving finite element models can reproduce computational biomechanical conditions, without compromising bioethics, as they involve no direct tests on animals or humans. This study aims to compare the morphologies of gunshot entrance holes caused by.40-caliber Smith & Wesson (S&W), .380-caliber, and 9×19-mm Luger bullets. A fully metal-jacketed.40 S&W projectile, a fully metal-jacketed.380 projectile, and a fully metal-jacketed 9×19-mm Luger projectile were computationally fired at the glabellar region of the finite element model from a distance of 10 cm, at perpendicular incidence. The results show different morphologies in the entrance holes produced by the three bullets, using the same skull at the same shot distance. The results and traits of the entrance holes are discussed. Finite element models allow feasible computational ballistic research, which may be useful to forensic experts when comparing and analyzing data related to gunshot wounds in the forehead. PMID:25343337

Numerical simulation of one-dimensional heat transfer in composite bodies with phase change. M.S. Thesis, 1980 Final Report; [wing deicing pads

NASA Technical Reports Server (NTRS)

Dewitt, K. J.; Baliga, G.

1982-01-01

A numerical simulation was developed to investigate the one dimensional heat transfer occurring in a system composed of a layered aircraft blade having an ice deposit on its surface. The finite difference representation of the heat conduction equations was done using the Crank-Nicolson implicit finite difference formulation. The simulation considers uniform or time dependent heat sources, from heaters which can be either point sources or of finite thickness. For the ice water phase change, a numerical method which approximates the latent heat effect by a large heat capacity over a small temperature interval was applied. The simulation describes the temperature profiles within the various layers of the de-icer pad, as well as the movement of the ice water interface. The simulation could also be used to predict the one dimensional temperature profiles in any composite slab having different boundary conditions.

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations. [with applications to Burger equation and stream function-vorticity problem

NASA Technical Reports Server (NTRS)

Kurtz, L. A.; Smith, R. E.; Parks, C. L.; Boney, L. R.

1978-01-01

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Fully kinetic 3D simulations of the Hermean magnetosphere under realistic conditions: a new approach

NASA Astrophysics Data System (ADS)

Amaya, Jorge; Gonzalez-Herrero, Diego; Lembège, Bertrand; Lapenta, Giovanni

2017-04-01

Simulations of the magnetosphere of planets are usually performed using the MHD and the hybrid approaches. However, these two methods still rely on approximations for the computation of the pressure tensor, and require the neutrality of the plasma at every point of the domain by construction. These approximations undermine the role of electrons on the emergence of plasma features in the magnetosphere of planets. The high mobility of electrons, their characteristic time and space scales, and the lack of perfect neutrality, are the source of many observed phenomena in the magnetospheres, including the turbulence energy cascade, the magnetic reconnection, the particle acceleration in the shock front and the formation of current systems around the magnetosphere. Fully kinetic codes are extremely demanding of computing time, and have been unable to perform simulations of the full magnetosphere at the real scales of a planet with realistic plasma conditions. This is caused by two main reasons: 1) explicit codes must resolve the electron scales limiting the time and space discretisation, and 2) current versions of semi-implicit codes are unstable for cell sizes larger than a few Debye lengths. In this work we present new simulations performed with ECsim, an Energy Conserving semi-implicit method [1], that can overcome these two barriers. We compare the solutions obtained with ECsim with the solutions obtained by the classic semi-implicit code iPic3D [2]. The new simulations with ECsim demand a larger computational effort, but the time and space discretisations are larger than those in iPic3D allowing for a faster simulation time of the full planetary environment. The new code, ECsim, can reach a resolution allowing the capture of significant large scale physics without loosing kinetic electron information, such as wave-electron interaction and non-Maxwellian electron velocity distributions [3]. The code is able to better capture the thickness of the different boundary layers of the magnetosphere of Mercury. Electron kinetics are consistent with the spatial and temporal scale resolutions. Simulations are compared with measurements from the MESSENGER spacecraft showing a better fit when compared against the classic fully kinetic code iPic3D. These results show that the new generation of Energy Conserving semi-implicit codes can be used for an accurate analysis and interpretation of particle data from magnetospheric missions like BepiColombo and MMS, including electron velocity distributions and electron temperature anisotropies. [1] Lapenta, G. (2016). Exactly Energy Conserving Implicit Moment Particle in Cell Formulation. arXiv preprint arXiv:1602.06326. [2] Markidis, S., & Lapenta, G. (2010). Multi-scale simulations of plasma with iPIC3D. Mathematics and Computers in Simulation, 80(7), 1509-1519. [3] Lapenta, G., Gonzalez-Herrero, D., & Boella, E. (2016). Multiple scale kinetic simulations with the energy conserving semi implicit particle in cell (PIC) method. arXiv preprint arXiv:1612.08289.

Finite Element Barotropic Model for the Indian and Western Pacific OceanBasin: Tidal Model Data Comparisons and Sensitivities

DTIC Science & Technology

2018-01-11

From - To) 01/11/2018 Final Technical Report June 01 2016 - Dec 30 2017 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Finite - Element Barotropic Model...grid finite - element barotropic fully hydrodynamic model in order to understand the shallow-water dynamics of the Indian Ocean and Western Pacific Ocean...dissipative dissipative processes are explored. 15. SUBJECTTERMS finite - element , unstructured grid, barotropic tides, bathymetry, internal tide

The computation of thermo-chemical nonequilibrium hypersonic flows

NASA Technical Reports Server (NTRS)

Candler, Graham

1989-01-01

Several conceptual designs for vehicles that would fly in the atmosphere at hypersonic speeds have been developed recently. For the proposed flight conditions the air in the shock layer that envelops the body is at a sufficiently high temperature to cause chemical reaction, vibrational excitation, and ionization. However, these processes occur at finite rates which, when coupled with large convection speeds, cause the gas to be removed from thermo-chemical equilibrium. This non-ideal behavior affects the aerothermal loading on the vehicle and has ramifications in its design. A numerical method to solve the equations that describe these types of flows in 2-D was developed. The state of the gas is represented with seven chemical species, a separate vibrational temperature for each diatomic species, an electron translational temperature, and a mass-average translational-rotational temperature for the heavy particles. The equations for this gas model are solved numerically in a fully coupled fashion using an implicit finite volume time-marching technique. Gauss-Seidel line-relaxation is used to reduce the cost of the solution and flux-dependent differencing is employed to maintain stability. The numerical method was tested against several experiments. The calculated bow shock wave detachment on a sphere and two cones was compared to those measured in ground testing facilities. The computed peak electron number density on a sphere-cone was compared to that measured in a flight test. In each case the results from the numerical method were in excellent agreement with experiment. The technique was used to predict the aerothermal loads on an Aeroassisted Orbital Transfer Vehicle including radiative heating. These results indicate that the current physical model of high temperature air is appropriate and that the numerical algorithm is capable of treating this class of flows.

Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons

PubMed Central

2012-01-01

We derive the mean-field equations arising as the limit of a network of interacting spiking neurons, as the number of neurons goes to infinity. The neurons belong to a fixed number of populations and are represented either by the Hodgkin-Huxley model or by one of its simplified version, the FitzHugh-Nagumo model. The synapses between neurons are either electrical or chemical. The network is assumed to be fully connected. The maximum conductances vary randomly. Under the condition that all neurons’ initial conditions are drawn independently from the same law that depends only on the population they belong to, we prove that a propagation of chaos phenomenon takes place, namely that in the mean-field limit, any finite number of neurons become independent and, within each population, have the same probability distribution. This probability distribution is a solution of a set of implicit equations, either nonlinear stochastic differential equations resembling the McKean-Vlasov equations or non-local partial differential equations resembling the McKean-Vlasov-Fokker-Planck equations. We prove the well-posedness of the McKean-Vlasov equations, i.e. the existence and uniqueness of a solution. We also show the results of some numerical experiments that indicate that the mean-field equations are a good representation of the mean activity of a finite size network, even for modest sizes. These experiments also indicate that the McKean-Vlasov-Fokker-Planck equations may be a good way to understand the mean-field dynamics through, e.g. a bifurcation analysis. Mathematics Subject Classification (2000): 60F99, 60B10, 92B20, 82C32, 82C80, 35Q80. PMID:22657695

Implicit Perceptual-Motor Skill Learning in Mild Cognitive Impairment and Parkinson's Disease

PubMed Central

Gobel, Eric W.; Blomeke, Kelsey; Zadikoff, Cindy; Simuni, Tanya; Weintraub, Sandy; Reber, Paul J.

2015-01-01

Objective Implicit skill learning is hypothesized to depend on nondeclarative memory that operates independent of the medial temporal lobe (MTL) memory system and instead depends on cortico-striatal circuits between the basal ganglia and cortical areas supporting motor function and planning. Research with the Serial Reaction Time (SRT) task suggests that patients with memory-disorders due to MTL damage exhibit normal implicit sequence learning. However, reports of intact learning rely on observations of no group differences, leading to speculation whether implicit sequence learning is fully intact in these patients. Patients with Parkinson's Disease (PD) often exhibit impaired sequence learning, but this impairment is not universally observed. Method Implicit perceptual-motor sequence learning was examined using the Serial Interception Sequence Learning (SISL) task in patients with amnestic Mild Cognitive Impairment (MCI; n=11) and patients with PD (n=15). Sequence learning in SISL is resistant to explicit learning and individually adapted task difficulty controls for baseline performance differences. Results Patients with MCI exhibited robust sequence learning, equivalent to healthy older adults (n=20), supporting the hypothesis that the MTL does not contribute to learning in this task. In contrast, the majority of patients with PD exhibited no sequence-specific learning in spite of matched overall task performance. Two patients with PD exhibited performance indicative of an explicit compensatory strategy suggesting that impaired implicit learning may lead to greater reliance on explicit memory in some individuals. Conclusion The differences in learning between patient groups provides strong evidence in favor of implicit sequence learning depending solely on intact basal ganglia function with no contribution from the MTL memory system. PMID:23688213

Numerical approach to optimal portfolio in a power utility regime-switching model

NASA Astrophysics Data System (ADS)

Gyulov, Tihomir B.; Koleva, Miglena N.; Vulkov, Lubin G.

2017-12-01

We consider a system of weakly coupled degenerate semi-linear parabolic equations of optimal portfolio in a regime-switching with power utility function, derived by A.R. Valdez and T. Vargiolu [14]. First, we discuss some basic properties of the solution of this system. Then, we develop and analyze implicit-explicit, flux limited finite difference schemes for the differential problem. Numerical experiments are discussed.

Explicit and implicit calculations of turbulent cavity flows with and without yaw angle

NASA Astrophysics Data System (ADS)

Yen, Guan-Wei

1989-08-01

Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.

Effect of absorption on nonlinear propagation of short ultrasound pulses generated by rectangular transducers

NASA Astrophysics Data System (ADS)

Khokhlova, Vera A.; Ponomaryov, Anatoly E.; Averkiou, Michalakis A.; Crum, Lawrence A.

2002-11-01

A numerical solution of the KZK-type parabolic nonlinear evolution equation is presented for finite-amplitude sound beams radiated by rectangular sources. The initial acoustic waveform is a short tone burst, similar to those used in diagnostic ultrasound. The generation of higher harmonic components and their spatial structure are investigated for media similar to tissue with various frequency dependent absorption properties. Nonlinear propagation in a thermoviscous fluid with a quadratic frequency law of absorption is compared to that in tissue with a nearly linear frequency law of absorption. The algorithm is based on that originally developed by Lee and Hamilton [J. Acoust. Soc. Am. 97, 906-917 (1995)] to model circular sources. The algorithm is generalized for two-dimensional sources without axial symmetry. The diffraction integral is adapted in the time-domain for two dimensions with the implicit backward finite difference (IBFD) scheme in the nearfield and with the alternate direction implicit (ADI) method at longer distances. Arbitrary frequency dependence of absorption is included in this model and solved in the frequency-domain using the FFT technique. The results of simulation may be used to better understand the nonlinear beam structure for tissue harmonic imaging in modern medical diagnostic scanners. [Work supported by CRDF and RFBR.

Explicit and implicit calculations of turbulent cavity flows with and without yaw angle. M.S. Thesis

NASA Technical Reports Server (NTRS)

Yen, Guan-Wei

1989-01-01

Computations were performed to simulate turbulent supersonic flows past three-dimensional deep cavities with and without yaw. Simulation of these self-sustained oscillatory flows were generated through time accurate solutions of the Reynolds averaged complete Navier-Stokes equations using two different schemes: (1) MacCormack, finite-difference; and (2) implicit, upwind, finite-volume schemes. The second scheme, which is approximately 30 percent faster, is found to produce better time accurate results. The Reynolds stresses were modeled, using the Baldwin-Lomax algebraic turbulence model with certain modifications. The computational results include instantaneous and time averaged flow properties everywhere in the computational domain. Time series analyses were performed for the instantaneous pressure values on the cavity floor. The time averaged computational results show good agreement with the experimental data along the cavity floor and walls. When the yaw angle is nonzero, there is no longer a single length scale (length-to-depth ratio) for the flow, as is the case for zero yaw angle flow. The dominant directions and inclinations of the vortices are dramatically different for this nonsymmetric flow. The vortex shedding from the cavity into the mainstream flow is captured computationally. This phenomenon, which is due to the oscillation of the shear layer, is confirmed by the solutions of both schemes.

Memory-optimized shift operator alternating direction implicit finite difference time domain method for plasma

NASA Astrophysics Data System (ADS)

Song, Wanjun; Zhang, Hou

2017-11-01

Through introducing the alternating direction implicit (ADI) technique and the memory-optimized algorithm to the shift operator (SO) finite difference time domain (FDTD) method, the memory-optimized SO-ADI FDTD for nonmagnetized collisional plasma is proposed and the corresponding formulae of the proposed method for programming are deduced. In order to further the computational efficiency, the iteration method rather than Gauss elimination method is employed to solve the equation set in the derivation of the formulae. Complicated transformations and convolutions are avoided in the proposed method compared with the Z transforms (ZT) ADI FDTD method and the piecewise linear JE recursive convolution (PLJERC) ADI FDTD method. The numerical dispersion of the SO-ADI FDTD method with different plasma frequencies and electron collision frequencies is analyzed and the appropriate ratio of grid size to the minimum wavelength is given. The accuracy of the proposed method is validated by the reflection coefficient test on a nonmagnetized collisional plasma sheet. The testing results show that the proposed method is advantageous for improving computational efficiency and saving computer memory. The reflection coefficient of a perfect electric conductor (PEC) sheet covered by multilayer plasma and the RCS of the objects coated by plasma are calculated by the proposed method and the simulation results are analyzed.

Unsteady streamflow simulation using a linear implicit finite-difference model

USGS Publications Warehouse

Land, Larry F.

1978-01-01

A computer program for simulating one-dimensional subcritical, gradually varied, unsteady flow in a stream has been developed and documented. Given upstream and downstream boundary conditions and channel geometry data, roughness coefficients, stage, and discharge can be calculated anywhere within the reach as a function of time. The program uses a linear implicit finite-difference technique that discritizes the partial differential equations. Then it arranges the coefficients of the continuity and momentum equations into a pentadiagonal matrix for solution. Because it is a reasonable compromise between computational accuracy, speed and ease of use,the technique is one of the most commonly used. The upstream boundary condition is a depth hydrograph. However, options also allow the boundary condition to be discharge or water-surface elevation. The downstream boundary condition is a depth which may be constant, self-setting, or unsteady. The reach may be divided into uneven increments and the cross sections may be nonprismatic and may vary from one to the other. Tributary and lateral inflow may enter the reach. The digital model will simulate such common problems as (1) flood waves, (2) releases from dams, and (3) channels where storage is a consideration. It may also supply the needed flow information for mass-transport simulation. (Woodard-USGS)

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

Aleman, S.E.

This report documents a finite element code designed to model subsurface flow and contaminant transport, named FACT. FACT is a transient three-dimensional, finite element code designed to simulate isothermal groundwater flow, moisture movement, and solute transport in variably saturated and fully saturated subsurface porous media.

The Use of Non-Standard Devices in Finite Element Analysis

NASA Technical Reports Server (NTRS)

Schur, Willi W.; Broduer, Steve (Technical Monitor)

2001-01-01

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Automatic partitioning of unstructured meshes for the parallel solution of problems in computational mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Lesoinne, Michel

1993-01-01

Most of the recently proposed computational methods for solving partial differential equations on multiprocessor architectures stem from the 'divide and conquer' paradigm and involve some form of domain decomposition. For those methods which also require grids of points or patches of elements, it is often necessary to explicitly partition the underlying mesh, especially when working with local memory parallel processors. In this paper, a family of cost-effective algorithms for the automatic partitioning of arbitrary two- and three-dimensional finite element and finite difference meshes is presented and discussed in view of a domain decomposed solution procedure and parallel processing. The influence of the algorithmic aspects of a solution method (implicit/explicit computations), and the architectural specifics of a multiprocessor (SIMD/MIMD, startup/transmission time), on the design of a mesh partitioning algorithm are discussed. The impact of the partitioning strategy on load balancing, operation count, operator conditioning, rate of convergence and processor mapping is also addressed. Finally, the proposed mesh decomposition algorithms are demonstrated with realistic examples of finite element, finite volume, and finite difference meshes associated with the parallel solution of solid and fluid mechanics problems on the iPSC/2 and iPSC/860 multiprocessors.

Convergence Acceleration for Multistage Time-Stepping Schemes

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, Eli L.; Rossow, C-C; Vasta, V. N.

2006-01-01

The convergence of a Runge-Kutta (RK) scheme with multigrid is accelerated by preconditioning with a fully implicit operator. With the extended stability of the Runge-Kutta scheme, CFL numbers as high as 1000 could be used. The implicit preconditioner addresses the stiffness in the discrete equations associated with stretched meshes. Numerical dissipation operators (based on the Roe scheme, a matrix formulation, and the CUSP scheme) as well as the number of RK stages are considered in evaluating the RK/implicit scheme. Both the numerical and computational efficiency of the scheme with the different dissipation operators are discussed. The RK/implicit scheme is used to solve the two-dimensional (2-D) and three-dimensional (3-D) compressible, Reynolds-averaged Navier-Stokes equations. In two dimensions, turbulent flows over an airfoil at subsonic and transonic conditions are computed. The effects of mesh cell aspect ratio on convergence are investigated for Reynolds numbers between 5.7 x 10(exp 6) and 100.0 x 10(exp 6). Results are also obtained for a transonic wing flow. For both 2-D and 3-D problems, the computational time of a well-tuned standard RK scheme is reduced at least a factor of four.

Implicit-Explicit Time Integration Methods for Non-hydrostatic Atmospheric Models

NASA Astrophysics Data System (ADS)

Gardner, D. J.; Guerra, J. E.; Hamon, F. P.; Reynolds, D. R.; Ullrich, P. A.; Woodward, C. S.

2016-12-01

The Accelerated Climate Modeling for Energy (ACME) project is developing a non-hydrostatic atmospheric dynamical core for high-resolution coupled climate simulations on Department of Energy leadership class supercomputers. An important factor in computational efficiency is avoiding the overly restrictive time step size limitations of fully explicit time integration methods due to the stiffest modes present in the model (acoustic waves). In this work we compare the accuracy and performance of different Implicit-Explicit (IMEX) splittings of the non-hydrostatic equations and various Additive Runge-Kutta (ARK) time integration methods. Results utilizing the Tempest non-hydrostatic atmospheric model and the ARKode package show that the choice of IMEX splitting and ARK scheme has a significant impact on the maximum stable time step size as well as solution quality. Horizontally Explicit Vertically Implicit (HEVI) approaches paired with certain ARK methods lead to greatly improved runtimes. With effective preconditioning IMEX splittings that incorporate some implicit horizontal dynamics can be competitive with HEVI results. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. LLNL-ABS-699187

A Semi-Implicit, Three-Dimensional Model for Estuarine Circulation

USGS Publications Warehouse

Smith, Peter E.

2006-01-01

A semi-implicit, finite-difference method for the numerical solution of the three-dimensional equations for circulation in estuaries is presented and tested. The method uses a three-time-level, leapfrog-trapezoidal scheme that is essentially second-order accurate in the spatial and temporal numerical approximations. The three-time-level scheme is shown to be preferred over a two-time-level scheme, especially for problems with strong nonlinearities. The stability of the semi-implicit scheme is free from any time-step limitation related to the terms describing vertical diffusion and the propagation of the surface gravity waves. The scheme does not rely on any form of vertical/horizontal mode-splitting to treat the vertical diffusion implicitly. At each time step, the numerical method uses a double-sweep method to transform a large number of small tridiagonal equation systems and then uses the preconditioned conjugate-gradient method to solve a single, large, five-diagonal equation system for the water surface elevation. The governing equations for the multi-level scheme are prepared in a conservative form by integrating them over the height of each horizontal layer. The layer-integrated volumetric transports replace velocities as the dependent variables so that the depth-integrated continuity equation that is used in the solution for the water surface elevation is linear. Volumetric transports are computed explicitly from the momentum equations. The resulting method is mass conservative, efficient, and numerically accurate.

An implicit time-marching method for the three-dimensional Navier-Stokes equations of contravariant velocity components

NASA Astrophysics Data System (ADS)

Daiguji, Hisaaki; Yamamoto, Satoru

1988-12-01

The implicit time-marching finite-difference method for solving the three-dimensional compressible Euler equations developed by the authors is extended to the Navier-Stokes equations. The distinctive features of this method are to make use of momentum equations of contravariant velocities instead of physical boundaries, and to be able to treat the periodic boundary condition for the three-dimensional impeller flow easily. These equations can be solved by using the same techniques as the Euler equations, such as the delta-form approximate factorization, diagonalization and upstreaming. In addition to them, a simplified total variation diminishing scheme by the authors is applied to the present method in order to capture strong shock waves clearly. Finally, the computed results of the three-dimensional flow through a transonic compressor rotor with tip clearance are shown.

On pseudo-spectral time discretizations in summation-by-parts form

NASA Astrophysics Data System (ADS)

Ruggiu, Andrea A.; Nordström, Jan

2018-05-01

Fully-implicit discrete formulations in summation-by-parts form for initial-boundary value problems must be invertible in order to provide well functioning procedures. We prove that, under mild assumptions, pseudo-spectral collocation methods for the time derivative lead to invertible discrete systems when energy-stable spatial discretizations are used.

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

A Single Session of Attentional Bias Modification Reduces Alcohol Craving and Implicit Measures of Alcohol Bias in Young Adult Drinkers.

PubMed

Luehring-Jones, Peter; Louis, Courtney; Dennis-Tiwary, Tracy A; Erblich, Joel

2017-12-01

Attentional bias modification (ABM) techniques for reducing problematic alcohol consumption hold promise as highly accessible and cost-effective treatment approaches. A growing body of literature has examined ABM as a potentially efficacious intervention for reducing drinking and drinking-related cognitions in alcohol-dependent individuals as well as those at-risk of developing problem drinking habits. This study tested the effectiveness of a single session of visual probe-based ABM training in a cohort of 60 non-treatment-seeking young adult drinkers, with a focus on examining mechanisms underlying training efficacy. Participants were randomly assigned to a single session of active ABM training or a sham training condition in a laboratory setting. Measures of implicit drinking-related cognitions (alcohol Stroop and an Implicit Association Task) and attentional bias (AB; alcohol visual probe) were administered, and subjective alcohol craving was reported in response to in vivo alcohol cues. Results showed that active ABM training, relative to sham, resulted in significant differences in measures of implicit alcohol-related cognition, alcohol-related AB, and self-reports of alcohol craving. Mediation analysis showed that reductions in craving were fully mediated by ABM-related reductions in alcohol-Stroop interference scores, suggesting a previously undocumented relationship between the 2 measures. Results document the efficacy of brief ABM to reduce both implicit and explicit processes related to drinking, and highlight the potential intervention-relevance of alcohol-related implicit cognitions in social drinkers. Copyright © 2017 by the Research Society on Alcoholism.

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.

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

Automated finite element modeling of the lumbar spine: Using a statistical shape model to generate a virtual population of models.

PubMed

Campbell, J Q; Petrella, A J

2016-09-06

Population-based modeling of the lumbar spine has the potential to be a powerful clinical tool. However, developing a fully parameterized model of the lumbar spine with accurate geometry has remained a challenge. The current study used automated methods for landmark identification to create a statistical shape model of the lumbar spine. The shape model was evaluated using compactness, generalization ability, and specificity. The primary shape modes were analyzed visually, quantitatively, and biomechanically. The biomechanical analysis was performed by using the statistical shape model with an automated method for finite element model generation to create a fully parameterized finite element model of the lumbar spine. Functional finite element models of the mean shape and the extreme shapes (±3 standard deviations) of all 17 shape modes were created demonstrating the robust nature of the methods. This study represents an advancement in finite element modeling of the lumbar spine and will allow population-based modeling in the future. Copyright © 2016 Elsevier Ltd. All rights reserved.

An Unstructured Finite Volume Approach for Structural Dynamics in Response to Fluid Motions.

PubMed

Xia, Guohua; Lin, Ching-Long

2008-04-01

A new cell-vortex unstructured finite volume method for structural dynamics is assessed for simulations of structural dynamics in response to fluid motions. A robust implicit dual-time stepping method is employed to obtain time accurate solutions. The resulting system of algebraic equations is matrix-free and allows solid elements to include structure thickness, inertia, and structural stresses for accurate predictions of structural responses and stress distributions. The method is coupled with a fluid dynamics solver for fluid-structure interaction, providing a viable alternative to the finite element method for structural dynamics calculations. A mesh sensitivity test indicates that the finite volume method is at least of second-order accuracy. The method is validated by the problem of vortex-induced vibration of an elastic plate with different initial conditions and material properties. The results are in good agreement with existing numerical data and analytical solutions. The method is then applied to simulate a channel flow with an elastic wall. The effects of wall inertia and structural stresses on the fluid flow are investigated.

Numerical simulation of hypersonic inlet flows with equilibrium or finite rate chemistry

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao; Hsieh, Kwang-Chung; Shuen, Jian-Shun; Mcbride, Bonnie J.

1988-01-01

An efficient numerical program incorporated with comprehensive high temperature gas property models has been developed to simulate hypersonic inlet flows. The computer program employs an implicit lower-upper time marching scheme to solve the two-dimensional Navier-Stokes equations with variable thermodynamic and transport properties. Both finite-rate and local-equilibrium approaches are adopted in the chemical reaction model for dissociation and ionization of the inlet air. In the finite rate approach, eleven species equations coupled with fluid dynamic equations are solved simultaneously. In the local-equilibrium approach, instead of solving species equations, an efficient chemical equilibrium package has been developed and incorporated into the flow code to obtain chemical compositions directly. Gas properties for the reaction products species are calculated by methods of statistical mechanics and fit to a polynomial form for C(p). In the present study, since the chemical reaction time is comparable to the flow residence time, the local-equilibrium model underpredicts the temperature in the shock layer. Significant differences of predicted chemical compositions in shock layer between finite rate and local-equilibrium approaches have been observed.

User's manual for the one-dimensional hypersonic experimental aero-thermodynamic (1DHEAT) data reduction code

NASA Technical Reports Server (NTRS)

Hollis, Brian R.

1995-01-01

A FORTRAN computer code for the reduction and analysis of experimental heat transfer data has been developed. This code can be utilized to determine heat transfer rates from surface temperature measurements made using either thin-film resistance gages or coaxial surface thermocouples. Both an analytical and a numerical finite-volume heat transfer model are implemented in this code. The analytical solution is based on a one-dimensional, semi-infinite wall thickness model with the approximation of constant substrate thermal properties, which is empirically corrected for the effects of variable thermal properties. The finite-volume solution is based on a one-dimensional, implicit discretization. The finite-volume model directly incorporates the effects of variable substrate thermal properties and does not require the semi-finite wall thickness approximation used in the analytical model. This model also includes the option of a multiple-layer substrate. Fast, accurate results can be obtained using either method. This code has been used to reduce several sets of aerodynamic heating data, of which samples are included in this report.

A time-spectral approach to numerical weather prediction

NASA Astrophysics Data System (ADS)

Scheffel, Jan; Lindvall, Kristoffer; Yik, Hiu Fai

2018-05-01

Finite difference methods are traditionally used for modelling the time domain in numerical weather prediction (NWP). Time-spectral solution is an attractive alternative for reasons of accuracy and efficiency and because time step limitations associated with causal CFL-like criteria, typical for explicit finite difference methods, are avoided. In this work, the Lorenz 1984 chaotic equations are solved using the time-spectral algorithm GWRM (Generalized Weighted Residual Method). Comparisons of accuracy and efficiency are carried out for both explicit and implicit time-stepping algorithms. It is found that the efficiency of the GWRM compares well with these methods, in particular at high accuracy. For perturbative scenarios, the GWRM was found to be as much as four times faster than the finite difference methods. A primary reason is that the GWRM time intervals typically are two orders of magnitude larger than those of the finite difference methods. The GWRM has the additional advantage to produce analytical solutions in the form of Chebyshev series expansions. The results are encouraging for pursuing further studies, including spatial dependence, of the relevance of time-spectral methods for NWP modelling.

Sample extraction and injection with a microscale preconcentrator.

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

Robinson, Alex Lockwood; Chan, Helena Kai Lun

2007-09-01

This report details the development of a microfabricated preconcentrator that functions as a fully integrated chemical extractor-injector for a microscale gas chromatograph (GC). The device enables parts-per-billion detection and quantitative analysis of volatile organic compounds (VOCs) in indoor air with size and power advantages over macro-scale systems. The 44 mm{sup 3} preconcentrator extracts VOCs using highly adsorptive, granular forms of graphitized carbon black and carbon molecular sieves. The micron-sized silicon cavities have integrated heating and temperature sensing allowing low power, yet rapid heating to thermally desorb the collected VOCs (GC injection). The keys to device construction are a new adsorbent-solventmore » filling technique and solvent-tolerant wafer-level silicon-gold eutectic bonding technology. The product is the first granular adsorbent preconcentrator integrated at the wafer level. Other advantages include exhaustive VOC extraction and injection peak widths an order of magnitude narrower than predecessor prototypes. A mass transfer model, the first for any microscale preconcentrator, is developed to describe both adsorption and desorption behaviors. The physically intuitive model uses implicit and explicit finite differences to numerically solve the required partial differential equations. The model is applied to the adsorption and desorption of decane at various concentrations to extract Langmuir adsorption isotherm parameters from effluent curve measurements where properties are unknown a priori.« less

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

McHugh, P.R.; Ramshaw, J.D.

MAGMA is a FORTRAN computer code designed to viscous flow in in situ vitrification melt pools. It models three-dimensional, incompressible, viscous flow and heat transfer. The momentum equation is coupled to the temperature field through the buoyancy force terms arising from the Boussinesq approximation. All fluid properties, except density, are assumed variable. Density is assumed constant except in the buoyancy force terms in the momentum equation. A simple melting model based on the enthalpy method allows the study of the melt front progression and latent heat effects. An indirect addressing scheme used in the numerical solution of the momentum equationmore » voids unnecessary calculations in cells devoid of liquid. Two-dimensional calculations can be performed using either rectangular or cylindrical coordinates, while three-dimensional calculations use rectangular coordinates. All derivatives are approximated by finite differences. The incompressible Navier-Stokes equations are solved using a new fully implicit iterative technique, while the energy equation is differenced explicitly in time. Spatial derivatives are written in conservative form using a uniform, rectangular, staggered mesh based on the marker and cell placement of variables. Convective terms are differenced using a weighted average of centered and donor cell differencing to ensure numerical stability. Complete descriptions of MAGMA governing equations, numerics, code structure, and code verification are provided. 14 refs.« less

A numerical study of mixing in supersonic combustors with hypermixing injectors

NASA Technical Reports Server (NTRS)

Lee, J.

1993-01-01

A numerical study was conducted to evaluate the performance of wall mounted fuel-injectors designed for potential Supersonic Combustion Ramjet (SCRAM-jet) engine applications. The focus of this investigation was to numerically simulate existing combustor designs for the purpose of validating the numerical technique and the physical models developed. Three different injector designs of varying complexity were studied to fully understand the computational implications involved in accurate predictions. A dual transverse injection system and two streamwise injector designs were studied. The streamwise injectors were designed with swept ramps to enhance fuel-air mixing and combustion characteristics at supersonic speeds without the large flow blockage and drag contribution of the transverse injection system. For this study, the Mass-Average Navier-Stokes equations and the chemical species continuity equations were solved. The computations were performed using a finite-volume implicit numerical technique and multiple block structured grid system. The interfaces of the multiple block structured grid systems were numerically resolved using the flux-conservative technique. Detailed comparisons between the computations and existing experimental data are presented. These comparisons show that numerical predictions are in agreement with the experimental data. These comparisons also show that a number of turbulence model improvements are needed for accurate combustor flowfield predictions.

A numerical study of mixing in supersonic combustors with hypermixing injectors

NASA Technical Reports Server (NTRS)

Lee, J.

1992-01-01

A numerical study was conducted to evaluate the performance of wall mounted fuel-injectors designed for potential Supersonic Combustion Ramjet (SCRAM-jet) engine applications. The focus of this investigation was to numerically simulate existing combustor designs for the purpose of validating the numerical technique and the physical models developed. Three different injector designs of varying complexity were studied to fully understand the computational implications involved in accurate predictions. A dual transverse injection system and two streamwise injector designs were studied. The streamwise injectors were designed with swept ramps to enhance fuel-air mixing and combustion characteristics at supersonic speeds without the large flow blockage and drag contribution of the transverse injection system. For this study, the Mass-Averaged Navier-Stokes equations and the chemical species continuity equations were solved. The computations were performed using a finite-volume implicit numerical technique and multiple block structured grid system. The interfaces of the multiple block structured grid systems were numerically resolved using the flux-conservative technique. Detailed comparisons between the computations and existing experimental data are presented. These comparisons show that numerical predictions are in agreement with the experimental data. These comparisons also show that a number of turbulence model improvements are needed for accurate combustor flowfield predictions.

Modeling of transitional flows

NASA Technical Reports Server (NTRS)

Lund, Thomas S.

1988-01-01

An effort directed at developing improved transitional models was initiated. The focus of this work was concentrated on the critical assessment of a popular existing transitional model developed by McDonald and Fish in 1972. The objective of this effort was to identify the shortcomings of the McDonald-Fish model and to use the insights gained to suggest modifications or alterations of the basic model. In order to evaluate the transitional model, a compressible boundary layer code was required. Accordingly, a two-dimensional compressible boundary layer code was developed. The program was based on a three-point fully implicit finite difference algorithm where the equations were solved in an uncoupled manner with second order extrapolation used to evaluate the non-linear coefficients. Iteration was offered as an option if the extrapolation error could not be tolerated. The differencing scheme was arranged to be second order in both spatial directions on an arbitrarily stretched mesh. A variety of boundary condition options were implemented including specification of an external pressure gradient, specification of a wall temperature distribution, and specification of an external temperature distribution. Overall the results of the initial phase of this work indicate that the McDonald-Fish model does a poor job at predicting the details of the turbulent flow structure during the transition region.

Development of an energy storage tank model

NASA Astrophysics Data System (ADS)

Buckley, Robert Christopher

A linearized, one-dimensional finite difference model employing an implicit finite difference method for energy storage tanks is developed, programmed with MATLAB, and demonstrated for different applications. A set of nodal energy equations is developed by considering the energy interactions on a small control volume. The general method of solving these equations is described as are other features of the simulation program. Two modeling applications are presented: the first using a hot water storage tank with a solar collector and an absorption chiller to cool a building in the summer, the second using a molten salt storage system with a solar collector and steam power plant to generate electricity. Recommendations for further study as well as all of the source code generated in the project are also provided.

Numerical Treatment of Degenerate Diffusion Equations via Feller's Boundary Classification, and Applications

NASA Technical Reports Server (NTRS)

Cacio, Emanuela; Cohn, Stephen E.; Spigler, Renato

2011-01-01

A numerical method is devised to solve a class of linear boundary-value problems for one-dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite-difference scheme, grid, and treatment of the boundary data. Second-order accuracy, unconditional stability, and unconditional convergence of solutions of the finite-difference scheme to a constant as the time-step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration.

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1990-01-01

A new computer code was developed for predicting the turbulent and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

Analysis of rotary engine combustion processes based on unsteady, three-dimensional computations

NASA Technical Reports Server (NTRS)

Raju, M. S.; Willis, E. A.

1989-01-01

A new computer code was developed for predicting the turbulent, and chemically reacting flows with sprays occurring inside of a stratified charge rotary engine. The solution procedure is based on an Eulerian Lagrangian approach where the unsteady, 3-D Navier-Stokes equations for a perfect gas mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite volume, Steger-Warming flux vector splitting scheme, and the liquid phase equations are solved in Lagrangian coordinates. Both the details of the numerical algorithm and the finite difference predictions of the combustor flow field during the opening of exhaust and/or intake, and also during fuel vaporization and combustion, are presented.

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

NASA Technical Reports Server (NTRS)

Godfrey, Andrew G.; Walters, Robert W.; Van Leer, Bram

1993-01-01

The preconditioning procedure for generalized finite-rate chemistry and the proper preconditioning for the one-dimensional Navier-Stokes equations are presented. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from the incompressible to the hypersonic. Specific benefits are realized at low and transonic flow speeds. The extended preconditioning matrix accounts for thermal and chemical non-equilibrium and its implementation is explained for both explicit and implicit time marching. The effect of higher-order spatial accuracy and various flux splittings is investigated. Numerical analysis reveals the possible theoretical improvements from using proconditioning at all Mach numbers. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number regions.

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)

Effects of Turbulence Model on Prediction of Hot-Gas Lateral Jet Interaction in a Supersonic Crossflow

DTIC Science & Technology

2015-07-01

performance computing time from the US Department of Defense (DOD) High Performance Computing Modernization program at the US Army Research Laboratory...Approved OMB No. 0704-0188 Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time ...dimensional, compressible, Reynolds-averaged Navier-Stokes (RANS) equations are solved using a finite volume method. A point-implicit time - integration

Phase Field Fracture Mechanics.

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

Robertson, Brett Anthony

For this assignment, a newer technique of fracture mechanics using a phase field approach, will be examined and compared with experimental data for a bend test and a tension test. The software being used is Sierra Solid Mechanics, an implicit/explicit finite element code developed at Sandia National Labs in Albuquerque, New Mexico. The bend test experimental data was also obtained at Sandia Labs while the tension test data was found in a report online from Purdue University.

Application of Parallel Time-Implicit Discontinuous Galerkin Finite Element Methods to Hypersonic Nonequilibrium Flow Problems

DTIC Science & Technology

2014-05-01

heating prediction to grid alignment along the shock . . . . . . . . 36 1-12 Large variation in heating predictions for 3D hypersonic flow over cylinder...100 4-12 Taylor Vortex problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 4-13 Taylor Vortex problem: 3D ...149 6-16 3D contours for temperature, T for MIG and US3D for only O2 test case . . . . 150 6-17 Stagnation line plots for only

Accuracy of the domain method for the material derivative approach to shape design sensitivities

NASA Technical Reports Server (NTRS)

Yang, R. J.; Botkin, M. E.

1987-01-01

Numerical accuracy for the boundary and domain methods of the material derivative approach to shape design sensitivities is investigated through the use of mesh refinement. The results show that the domain method is generally more accurate than the boundary method, using the finite element technique. It is also shown that the domain method is equivalent, under certain assumptions, to the implicit differentiation approach not only theoretically but also numerically.

Effects of Crimped Fiber Paths on Mixed Mode Delamination Behaviors in Woven Fabric Composites

DTIC Science & Technology

2016-09-01

continuum finite - element models. Three variations of a plain-woven fabric architecture—each of which had different crimped fiber paths—were considered... Finite - Element Analysis Fracture Mechanics Fracture Toughness Mixed Modes Strain Energy Release Rate 16. SECURITY...polymer FB Fully balanced laminate FEA Finite - element analysis FTCM Fracture toughness conversion mechanism G Shear modulus GI, GII, GIII Mode

Reference Models for Multi-Layer Tissue Structures

DTIC Science & Technology

2016-09-01

simulation,  finite   element  analysis 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18. NUMBER OF PAGES 19a. NAME OF RESPONSIBLE PERSON USAMRMC...Physiologically realistic, fully specimen-specific, nonlinear reference models. Tasks. Finite element analysis of non-linear mechanics of cadaver...models. Tasks. Finite element analysis of non-linear mechanics of multi-layer tissue regions of human subjects. Deliverables. Partially subject- and

An Assessment of Some Design Constraints on Heat Production of a 3D Conceptual EGS Model Using an Open-Source Geothermal Reservoir Simulation Code

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

Yidong Xia; Mitch Plummer; Robert Podgorney

2016-02-01

Performance of heat production process over a 30-year period is assessed in a conceptual EGS model with a geothermal gradient of 65K per km depth in the reservoir. Water is circulated through a pair of parallel wells connected by a set of single large wing fractures. The results indicate that the desirable output electric power rate and lifespan could be obtained under suitable material properties and system parameters. A sensitivity analysis on some design constraints and operation parameters indicates that 1) the fracture horizontal spacing has profound effect on the long-term performance of heat production, 2) the downward deviation anglemore » for the parallel doublet wells may help overcome the difficulty of vertical drilling to reach a favorable production temperature, and 3) the thermal energy production rate and lifespan has close dependence on water mass flow rate. The results also indicate that the heat production can be improved when the horizontal fracture spacing, well deviation angle, and production flow rate are under reasonable conditions. To conduct the reservoir modeling and simulations, an open-source, finite element based, fully implicit, fully coupled hydrothermal code, namely FALCON, has been developed and used in this work. Compared with most other existing codes that are either closed-source or commercially available in this area, this new open-source code has demonstrated a code development strategy that aims to provide an unparalleled easiness for user-customization and multi-physics coupling. Test results have shown that the FALCON code is able to complete the long-term tests efficiently and accurately, thanks to the state-of-the-art nonlinear and linear solver algorithms implemented in the code.« less

FINIFLUX: An implicit finite element model for quantification of groundwater fluxes and hyporheic exchange in streams and rivers using radon

NASA Astrophysics Data System (ADS)

Frei, S.; Gilfedder, B. S.

2015-08-01

A quantitative understanding of groundwater-surface water interactions is vital for sustainable management of water quantity and quality. The noble gas radon-222 (Rn) is becoming increasingly used as a sensitive tracer to quantify groundwater discharge to wetlands, lakes, and rivers: a development driven by technical and methodological advances in Rn measurement. However, quantitative interpretation of these data is not trivial, and the methods used to date are based on the simplest solutions to the mass balance equation (e.g., first-order finite difference and inversion). Here we present a new implicit numerical model (FINIFLUX) based on finite elements for quantifying groundwater discharge to streams and rivers using Rn surveys at the reach scale (1-50 km). The model is coupled to a state-of-the-art parameter optimization code Parallel-PEST to iteratively solve the mass balance equation for groundwater discharge and hyporheic exchange. The major benefit of this model is that it is programed to be very simple to use, reduces nonuniqueness, and provides numerically stable estimates of groundwater fluxes and hyporheic residence times from field data. FINIFLUX was tested against an analytical solution and then implemented on two German rivers of differing magnitude, the Salzach (˜112 m3 s-1) and the Rote Main (˜4 m3 s-1). We show that using previous inversion techniques numerical instability can lead to physically impossible negative values, whereas the new model provides stable positive values for all scenarios. We hope that by making FINIFLUX freely available to the community that Rn might find wider application in quantifying groundwater discharge to streams and rivers and thus assist in a combined management of surface and groundwater systems.

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

Direct Numerical Simulations of Turbulent Autoigniting Hydrogen Jets

NASA Astrophysics Data System (ADS)

Asaithambi, Rajapandiyan

Autoignition is an important phenomenon and a tool in the design of combustion engines. To study autoignition in a canonical form a direct numerical simulation of a turbulent autoigniting hydrogen jet in vitiated coflow conditions at a jet Reynolds number of 10,000 is performed. A detailed chemical mechanism for hydrogen-air combustion and non-unity Lewis numbers for species transport is used. Realistic inlet conditions are prescribed by obtaining the velocity eld from a fully developed turbulent pipe flow simulation. To perform this simulation a scalable modular density based method for direct numerical simulation (DNS) and large eddy simulation (LES) of compressible reacting flows is developed. The algorithm performs explicit time advancement of transport variables on structured grids. An iterative semi-implicit time advancement is developed for the chemical source terms to alleviate the chemical stiffness of detailed mechanisms. The algorithm is also extended from a Cartesian grid to a cylindrical coordinate system which introduces a singularity at the pole r = 0 where terms with a factor 1/r can be ill-defined. There are several approaches to eliminate this pole singularity and finite volume methods can bypass this issue by not storing or computing data at the pole. All methods however face a very restrictive time step when using a explicit time advancement scheme in the azimuthal direction (theta) where the cell sizes are of the order DelrDeltheta. We use a conservative finite volume based approach to remove the severe time step restriction imposed by the CFL condition by merging cells in the azimuthal direction. In addition, fluxes in the radial direction are computed with an implicit scheme to allow cells to be clustered along the jet's shear layer. This method is validated and used to perform the large scale turbulent reacting simulation. The resulting flame structure is found to be similar to a turbulent diusion flame but stabilized by autoignition at the flame base. Mass-fraction of the hydroperoxyl radical, HO2, peaks in magnitude upstream of the flame's stabilization point indicating autoignition. A flame structure similar to a triple-flame, with a lean premixed flame and a rich premixed flame flanking a thick diffusion flame is identified by the flame index. Radicals formed in the shear layer ahead of ignition and oxygen from the coflow do not get fully consumed by the flame and are transported along the edges of the flame brush into the core of the jet. Ignition delays from a well-stirred reactor model and an autoigniting diffusion flame model are able predict the lift-off height of the turbulent flame. The local entrainment rate was observed to increase with axial distance until the flame stabilization point and then decrease downstream. Data from probes placed along the flame reveals a highly turbulent flow field with variable composition at a given location. In general however, it is observed that the turbulent kinetic energy (TKE) is very high in cold fuel rich mixtures and is lowest in hot fuel lean mixtures. Autoignition occurs at the most-reactive hot and lean mixture fractions where the TKE is the lowest.

Discrimination of Native-like States of Membrane Proteins with Implicit Membrane-based Scoring Functions.

PubMed

Dutagaci, Bercem; Wittayanarakul, Kitiyaporn; Mori, Takaharu; Feig, Michael

2017-06-13

A scoring protocol based on implicit membrane-based scoring functions and a new protocol for optimizing the positioning of proteins inside the membrane was evaluated for its capacity to discriminate native-like states from misfolded decoys. A decoy set previously established by the Baker lab (Proteins: Struct., Funct., Genet. 2006, 62, 1010-1025) was used along with a second set that was generated to cover higher resolution models. The Implicit Membrane Model 1 (IMM1), IMM1 model with CHARMM 36 parameters (IMM1-p36), generalized Born with simple switching (GBSW), and heterogeneous dielectric generalized Born versions 2 (HDGBv2) and 3 (HDGBv3) were tested along with the new HDGB van der Waals (HDGBvdW) model that adds implicit van der Waals contributions to the solvation free energy. For comparison, scores were also calculated with the distance-scaled finite ideal-gas reference (DFIRE) scoring function. Z-scores for native state discrimination, energy vs root-mean-square deviation (RMSD) correlations, and the ability to select the most native-like structures as top-scoring decoys were evaluated to assess the performance of the scoring functions. Ranking of the decoys in the Baker set that were relatively far from the native state was challenging and dominated largely by packing interactions that were captured best by DFIRE with less benefit of the implicit membrane-based models. Accounting for the membrane environment was much more important in the second decoy set where especially the HDGB-based scoring functions performed very well in ranking decoys and providing significant correlations between scores and RMSD, which shows promise for improving membrane protein structure prediction and refinement applications. The new membrane structure scoring protocol was implemented in the MEMScore web server ( http://feiglab.org/memscore ).

Theoretical restrictions on longest implicit time scales in Markov state models of biomolecular dynamics

NASA Astrophysics Data System (ADS)

Sinitskiy, Anton V.; Pande, Vijay S.

2018-01-01

Markov state models (MSMs) have been widely used to analyze computer simulations of various biomolecular systems. They can capture conformational transitions much slower than an average or maximal length of a single molecular dynamics (MD) trajectory from the set of trajectories used to build the MSM. A rule of thumb claiming that the slowest implicit time scale captured by an MSM should be comparable by the order of magnitude to the aggregate duration of all MD trajectories used to build this MSM has been known in the field. However, this rule has never been formally proved. In this work, we present analytical results for the slowest time scale in several types of MSMs, supporting the above rule. We conclude that the slowest implicit time scale equals the product of the aggregate sampling and four factors that quantify: (1) how much statistics on the conformational transitions corresponding to the longest implicit time scale is available, (2) how good the sampling of the destination Markov state is, (3) the gain in statistics from using a sliding window for counting transitions between Markov states, and (4) a bias in the estimate of the implicit time scale arising from finite sampling of the conformational transitions. We demonstrate that in many practically important cases all these four factors are on the order of unity, and we analyze possible scenarios that could lead to their significant deviation from unity. Overall, we provide for the first time analytical results on the slowest time scales captured by MSMs. These results can guide further practical applications of MSMs to biomolecular dynamics and allow for higher computational efficiency of simulations.

A transient FETI methodology for large-scale parallel implicit computations in structural mechanics

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Crivelli, Luis; Roux, Francois-Xavier

1992-01-01

Explicit codes are often used to simulate the nonlinear dynamics of large-scale structural systems, even for low frequency response, because the storage and CPU requirements entailed by the repeated factorizations traditionally found in implicit codes rapidly overwhelm the available computing resources. With the advent of parallel processing, this trend is accelerating because explicit schemes are also easier to parallelize than implicit ones. However, the time step restriction imposed by the Courant stability condition on all explicit schemes cannot yet -- and perhaps will never -- be offset by the speed of parallel hardware. Therefore, it is essential to develop efficient and robust alternatives to direct methods that are also amenable to massively parallel processing because implicit codes using unconditionally stable time-integration algorithms are computationally more efficient when simulating low-frequency dynamics. Here we present a domain decomposition method for implicit schemes that requires significantly less storage than factorization algorithms, that is several times faster than other popular direct and iterative methods, that can be easily implemented on both shared and local memory parallel processors, and that is both computationally and communication-wise efficient. The proposed transient domain decomposition method is an extension of the method of Finite Element Tearing and Interconnecting (FETI) developed by Farhat and Roux for the solution of static problems. Serial and parallel performance results on the CRAY Y-MP/8 and the iPSC-860/128 systems are reported and analyzed for realistic structural dynamics problems. These results establish the superiority of the FETI method over both the serial/parallel conjugate gradient algorithm with diagonal scaling and the serial/parallel direct method, and contrast the computational power of the iPSC-860/128 parallel processor with that of the CRAY Y-MP/8 system.

Estimation of daily stream flow of southeastern coastal plain watersheds by combining estimated magnitude and sequence

Treesearch

Herbert Ssegane; Devendra M. Amatya; E.W. Tollner; Zhaohua Dai; Jami E. Nettles

2013-01-01

Commonly used methods to predict streamflow at ungauged watersheds implicitly predict streamflow magnitude and temporal sequence concurrently. An alternative approach that has not been fully explored is the conceptualization of streamflow as a composite of two separable components of magnitude and sequence, where each component is estimated separately and then combined...

Flux-split algorithms for flows with non-equilibrium chemistry and vibrational relaxation

NASA Technical Reports Server (NTRS)

Grossman, B.; Cinnella, P.

1990-01-01

The present consideration of numerical computation methods for gas flows with nonequilibrium chemistry thermodynamics gives attention to an equilibrium model, a general nonequilibrium model, and a simplified model based on vibrational relaxation. Flux-splitting procedures are developed for the fully-coupled inviscid equations encompassing fluid dynamics and both chemical and internal energy-relaxation processes. A fully coupled and implicit large-block structure is presented which embodies novel forms of flux-vector split and flux-difference split algorithms valid for nonequilibrium flow; illustrative high-temperature shock tube and nozzle flow examples are given.

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.

An implicit solution of the three-dimensional Navier-Stokes equations for an airfoil spanning a wind tunnel. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Moitra, A.

1982-01-01

An implicit finite-difference algorithm is developed for the numerical solution of the incompressible three dimensional Navier-Stokes equations in the non-conservative primitive-variable formulation. The flow field about an airfoil spanning a wind-tunnel is computed. The coordinate system is generated by an extension of the two dimensional body-fitted coordinate generation techniques of Thompson, as well as that of Sorenson, into three dimensions. Two dimensional grids are stacked along a spanwise coordinate defined by a simple analytical function. A Poisson pressure equation for advancing the pressure in time is arrived at by performing a divergence operation on the momentum equations. The pressure at each time-step is calculated on the assumption that continuity be unconditionally satisfied. An eddy viscosity coefficient, computed according to the algebraic turbulence formulation of Baldwin and Lomax, simulates the effects of turbulence.

An unstructured grid, three-dimensional model based on the shallow water equations

USGS Publications Warehouse

Casulli, V.; Walters, R.A.

2000-01-01

A semi-implicit finite difference model based on the three-dimensional shallow water equations is modified to use unstructured grids. There are obvious advantages in using unstructured grids in problems with a complicated geometry. In this development, the concept of unstructured orthogonal grids is introduced and applied to this model. The governing differential equations are discretized by means of a semi-implicit algorithm that is robust, stable and very efficient. The resulting model is relatively simple, conserves mass, can fit complicated boundaries and yet is sufficiently flexible to permit local mesh refinements in areas of interest. Moreover, the simulation of the flooding and drying is included in a natural and straightforward manner. These features are illustrated by a test case for studies of convergence rates and by examples of flooding on a river plain and flow in a shallow estuary. Copyright ?? 2000 John Wiley & Sons, Ltd.

Numerical simulation of flow path in the oxidizer side hot gas manifold of the Space Shuttle main engine

NASA Technical Reports Server (NTRS)

Lin, S. J.; Yang, R. J.; Chang, James L. C.; Kwak, D.

1987-01-01

The purpose of this study is to examine in detail incompressible laminar and turbulent flows inside the oxidizer side Hot Gas Manifold of the Space Shuttle Main Engine. To perform this study, an implicit finite difference code cast in general curvilinear coordinates is further developed. The code is based on the method of pseudo-compressibility and utilize ADI or implicit approximate factorization algorithm to achieve computational efficiency. A multiple-zone method is developed to overcome the complexity of the geometry. In the present study, the laminar and turbulent flows in the oxidizer side Hot Gas Manifold have been computed. The study reveals that: (1) there exists large recirculation zones inside the bowl if no vanes are present; (2) strong secondary flows are observed in the transfer tube; and (3) properly shaped and positioned guide vanes are effective in eliminating flow separation.

Calculation of flow about two-dimensional bodies by means of the velocity-vorticity formulation on a staggered grid

NASA Technical Reports Server (NTRS)

Stremel, Paul M.

1991-01-01

A method for calculating the incompressible viscous flow about two-dimensional bodies, utilizing the velocity-vorticity form of the Navier-Stokes equations using a staggered-grid formulation is presented. The solution is obtained by employing an alternative-direction implicit method for the solution of the block tridiagonal matrix resulting from the finite-difference representation of the governing equations. The boundary vorticity and the conservation of mass are calculated implicitly as a part of the solution. The mass conservation is calculated to machine zero for the duration of the computation. Calculations for the flow about a circular cylinder, a 2-pct thick flat plate at 90-deg incidence, an elliptic cylinder at 45-deg incidence, and a NACA 0012, with and without a deflected flap, at - 90-deg incidence are performed and compared with the results of other numerical investigations.

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.

Complex-envelope alternating-direction-implicit FDTD method for simulating active photonic devices with semiconductor/solid-state media.

PubMed

Singh, Gurpreet; Ravi, Koustuban; Wang, Qian; Ho, Seng-Tiong

2012-06-15

A complex-envelope (CE) alternating-direction-implicit (ADI) finite-difference time-domain (FDTD) approach to treat light-matter interaction self-consistently with electromagnetic field evolution for efficient simulations of active photonic devices is presented for the first time (to our best knowledge). The active medium (AM) is modeled using an efficient multilevel system of carrier rate equations to yield the correct carrier distributions, suitable for modeling semiconductor/solid-state media accurately. To include the AM in the CE-ADI-FDTD method, a first-order differential system involving CE fields in the AM is first set up. The system matrix that includes AM parameters is then split into two time-dependent submatrices that are then used in an efficient ADI splitting formula. The proposed CE-ADI-FDTD approach with AM takes 22% of the time as the approach of the corresponding explicit FDTD, as validated by semiconductor microdisk laser simulations.

Application of an efficient hybrid scheme for aeroelastic analysis of advanced propellers

NASA Technical Reports Server (NTRS)

Srivastava, R.; Sankar, N. L.; Reddy, T. S. R.; Huff, D. L.

1989-01-01

An efficient 3-D hybrid scheme is applied for solving Euler equations to analyze advanced propellers. The scheme treats the spanwise direction semi-explicitly and the other two directions implicitly, without affecting the accuracy, as compared to a fully implicit scheme. This leads to a reduction in computer time and memory requirement. The calculated power coefficients for two advanced propellers, SR3 and SR7L, and various advanced ratios showed good correlation with experiment. Spanwise distribution of elemental power coefficient and steady pressure coefficient differences also showed good agreement with experiment. A study of the effect of structural flexibility on the performance of the advanced propellers showed that structural deformation due to centrifugal and aero loading should be included for better correlation.

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.

Finite element techniques for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation

NASA Technical Reports Server (NTRS)

Glaisner, F.; Tezduyar, T. E.

1987-01-01

Finite element procedures for the Navier-Stokes equations in the primitive variable formulation and the vorticity stream-function formulation have been implemented. For both formulations, streamline-upwind/Petrov-Galerkin techniques are used for the discretization of the transport equations. The main problem associated with the vorticity stream-function formulation is the lack of boundary conditions for vorticity at solid surfaces. Here an implicit treatment of the vorticity at no-slip boundaries is incorporated in a predictor-multicorrector time integration scheme. For the primitive variable formulation, mixed finite-element approximations are used. A nine-node element and a four-node + bubble element have been implemented. The latter is shown to exhibit a checkerboard pressure mode and a numerical treatment for this spurious pressure mode is proposed. The two methods are compared from the points of view of simulating internal and external flows and the possibilities of extensions to three dimensions.

Static Buckling Model Tests and Elasto-plastic Finite Element Analysis of a Pile in Layers with Various Thicknesses

NASA Astrophysics Data System (ADS)

Okajima, Kenji; Imai, Junichi; Tanaka, Tadatsugu; Iida, Toshiaki

Damage to piles in the liquefied ground is frequently reported. Buckling by the excess vertical load could be one of the causes of the pile damage, as well as the lateral flow of the ground and the lateral load at the pile head. The buckling mechanism is described as a complicated interaction between the pile deformation by the vertical load and the earth pressure change cased by the pile deformation. In this study, series of static buckling model tests of a pile were carried out in dried sand ground with various thickness of the layer. Finite element analysis was applied to the test results to verify the effectiveness of the elasto-plastic finite element analysis combining the implicit-explicit mixed type dynamic relaxation method with the return mapping method to the pile buckling problems. The test results and the analysis indicated the possibility that the buckling load of a pile decreases greatly where the thickness of the layer increases.

Real-time adaptive finite element solution of time-dependent Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Bao, Gang; Hu, Guanghui; Liu, Di

2015-01-01

In our previous paper (Bao et al., 2012 [1]), a general framework of using adaptive finite element methods to solve the Kohn-Sham equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.

One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure

NASA Technical Reports Server (NTRS)

Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.

2007-01-01

The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.

Split Space-Marching Finite-Volume Method for Chemically Reacting Supersonic Flow

NASA Technical Reports Server (NTRS)

Rizzi, Arthur W.; Bailey, Harry E.

1976-01-01

A space-marching finite-volume method employing a nonorthogonal coordinate system and using a split differencing scheme for calculating steady supersonic flow over aerodynamic shapes is presented. It is a second-order-accurate mixed explicit-implicit procedure that solves the inviscid adiabatic and nondiffusive equations for chemically reacting flow in integral conservation-law form. The relationship between the finite-volume and differential forms of the equations is examined and the relative merits of each discussed. The method admits initial Cauchy data situated on any arbitrary surface and integrates them forward along a general curvilinear coordinate, distorting and deforming the surface as it advances. The chemical kinetics term is split from the convective terms which are themselves dimensionally split, thereby freeing the fluid operators from the restricted step size imposed by the chemical reactions and increasing the computational efficiency. The accuracy of this splitting technique is analyzed, a sufficient stability criterion is established, a representative flow computation is discussed, and some comparisons are made with another method.

A high order accurate finite element algorithm for high Reynolds number flow prediction

NASA Technical Reports Server (NTRS)

Baker, A. J.

1978-01-01

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Integration of the shallow water equations on the sphere using a vector semi-Lagrangian scheme with a multigrid solver

NASA Technical Reports Server (NTRS)

Bates, J. R.; Semazzi, F. H. M.; Higgins, R. W.; Barros, Saulo R. M.

1990-01-01

A vector semi-Lagrangian semi-implicit two-time-level finite-difference integration scheme for the shallow water equations on the sphere is presented. A C-grid is used for the spatial differencing. The trajectory-centered discretization of the momentum equation in vector form eliminates pole problems and, at comparable cost, gives greater accuracy than a previous semi-Lagrangian finite-difference scheme which used a rotated spherical coordinate system. In terms of the insensitivity of the results to increasing timestep, the new scheme is as successful as recent spectral semi-Lagrangian schemes. In addition, the use of a multigrid method for solving the elliptic equation for the geopotential allows efficient integration with an operation count which, at high resolution, is of lower order than in the case of the spectral models. The properties of the new scheme should allow finite-difference models to compete with spectral models more effectively than has previously been possible.

Analysis of turbulent free-jet hydrogen-air diffusion flames with finite chemical reaction rates

NASA Technical Reports Server (NTRS)

Sislian, J. P.; Glass, I. I.; Evans, J. S.

1979-01-01

A numerical analysis is presented of the nonequilibrium flow field resulting from the turbulent mixing and combustion of an axisymmetric hydrogen jet in a supersonic parallel ambient air stream. The effective turbulent transport properties are determined by means of a two-equation model of turbulence. The finite-rate chemistry model considers eight elementary reactions among six chemical species: H, O, H2O, OH, O2 and H2. The governing set of nonlinear partial differential equations was solved by using an implicit finite-difference procedure. Radial distributions were obtained at two downstream locations for some important variables affecting the flow development, such as the turbulent kinetic energy and its dissipation rate. The results show that these variables attain their peak values on the axis of symmetry. The computed distribution of velocity, temperature, and mass fractions of the chemical species gives a complete description of the flow field. The numerical predictions were compared with two sets of experimental data. Good qualitative agreement was obtained.

Computation of airfoil buffet boundaries

NASA Technical Reports Server (NTRS)

Levy, L. L., Jr.; Bailey, H. E.

1981-01-01

The ILLIAC IV computer has been programmed with an implicit, finite-difference code for solving the thin layer compressible Navier-Stokes equation. Results presented for the case of the buffet boundaries of a conventional and a supercritical airfoil section at high Reynolds numbers are found to be in agreement with experimentally determined buffet boundaries, especially at the higher freestream Mach numbers and lower lift coefficients where the onset of unsteady flows is associated with shock wave-induced boundary layer separation.

Combined effect of cortical cytoskeleton and transmembrane proteins on domain formation in biomembranes

PubMed Central

Sikder, Md. Kabir Uddin; Stone, Kyle A.; Kumar, P. B. Sunil; Laradji, Mohamed

2014-01-01

We investigate the combined effects of transmembrane proteins and the subjacent cytoskeleton on the dynamics of phase separation in multicomponent lipid bilayers using computer simulations of a particle-based implicit solvent model for lipid membranes with soft-core interactions. We find that microphase separation can be achieved by the protein confinement by the cytoskeleton. Our results have relevance to the finite size of lipid rafts in the plasma membrane of mammalian cells. PMID:25106608

An h-p Taylor-Galerkin finite element method for compressible Euler equations

NASA Technical Reports Server (NTRS)

Demkowicz, L.; Oden, J. T.; Rachowicz, W.; Hardy, O.

1991-01-01

An extension of the familiar Taylor-Galerkin method to arbitrary h-p spatial approximations is proposed. Boundary conditions are analyzed, and a linear stability result for arbitrary meshes is given, showing the unconditional stability for the parameter of implicitness alpha not less than 0.5. The wedge and blunt body problems are solved with both linear, quadratic, and cubic elements and h-adaptivity, showing the feasibility of higher orders of approximation for problems with shocks.

An optimal implicit staggered-grid finite-difference scheme based on the modified Taylor-series expansion with minimax approximation method for elastic modeling

NASA Astrophysics Data System (ADS)

Yang, Lei; Yan, Hongyong; Liu, Hong

2017-03-01

Implicit staggered-grid finite-difference (ISFD) scheme is competitive for its great accuracy and stability, whereas its coefficients are conventionally determined by the Taylor-series expansion (TE) method, leading to a loss in numerical precision. In this paper, we modify the TE method using the minimax approximation (MA), and propose a new optimal ISFD scheme based on the modified TE (MTE) with MA method. The new ISFD scheme takes the advantage of the TE method that guarantees great accuracy at small wavenumbers, and keeps the property of the MA method that keeps the numerical errors within a limited bound at the same time. Thus, it leads to great accuracy for numerical solution of the wave equations. We derive the optimal ISFD coefficients by applying the new method to the construction of the objective function, and using a Remez algorithm to minimize its maximum. Numerical analysis is made in comparison with the conventional TE-based ISFD scheme, indicating that the MTE-based ISFD scheme with appropriate parameters can widen the wavenumber range with high accuracy, and achieve greater precision than the conventional ISFD scheme. The numerical modeling results also demonstrate that the MTE-based ISFD scheme performs well in elastic wave simulation, and is more efficient than the conventional ISFD scheme for elastic modeling.

Efficient and robust compositional two-phase reservoir simulation in fractured media

NASA Astrophysics Data System (ADS)

Zidane, A.; Firoozabadi, A.

2015-12-01

Compositional and compressible two-phase flow in fractured media has wide applications including CO2 injection. Accurate simulations are currently based on the discrete fracture approach using the cross-flow equilibrium model. In this approach the fractures and a small part of the matrix blocks are combined to form a grid cell. The major drawback is low computational efficiency. In this work we use the discrete-fracture approach to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross-flow equilibrium in the fractures (FCFE). This allows using large matrix elements in the neighborhood of the fractures. We solve the fracture transport equations implicitly to overcome the Courant-Freidricks-Levy (CFL) condition in the small fracture elements. Our implicit approach is based on calculation of the derivative of the molar concentration of component i in phase (cαi ) with respect to the total molar concentration (ci ) at constant volume V and temperature T. This contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix, and a finite volume (FV) discretization in the fractures. In large scale problems the proposed approach is orders of magnitude faster than the existing models.

The generalizability of gender bias: Testing the effects of contextual, explicit, and implicit sexism on labor arbitration decisions.

PubMed

Girvan, Erik J; Deason, Grace; Borgida, Eugene

2015-10-01

Decades of social-psychological research show that gender bias can result from features of the social context and from individual-level psychological predispositions. Do these sources of bias impact legal decisions, which are frequently made by people subject to factors that have been proposed to reduce bias (training and accountability)? To answer the question, we examined the potential for 3 major social-psychological theories of gender bias (role-congruity theory, ambivalent sexism, and implicit bias) to predict outcomes of labor arbitration decisions. In the first study, undergraduate students and professional arbitrators made decisions about 2 mock arbitration cases in which the gender of the employee-grievants was experimentally manipulated. Student participants' decisions showed the predicted gender bias, whereas the decisions of experienced professionals did not. Individual-level attitudes did not predict the extent of the observed bias and accountability did not attenuate it. In the second study, arbitrators' explicit and implicit gender attitudes were significant predictors of their decisions in published cases. The laboratory and field results suggest that context, expertise, and implicit and explicit attitudes are relevant to legal decision-making, but that laboratory experiments alone may not fully capture the nature of their effect on legal professionals' decisions in real cases. (c) 2015 APA, all rights reserved).

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).

Further analytical study of hybrid rocket combustion

NASA Technical Reports Server (NTRS)

Hung, W. S. Y.; Chen, C. S.; Haviland, J. K.

1972-01-01

Analytical studies of the transient and steady-state combustion processes in a hybrid rocket system are discussed. The particular system chosen consists of a gaseous oxidizer flowing within a tube of solid fuel, resulting in a heterogeneous combustion. Finite rate chemical kinetics with appropriate reaction mechanisms were incorporated in the model. A temperature dependent Arrhenius type fuel surface regression rate equation was chosen for the current study. The governing mathematical equations employed for the reacting gas phase and for the solid phase are the general, two-dimensional, time-dependent conservation equations in a cylindrical coordinate system. Keeping the simplifying assumptions to a minimum, these basic equations were programmed for numerical computation, using two implicit finite-difference schemes, the Lax-Wendroff scheme for the gas phase, and, the Crank-Nicolson scheme for the solid phase.

A globally well-posed finite element algorithm for aerodynamics applications

NASA Technical Reports Server (NTRS)

Iannelli, G. S.; Baker, A. J.

1991-01-01

A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.

Weak imposition of frictionless contact constraints on automatically recovered high-order, embedded interfaces using the finite cell method

NASA Astrophysics Data System (ADS)

Bog, Tino; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst

2018-04-01

The finite cell method (FCM) is a fictitious domain approach that greatly simplifies simulations involving complex structures. Recently, the FCM has been applied to contact problems. The current study continues in this field by extending the concept of weakly enforced boundary conditions to inequality constraints for frictionless contact. Furthermore, it formalizes an approach that automatically recovers high-order contact surfaces of (implicitly defined) embedded geometries by means of an extended Marching Cubes algorithm. To further improve the accuracy of the discretization, irregularities at the boundary of contact zones are treated with multi-level hp-refinements. Numerical results and a systematic study of h-, p- and hp-refinements show that the FCM can efficiently provide accurate results for problems involving contact.

Finite element implementation of state variable-based viscoplasticity models

NASA Technical Reports Server (NTRS)

Iskovitz, I.; Chang, T. Y. P.; Saleeb, A. F.

1991-01-01

The implementation of state variable-based viscoplasticity models is made in a general purpose finite element code for structural applications of metals deformed at elevated temperatures. Two constitutive models, Walker's and Robinson's models, are studied in conjunction with two implicit integration methods: the trapezoidal rule with Newton-Raphson iterations and an asymptotic integration algorithm. A comparison is made between the two integration methods, and the latter method appears to be computationally more appealing in terms of numerical accuracy and CPU time. However, in order to make the asymptotic algorithm robust, it is necessary to include a self adaptive scheme with subincremental step control and error checking of the Jacobian matrix at the integration points. Three examples are given to illustrate the numerical aspects of the integration methods tested.

Efficient Computation of Atmospheric Flows with Tempest: Development of Next-Generation Climate and Weather Prediction Algorithms at Non-Hydrostatic Scales

NASA Astrophysics Data System (ADS)

Guerra, J. E.; Ullrich, P. A.

2015-12-01

Tempest is a next-generation global climate and weather simulation platform designed to allow experimentation with numerical methods at very high spatial resolutions. The atmospheric fluid equations are discretized by continuous / discontinuous finite elements in the horizontal and by a staggered nodal finite element method (SNFEM) in the vertical, coupled with implicit/explicit time integration. At global horizontal resolutions below 10km, many important questions remain on optimal techniques for solving the fluid equations. We present results from a suite of meso-scale test cases to validate the performance of the SNFEM applied in the vertical. Internal gravity wave, mountain wave, convective, and Cartesian baroclinic instability tests will be shown at various vertical orders of accuracy and compared with known results.

Two-dimensional evolution equation of finite-amplitude internal gravity waves in a uniformly stratified fluid

PubMed

Kataoka; Tsutahara; Akuzawa

2000-02-14

We derive a fully nonlinear evolution equation that can describe the two-dimensional motion of finite-amplitude long internal waves in a uniformly stratified three-dimensional fluid of finite depth. The derived equation is the two-dimensional counterpart of the evolution equation obtained by Grimshaw and Yi [J. Fluid Mech. 229, 603 (1991)]. In the small-amplitude limit, our equation is reduced to the celebrated Kadomtsev-Petviashvili equation.

Numerical simulation of weakly ionized hypersonic flow over reentry capsules

NASA Astrophysics Data System (ADS)

Scalabrin, Leonardo C.

The mathematical and numerical formulation employed in the development of a new multi-dimensional Computational Fluid Dynamics (CFD) code for the simulation of weakly ionized hypersonic flows in thermo-chemical non-equilibrium over reentry configurations is presented. The flow is modeled using the Navier-Stokes equations modified to include finite-rate chemistry and relaxation rates to compute the energy transfer between different energy modes. The set of equations is solved numerically by discretizing the flowfield using unstructured grids made of any mixture of quadrilaterals and triangles in two-dimensions or hexahedra, tetrahedra, prisms and pyramids in three-dimensions. The partial differential equations are integrated on such grids using the finite volume approach. The fluxes across grid faces are calculated using a modified form of the Steger-Warming Flux Vector Splitting scheme that has low numerical dissipation inside boundary layers. The higher order extension of inviscid fluxes in structured grids is generalized in this work to be used in unstructured grids. Steady state solutions are obtained by integrating the solution over time implicitly. The resulting sparse linear system is solved by using a point implicit or by a line implicit method in which a tridiagonal matrix is assembled by using lines of cells that are formed starting at the wall. An algorithm that assembles these lines using completely general unstructured grids is developed. The code is parallelized to allow simulation of computationally demanding problems. The numerical code is successfully employed in the simulation of several hypersonic entry flows over space capsules as part of its validation process. Important quantities for the aerothermodynamics design of capsules such as aerodynamic coefficients and heat transfer rates are compared to available experimental and flight test data and other numerical results yielding very good agreement. A sensitivity analysis of predicted radiative heating of a space capsule to several thermo-chemical non-equilibrium models is also performed.

Increasing Facilitator Effectiveness by Bridging Two Modes of Consciousness.

ERIC Educational Resources Information Center

Alperson, Erma Dosamantes

To fully explore the range of our human consciousness, we must have access to all available modes of experiencing: the bodily-implicit and the rational-explicit. To the extent that we become alienated from our bodily-felt side, we respond solely in terms of what the external situation demands. We lose sight of our own feelings and needs and…

Liberal Education and the Teleological Question; or Why Should a Dentist Read Chaucer?

ERIC Educational Resources Information Center

McIntyre, Kenneth B.

2013-01-01

This essay consists of an examination of the work of three thinkers who conceive of liberal education primarily in teleological terms, and, implicitly if not explicitly, attempt to offer some answer to the question: what does it mean to be fully human? John Henry Newman, T. S. Eliot, and Josef Pieper developed their understanding of liberal…

Numerical investigation of nonlinear fluid-structure interaction dynamic behaviors under a general Immersed Boundary-Lattice Boltzmann-Finite Element method

NASA Astrophysics Data System (ADS)

Gong, Chun-Lin; Fang, Zhe; Chen, Gang

A numerical approach based on the immersed boundary (IB), lattice Boltzmann and nonlinear finite element method (FEM) is proposed to simulate hydrodynamic interactions of very flexible objects. In the present simulation framework, the motion of fluid is obtained by solving the discrete lattice Boltzmann equations on Eulerian grid, the behaviors of flexible objects are calculated through nonlinear dynamic finite element method, and the interactive forces between them are implicitly obtained using velocity correction IB method which satisfies the no-slip conditions well at the boundary points. The efficiency and accuracy of the proposed Immersed Boundary-Lattice Boltzmann-Finite Element method is first validated by a fluid-structure interaction (F-SI) benchmark case, in which a flexible filament flaps behind a cylinder in channel flow, then the nonlinear vibration mechanism of the cylinder-filament system is investigated by altering the Reynolds number of flow and the material properties of filament. The interactions between two tandem and side-by-side identical objects in a uniform flow are also investigated, and the in-phase and out-of-phase flapping behaviors are captured by the proposed method.

A fully implicit numerical integration of the relativistic particle equation of motion

NASA Astrophysics Data System (ADS)

Pétri, J.

2017-04-01

Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of relativistic plasmas require accurate computations able to catch the full spatial and temporal dynamics of the system. Numerical simulations of ultra-relativistic plasmas face severe restrictions due to limitations in the maximum possible Lorentz factors that current algorithms can reproduce to good accuracy. In order to circumvent this flaw and repel the limit to 9$ , we design a new fully implicit scheme to solve the relativistic particle equation of motion in an external electromagnetic field using a three-dimensional Cartesian geometry. We show some examples of numerical integrations in constant electromagnetic fields to prove the efficiency of our algorithm. The code is also able to follow the electric drift motion for high Lorentz factors. In the most general case of spatially and temporally varying electromagnetic fields, the code performs extremely well, as shown by comparison with exact analytical solutions for the relativistic electrostatic Kepler problem as well as for linearly and circularly polarized plane waves.

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.

Viscous-shock-layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

NASA Technical Reports Server (NTRS)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous-shock-layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially-symmetric flow fields. Solutions were obtained using an implicit finite-difference scheme and results are presented for hypersonic flow over spherically-blunted cone configurations at freestream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

Viscous shock layer solutions for turbulent flow of radiating gas mixtures in chemical equilibrium

NASA Technical Reports Server (NTRS)

Anderson, E. C.; Moss, J. N.

1975-01-01

The viscous shock layer equations for hypersonic laminar and turbulent flows of radiating or nonradiating gas mixtures in chemical equilibrium are presented for two-dimensional and axially symmetric flow fields. Solutions are obtained using an implicit finite difference scheme and results are presented for hypersonic flow over spherically blunted cone configurations at free stream conditions representative of entry into the atmosphere of Venus. These data are compared with solutions obtained using other methods of analysis.

A New Discretization Method of Order Four for the Numerical Solution of One-Space Dimensional Second-Order Quasi-Linear Hyperbolic Equation

ERIC Educational Resources Information Center

Mohanty, R. K.; Arora, Urvashi

2002-01-01

Three level-implicit finite difference methods of order four are discussed for the numerical solution of the mildly quasi-linear second-order hyperbolic equation A(x, t, u)u[subscript xx] + 2B(x, t, u)u[subscript xt] + C(x, t, u)u[subscript tt] = f(x, t, u, u[subscript x], u[subscript t]), 0 less than x less than 1, t greater than 0 subject to…

Numerical solution of a coupled pair of elliptic equations from solid state electronics

NASA Technical Reports Server (NTRS)

Phillips, T. N.

1983-01-01

Iterative methods are considered for the solution of a coupled pair of second order elliptic partial differential equations which arise in the field of solid state electronics. A finite difference scheme is used which retains the conservative form of the differential equations. Numerical solutions are obtained in two ways, by multigrid and dynamic alternating direction implicit methods. Numerical results are presented which show the multigrid method to be an efficient way of solving this problem.

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

Computation of Laminar and Turbulent Flow in 90-Degree Square-Duct and Pipe Bends Using the Navier-Stokes Equations

DTIC Science & Technology

1982-04-01

R.M. and Warming, R.F.: An Implicit Finite - Difference Algorithm for Hyperbolic Systems in Conservation Law Form. Journal of Computational Physics...Quincy Street C-40) Arlington, VA 22217 D 82 05-.10 I0, S4CURITY CLASSIFICATION OF THIS ’E(Wha, Doae Entotwed) Slength scale. Six different flow cases...forces upstream have produced a non-zero velocity gradient normal to the plane of curvature. Fluid with above (/below) average nioiiiei.tuili migrates

Navier-Stokes computations for circulation control airfoils

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.; Jespersen, Dennis C.; Barth, Timothy J.

1987-01-01

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

International Conference on Numerical Ship Hydrodynamics (6th), Held in Iowa City, Iowa on 2-5 August 1993,

DTIC Science & Technology

1994-01-01

length scales mensional hydrofoil and tip vortex flow around a F circulation three dimensional hydrofoil. The simulated mean v molecular viscosity flow...Unstructured Grid for Free Surface Flow Simulations , by T. Hino, L. Martinelli, and A. Jameson 173 "A Semi-Implicit Semi-Lagrangian Finite Element Model...Haussling Solid-Fluid Juncture Boundary Layer and Wake with Waves, by J.E. Choi and F. Stern 215 Direct Numerical and Large-Eddy Simulations of Turbulent

Navier-Stokes computations for circulation controlled airfoils

NASA Technical Reports Server (NTRS)

Pulliam, T. H.; Jesperen, D. C.; Barth, T. J.

1986-01-01

Navier-Stokes computations of subsonic to transonic flow past airfoils with augmented lift due to rearward jet blowing over a curved trailing edge are presented. The approach uses a spiral grid topology. Solutions are obtained using a Navier-Stokes code which employs an implicit finite difference method, an algebraic turbulence model, and developments which improve stability, convergence, and accuracy. Results are compared against experiments for no jet blowing and moderate jet pressures and demonstrate the capability to compute these complicated flows.

Multi-scale and multi-physics simulations using the multi-fluid plasma model

DTIC Science & Technology

2017-04-25

small The simulation uses 512 second-order elements Bz = 1.0, Te = Ti = 0.01, ui = ue = 0 ne = ni = 1.0 + e−10(x−6) 2 Baboolal, Math . and Comp. Sim. 55...DISTRIBUTION Clearance No. 17211 23 / 31 SUMMARY The blended finite element method (BFEM) is presented DG spatial discretization with explicit Runge...Kutta (i+, n) CG spatial discretization with implicit Crank-Nicolson (e−, fileds) DG captures shocks and discontinuities CG is efficient and robust for

Comparison of Implicit Collocation Methods for the Heat Equation

NASA Technical Reports Server (NTRS)

Kouatchou, Jules; Jezequel, Fabienne; Zukor, Dorothy (Technical Monitor)

2001-01-01

We combine a high-order compact finite difference scheme to approximate spatial derivatives arid collocation techniques for the time component to numerically solve the two dimensional heat equation. We use two approaches to implement the collocation methods. The first one is based on an explicit computation of the coefficients of polynomials and the second one relies on differential quadrature. We compare them by studying their merits and analyzing their numerical performance. All our computations, based on parallel algorithms, are carried out on the CRAY SV1.