Semi-implicit iterative methods for low Mach number turbulent reacting flows: Operator splitting versus approximate factorization

NASA Astrophysics Data System (ADS)

MacArt, Jonathan F.; Mueller, Michael E.

2016-12-01

Two formally second-order accurate, semi-implicit, iterative methods for the solution of scalar transport-reaction equations are developed for Direct Numerical Simulation (DNS) of low Mach number turbulent reacting flows. The first is a monolithic scheme based on a linearly implicit midpoint method utilizing an approximately factorized exact Jacobian of the transport and reaction operators. The second is an operator splitting scheme based on the Strang splitting approach. The accuracy properties of these schemes, as well as their stability, cost, and the effect of chemical mechanism size on relative performance, are assessed in two one-dimensional test configurations comprising an unsteady premixed flame and an unsteady nonpremixed ignition, which have substantially different Damköhler numbers and relative stiffness of transport to chemistry. All schemes demonstrate their formal order of accuracy in the fully-coupled convergence tests. Compared to a (non-)factorized scheme with a diagonal approximation to the chemical Jacobian, the monolithic, factorized scheme using the exact chemical Jacobian is shown to be both more stable and more economical. This is due to an improved convergence rate of the iterative procedure, and the difference between the two schemes in convergence rate grows as the time step increases. The stability properties of the Strang splitting scheme are demonstrated to outpace those of Lie splitting and monolithic schemes in simulations at high Damköhler number; however, in this regime, the monolithic scheme using the approximately factorized exact Jacobian is found to be the most economical at practical CFL numbers. The performance of the schemes is further evaluated in a simulation of a three-dimensional, spatially evolving, turbulent nonpremixed planar jet flame.

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

NASA Astrophysics Data System (ADS)

Cavaglieri, Daniele; Bewley, Thomas

2015-04-01

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

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Warming, R. F.; Harten, A.

1983-01-01

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Extension of a streamwise upwind algorithm to a moving grid system

NASA Technical Reports Server (NTRS)

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

1990-01-01

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

Implicit and semi-implicit schemes in the Versatile Advection Code: numerical tests

NASA Astrophysics Data System (ADS)

Toth, G.; Keppens, R.; Botchev, M. A.

1998-04-01

We describe and evaluate various implicit and semi-implicit time integration schemes applied to the numerical simulation of hydrodynamical and magnetohydrodynamical problems. The schemes were implemented recently in the software package Versatile Advection Code, which uses modern shock capturing methods to solve systems of conservation laws with optional source terms. The main advantage of implicit solution strategies over explicit time integration is that the restrictive constraint on the allowed time step can be (partially) eliminated, thus the computational cost is reduced. The test problems cover one and two dimensional, steady state and time accurate computations, and the solutions contain discontinuities. For each test, we confront explicit with implicit solution strategies.

Stability of mixed time integration schemes for transient thermal analysis

NASA Technical Reports Server (NTRS)

Liu, W. K.; Lin, J. I.

1982-01-01

A current research topic in coupled-field problems is the development of effective transient algorithms that permit different time integration methods with different time steps to be used simultaneously in various regions of the problems. The implicit-explicit approach seems to be very successful in structural, fluid, and fluid-structure problems. This paper summarizes this research direction. A family of mixed time integration schemes, with the capabilities mentioned above, is also introduced for transient thermal analysis. A stability analysis and the computer implementation of this technique are also presented. In particular, it is shown that the mixed time implicit-explicit methods provide a natural framework for the further development of efficient, clean, modularized computer codes.

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.

Hybrid upwind discretization of nonlinear two-phase flow with gravity

NASA Astrophysics Data System (ADS)

Lee, S. H.; Efendiev, Y.; Tchelepi, H. A.

2015-08-01

Multiphase flow in porous media is described by coupled nonlinear mass conservation laws. For immiscible Darcy flow of multiple fluid phases, whereby capillary effects are negligible, the transport equations in the presence of viscous and buoyancy forces are highly nonlinear and hyperbolic. Numerical simulation of multiphase flow processes in heterogeneous formations requires the development of discretization and solution schemes that are able to handle the complex nonlinear dynamics, especially of the saturation evolution, in a reliable and computationally efficient manner. In reservoir simulation practice, single-point upwinding of the flux across an interface between two control volumes (cells) is performed for each fluid phase, whereby the upstream direction is based on the gradient of the phase-potential (pressure plus gravity head). This upwinding scheme, which we refer to as Phase-Potential Upwinding (PPU), is combined with implicit (backward-Euler) time discretization to obtain a Fully Implicit Method (FIM). Even though FIM suffers from numerical dispersion effects, it is widely used in practice. This is because of its unconditional stability and because it yields conservative, monotone numerical solutions. However, FIM is not unconditionally convergent. The convergence difficulties are particularly pronounced when the different immiscible fluid phases switch between co-current and counter-current states as a function of time, or (Newton) iteration. Whether the multiphase flow across an interface (between two control-volumes) is co-current, or counter-current, depends on the local balance between the viscous and buoyancy forces, and how the balance evolves in time. The sensitivity of PPU to small changes in the (local) pressure distribution exacerbates the problem. The common strategy to deal with these difficulties is to cut the timestep and try again. Here, we propose a Hybrid-Upwinding (HU) scheme for the phase fluxes, then HU is combined with implicit time discretization to yield a fully implicit method. In the HU scheme, the phase flux is divided into two parts based on the driving force. The viscous-driven and buoyancy-driven phase fluxes are upwinded differently. Specifically, the viscous flux, which is always co-current, is upwinded based on the direction of the total-velocity. The buoyancy-driven flux across an interface is always counter-current and is upwinded such that the heavier fluid goes downward and the lighter fluid goes upward. We analyze the properties of the Implicit Hybrid Upwinding (IHU) scheme. It is shown that IHU is locally conservative and produces monotone, physically-consistent numerical solutions. The IHU solutions show numerical diffusion levels that are slightly higher than those for standard FIM (i.e., implicit PPU). The primary advantage of the IHU scheme is that the numerical overall-flux of a fluid phase remains continuous and differentiable as the flow regime changes between co-current and counter-current conditions. This is in contrast to the standard phase-potential upwinding scheme, in which the overall fractional-flow (flux) function is non-differentiable across the boundary between co-current and counter-current flows.

Aerodynamics of Engine-Airframe Interaction

NASA Technical Reports Server (NTRS)

Caughey, D. A.

1986-01-01

The report describes progress in research directed towards the efficient solution of the inviscid Euler and Reynolds-averaged Navier-Stokes equations for transonic flows through engine inlets, and past complete aircraft configurations, with emphasis on the flowfields in the vicinity of engine inlets. The research focusses upon the development of solution-adaptive grid procedures for these problems, and the development of multi-grid algorithms in conjunction with both, implicit and explicit time-stepping schemes for the solution of three-dimensional problems. The work includes further development of mesh systems suitable for inlet and wing-fuselage-inlet geometries using a variational approach. Work during this reporting period concentrated upon two-dimensional problems, and has been in two general areas: (1) the development of solution-adaptive procedures to cluster the grid cells in regions of high (truncation) error;and (2) the development of a multigrid scheme for solution of the two-dimensional Euler equations using a diagonalized alternating direction implicit (ADI) smoothing algorithm.

An Implicit LU/AF FDTD Method

NASA Technical Reports Server (NTRS)

Beggs, John H.; Briley, W. Roger

2001-01-01

There has been some recent work to develop two and three-dimensional alternating direction implicit (ADI) FDTD schemes. These ADI schemes are based upon the original ADI concept developed by Peaceman and Rachford and Douglas and Gunn, which is a popular solution method in Computational Fluid Dynamics (CFD). These ADI schemes work well and they require solution of a tridiagonal system of equations. A new approach proposed in this paper applies a LU/AF approximate factorization technique from CFD to Maxwell s equations in flux conservative form for one space dimension. The result is a scheme that will retain its unconditional stability in three space dimensions, but does not require the solution of tridiagonal systems. The theory for this new algorithm is outlined in a one-dimensional context for clarity. An extension to two and threedimensional cases is discussed. Results of Fourier analysis are discussed for both stability and dispersion/damping properties of the algorithm. Results are presented for a one-dimensional model problem, and the explicit FDTD algorithm is chosen as a convenient reference for comparison.

A semi-implicit level set method for multiphase flows and fluid-structure interaction problems

NASA Astrophysics Data System (ADS)

Cottet, Georges-Henri; Maitre, Emmanuel

2016-06-01

In this paper we present a novel semi-implicit time-discretization of the level set method introduced in [8] for fluid-structure interaction problems. The idea stems from a linear stability analysis derived on a simplified one-dimensional problem. The semi-implicit scheme relies on a simple filter operating as a pre-processing on the level set function. It applies to multiphase flows driven by surface tension as well as to fluid-structure interaction problems. The semi-implicit scheme avoids the stability constraints that explicit scheme need to satisfy and reduces significantly the computational cost. It is validated through comparisons with the original explicit scheme and refinement studies on two-dimensional benchmarks.

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

NASA Astrophysics Data System (ADS)

NAM, H.

2015-12-01

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

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.

A multidimensional unified gas-kinetic scheme for radiative transfer equations on unstructured mesh

NASA Astrophysics Data System (ADS)

Sun, Wenjun; Jiang, Song; Xu, Kun

2017-12-01

In order to extend the unified gas kinetic scheme (UGKS) to solve radiative transfer equations in a complex geometry, a multidimensional asymptotic preserving implicit method on unstructured mesh is constructed in this paper. With an implicit formulation, the CFL condition for the determination of the time step in UGKS can be much relaxed, and a large time step is used in simulations. Differently from previous direction-by-direction UGKS on orthogonal structured mesh, on unstructured mesh the interface flux transport takes into account multi-dimensional effect, where gradients of radiation intensity and material temperature in both normal and tangential directions of a cell interface are included in the flux evaluation. The multiple scale nature makes the UGKS be able to capture the solutions in both optically thin and thick regions seamlessly. In the optically thick region the condition of cell size being less than photon's mean free path is fully removed, and the UGKS recovers a solver for diffusion equation in such a limit on unstructured mesh. For a distorted quadrilateral mesh, the UGKS goes to a nine-point scheme for the diffusion equation, and it naturally reduces to the standard five-point scheme for a orthogonal quadrilateral mesh. Numerical computations covering a wide range of transport regimes on unstructured and distorted quadrilateral meshes will be presented to validate the current approach.

High-Order Implicit-Explicit Multi-Block Time-stepping Method for Hyperbolic PDEs

NASA Technical Reports Server (NTRS)

Nielsen, Tanner B.; Carpenter, Mark H.; Fisher, Travis C.; Frankel, Steven H.

2014-01-01

This work seeks to explore and improve the current time-stepping schemes used in computational fluid dynamics (CFD) in order to reduce overall computational time. A high-order scheme has been developed using a combination of implicit and explicit (IMEX) time-stepping Runge-Kutta (RK) schemes which increases numerical stability with respect to the time step size, resulting in decreased computational time. The IMEX scheme alone does not yield the desired increase in numerical stability, but when used in conjunction with an overlapping partitioned (multi-block) domain significant increase in stability is observed. To show this, the Overlapping-Partition IMEX (OP IMEX) scheme is applied to both one-dimensional (1D) and two-dimensional (2D) problems, the nonlinear viscous Burger's equation and 2D advection equation, respectively. The method uses two different summation by parts (SBP) derivative approximations, second-order and fourth-order accurate. The Dirichlet boundary conditions are imposed using the Simultaneous Approximation Term (SAT) penalty method. The 6-stage additive Runge-Kutta IMEX time integration schemes are fourth-order accurate in time. An increase in numerical stability 65 times greater than the fully explicit scheme is demonstrated to be achievable with the OP IMEX method applied to 1D Burger's equation. Results from the 2D, purely convective, advection equation show stability increases on the order of 10 times the explicit scheme using the OP IMEX method. Also, the domain partitioning method in this work shows potential for breaking the computational domain into manageable sizes such that implicit solutions for full three-dimensional CFD simulations can be computed using direct solving methods rather than the standard iterative methods currently used.

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.

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

NASA Astrophysics Data System (ADS)

Xie, Qing; Xiao, Zhixiang; Ren, Zhuyin

2018-09-01

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

Implicit Space-Time Conservation Element and Solution Element Schemes

NASA Technical Reports Server (NTRS)

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

1999-01-01

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

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.

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.

Numerical experiments with a symmetric high-resolution shock-capturing scheme

NASA Technical Reports Server (NTRS)

Yee, H. C.

1986-01-01

Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.

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.

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

NASA Technical Reports Server (NTRS)

Marx, Yves P.

1990-01-01

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

Three-dimensional simulation of vortex breakdown

NASA Technical Reports Server (NTRS)

Kuruvila, G.; Salas, M. D.

1990-01-01

The integral form of the complete, unsteady, compressible, three-dimensional Navier-Stokes equations in the conservation form, cast in generalized coordinate system, are solved, numerically, to simulate the vortex breakdown phenomenon. The inviscid fluxes are discretized using Roe's upwind-biased flux-difference splitting scheme and the viscous fluxes are discretized using central differencing. Time integration is performed using a backward Euler ADI (alternating direction implicit) scheme. A full approximation multigrid is used to accelerate the convergence to steady state.

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.

An exponential time-integrator scheme for steady and unsteady inviscid flows

NASA Astrophysics Data System (ADS)

Li, Shu-Jie; Luo, Li-Shi; Wang, Z. J.; Ju, Lili

2018-07-01

An exponential time-integrator scheme of second-order accuracy based on the predictor-corrector methodology, denoted PCEXP, is developed to solve multi-dimensional nonlinear partial differential equations pertaining to fluid dynamics. The effective and efficient implementation of PCEXP is realized by means of the Krylov method. The linear stability and truncation error are analyzed through a one-dimensional model equation. The proposed PCEXP scheme is applied to the Euler equations discretized with a discontinuous Galerkin method in both two and three dimensions. The effectiveness and efficiency of the PCEXP scheme are demonstrated for both steady and unsteady inviscid flows. The accuracy and efficiency of the PCEXP scheme are verified and validated through comparisons with the explicit third-order total variation diminishing Runge-Kutta scheme (TVDRK3), the implicit backward Euler (BE) and the implicit second-order backward difference formula (BDF2). For unsteady flows, the PCEXP scheme generates a temporal error much smaller than the BDF2 scheme does, while maintaining the expected acceleration at the same time. Moreover, the PCEXP scheme is also shown to achieve the computational efficiency comparable to the implicit schemes for steady flows.

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.

Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes

NASA Technical Reports Server (NTRS)

Movriplis, Dimitri J.

1998-01-01

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

An unconditionally stable Runge-Kutta method for unsteady flows

NASA Technical Reports Server (NTRS)

Jorgenson, Philip C. E.; Chima, Rodrick V.

1988-01-01

A quasi-three dimensional analysis was developed for unsteady rotor-stator interaction in turbomachinery. The analysis solves the unsteady Euler or thin-layer Navier-Stokes equations in a body fitted coordinate system. It accounts for the effects of rotation, radius change, and stream surface thickness. The Baldwin-Lomax eddy viscosity model is used for turbulent flows. The equations are integrated in time using a four stage Runge-Kutta scheme with a constant time step. Implicit residual smoothing was employed to accelerate the solution of the time accurate computations. The scheme is described and accuracy analyses are given. Results are shown for a supersonic through-flow fan designed for NASA Lewis. The rotor:stator blade ratio was taken as 1:1. Results are also shown for the first stage of the Space Shuttle Main Engine high pressure fuel turbopump. Here the blade ratio is 2:3. Implicit residual smoothing was used to increase the time step limit of the unsmoothed scheme by a factor of six with negligible differences in the unsteady results. It is felt that the implicitly smoothed Runge-Kutta scheme is easily competitive with implicit schemes for unsteady flows while retaining the simplicity of an explicit scheme.

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.

A Multistep Algorithm for the Radiation Hydrodynamical Transport of Cosmological Ionization Fronts and Ionized Flows

NASA Astrophysics Data System (ADS)

Whalen, Daniel; Norman, Michael L.

2006-02-01

Radiation hydrodynamical transport of ionization fronts (I-fronts) in the next generation of cosmological reionization simulations holds the promise of predicting UV escape fractions from first principles as well as investigating the role of photoionization in feedback processes and structure formation. We present a multistep integration scheme for radiative transfer and hydrodynamics for accurate propagation of I-fronts and ionized flows from a point source in cosmological simulations. The algorithm is a photon-conserving method that correctly tracks the position of I-fronts at much lower resolutions than nonconservative techniques. The method applies direct hierarchical updates to the ionic species, bypassing the need for the costly matrix solutions required by implicit methods while retaining sufficient accuracy to capture the true evolution of the fronts. We review the physics of ionization fronts in power-law density gradients, whose analytical solutions provide excellent validation tests for radiation coupling schemes. The advantages and potential drawbacks of direct and implicit schemes are also considered, with particular focus on problem time-stepping, which if not properly implemented can lead to morphologically plausible I-front behavior that nonetheless departs from theory. We also examine the effect of radiation pressure from very luminous central sources on the evolution of I-fronts and flows.

MagIC: Fluid dynamics in a spherical shell simulator

NASA Astrophysics Data System (ADS)

Wicht, J.; Gastine, T.; Barik, A.; Putigny, B.; Yadav, R.; Duarte, L.; Dintrans, B.

2017-09-01

MagIC simulates fluid dynamics in a spherical shell. It solves for the Navier-Stokes equation including Coriolis force, optionally coupled with an induction equation for Magneto-Hydro Dynamics (MHD), a temperature (or entropy) equation and an equation for chemical composition under both the anelastic and the Boussinesq approximations. MagIC uses either Chebyshev polynomials or finite differences in the radial direction and spherical harmonic decomposition in the azimuthal and latitudinal directions. The time-stepping scheme relies on a semi-implicit Crank-Nicolson for the linear terms of the MHD equations and a Adams-Bashforth scheme for the non-linear terms and the Coriolis force.

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.

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.

An O(Nm(sup 2)) Plane Solver for the Compressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Thomas, J. L.; Bonhaus, D. L.; Anderson, W. K.; Rumsey, C. L.; Biedron, R. T.

1999-01-01

A hierarchical multigrid algorithm for efficient steady solutions to the two-dimensional compressible Navier-Stokes equations is developed and demonstrated. The algorithm applies multigrid in two ways: a Full Approximation Scheme (FAS) for a nonlinear residual equation and a Correction Scheme (CS) for a linearized defect correction implicit equation. Multigrid analyses which include the effect of boundary conditions in one direction are used to estimate the convergence rate of the algorithm for a model convection equation. Three alternating-line- implicit algorithms are compared in terms of efficiency. The analyses indicate that full multigrid efficiency is not attained in the general case; the number of cycles to attain convergence is dependent on the mesh density for high-frequency cross-stream variations. However, the dependence is reasonably small and fast convergence is eventually attained for any given frequency with either the FAS or the CS scheme alone. The paper summarizes numerical computations for which convergence has been attained to within truncation error in a few multigrid cycles for both inviscid and viscous ow simulations on highly stretched meshes.

Implicit methods for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Yoon, S.; Kwak, D.

1990-01-01

Numerical solutions of the Navier-Stokes equations using explicit schemes can be obtained at the expense of efficiency. Conventional implicit methods which often achieve fast convergence rates suffer high cost per iteration. A new implicit scheme based on lower-upper factorization and symmetric Gauss-Seidel relaxation offers very low cost per iteration as well as fast convergence. High efficiency is achieved by accomplishing the complete vectorizability of the algorithm on oblique planes of sweep in three dimensions.

An Optimally Stable and Accurate Second-Order SSP Runge-Kutta IMEX Scheme for Atmospheric Applications

NASA Astrophysics Data System (ADS)

Rokhzadi, Arman; Mohammadian, Abdolmajid; Charron, Martin

2018-01-01

The objective of this paper is to develop an optimized implicit-explicit (IMEX) Runge-Kutta scheme for atmospheric applications focusing on stability and accuracy. Following the common terminology, the proposed method is called IMEX-SSP2(2,3,2), as it has second-order accuracy and is composed of diagonally implicit two-stage and explicit three-stage parts. This scheme enjoys the Strong Stability Preserving (SSP) property for both parts. This new scheme is applied to nonhydrostatic compressible Boussinesq equations in two different arrangements, including (i) semiimplicit and (ii) Horizontally Explicit-Vertically Implicit (HEVI) forms. The new scheme preserves the SSP property for larger regions of absolute monotonicity compared to the well-studied scheme in the same class. In addition, numerical tests confirm that the IMEX-SSP2(2,3,2) improves the maximum stable time step as well as the level of accuracy and computational cost compared to other schemes in the same class. It is demonstrated that the A-stability property as well as satisfying "second-stage order" and stiffly accurate conditions lead the proposed scheme to better performance than existing schemes for the applications examined herein.

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.

High-Order Space-Time Methods for Conservation Laws

NASA Technical Reports Server (NTRS)

Huynh, H. T.

2013-01-01

Current high-order methods such as discontinuous Galerkin and/or flux reconstruction can provide effective discretization for the spatial derivatives. Together with a time discretization, such methods result in either too small a time step size in the case of an explicit scheme or a very large system in the case of an implicit one. To tackle these problems, two new high-order space-time schemes for conservation laws are introduced: the first is explicit and the second, implicit. The explicit method here, also called the moment scheme, achieves a Courant-Friedrichs-Lewy (CFL) condition of 1 for the case of one-spatial dimension regardless of the degree of the polynomial approximation. (For standard explicit methods, if the spatial approximation is of degree p, then the time step sizes are typically proportional to 1/p(exp 2)). Fourier analyses for the one and two-dimensional cases are carried out. The property of super accuracy (or super convergence) is discussed. The implicit method is a simplified but optimal version of the discontinuous Galerkin scheme applied to time. It reduces to a collocation implicit Runge-Kutta (RK) method for ordinary differential equations (ODE) called Radau IIA. The explicit and implicit schemes are closely related since they employ the same intermediate time levels, and the former can serve as a key building block in an iterative procedure for the latter. A limiting technique for the piecewise linear scheme is also discussed. The technique can suppress oscillations near a discontinuity while preserving accuracy near extrema. Preliminary numerical results are shown

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.

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.

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

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.

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

NASA Astrophysics Data System (ADS)

Tomaro, Robert F.

1998-07-01

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

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.

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.

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

NASA Astrophysics Data System (ADS)

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

2009-11-01

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

A 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.

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).

Diablo 2.0: A modern DNS/LES code for the incompressible NSE leveraging new time-stepping and multigrid algorithms

NASA Astrophysics Data System (ADS)

Cavaglieri, Daniele; Bewley, Thomas; Mashayek, Ali

2015-11-01

We present a new code, Diablo 2.0, for the simulation of the incompressible NSE in channel and duct flows with strong grid stretching near walls. The code leverages the fractional step approach with a few twists. New low-storage IMEX (implicit-explicit) Runge-Kutta time-marching schemes are tested which are superior to the traditional and widely-used CN/RKW3 (Crank-Nicolson/Runge-Kutta-Wray) approach; the new schemes tested are L-stable in their implicit component, and offer improved overall order of accuracy and stability with, remarkably, similar computational cost and storage requirements. For duct flow simulations, our new code also introduces a new smoother for the multigrid solver for the pressure Poisson equation. The classic approach, involving alternating-direction zebra relaxation, is replaced by a new scheme, dubbed tweed relaxation, which achieves the same convergence rate with roughly half the computational cost. The code is then tested on the simulation of a shear flow instability in a duct, a classic problem in fluid mechanics which has been the object of extensive numerical modelling for its role as a canonical pathway to energetic turbulence in several fields of science and engineering.

Application of TVD schemes for the Euler equations of gas dynamics. [total variation diminishing for nonlinear hyperbolic systems

NASA Technical Reports Server (NTRS)

Yee, H. C.; Warming, R. F.; Harten, A.

1985-01-01

First-order, second-order, and implicit total variation diminishing (TVD) schemes are reviewed using the modified flux approach. Some transient and steady-state calculations are then carried out to illustrate the applicability of these schemes to the Euler equations. It is shown that the second-order explicit TVD schemes generate good shock resolution for both transient and steady-state one-dimensional and two-dimensional problems. Numerical experiments for a quasi-one-dimensional nozzle problem show that the second-order implicit TVD scheme produces a fairly rapid convergence rate and remains stable even when running with a Courant number of 10 to the 6th.

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part I: numerical scheme

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres

2007-10-01

Two-time-level, semi-implicit, semi-Lagrangian (SISL) scheme is applied to the non-hydrostatic pressure coordinate equations, constituting a modified Miller-Pearce-White model, in hybrid-coordinate framework. Neutral background is subtracted in the initial continuous dynamics, yielding modified equations for geopotential, temperature and logarithmic surface pressure fluctuation. Implicit Lagrangian marching formulae for single time-step are derived. A disclosure scheme is presented, which results in an uncoupled diagnostic system, consisting of 3-D Poisson equation for omega velocity and 2-D Helmholtz equation for logarithmic pressure fluctuation. The model is discretized to create a non-hydrostatic extension to numerical weather prediction model HIRLAM. The discretization schemes, trajectory computation algorithms and interpolation routines, as well as the physical parametrization package are maintained from parent hydrostatic HIRLAM. For stability investigation, the derived SISL model is linearized with respect to the initial, thermally non-equilibrium resting state. Explicit residuals of the linear model prove to be sensitive to the relative departures of temperature and static stability from the reference state. Relayed on the stability study, the semi-implicit term in the vertical momentum equation is replaced to the implicit term, which results in stability increase of the model.

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

NASA Astrophysics Data System (ADS)

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

2017-04-01

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

TTLEM - an implicit-explicit (IMEX) scheme for modelling landscape evolution in MATLAB

NASA Astrophysics Data System (ADS)

Campforts, Benjamin; Schwanghart, Wolfgang

2016-04-01

Landscape evolution models (LEM) are essential to unravel interdependent earth surface processes. They are proven very useful to bridge several temporal and spatial timescales and have been successfully used to integrate existing empirical datasets. There is a growing consensus that landscapes evolve at least as much in the horizontal as in the vertical direction urging for an efficient implementation of dynamic drainage networks. Here we present a spatially explicit LEM, which is based on the object-oriented function library TopoToolbox 2 (Schwanghart and Scherler, 2014). Similar to other LEMs, rivers are considered to be the main drivers for simulated landscape evolution as they transmit pulses of tectonic perturbations and set the base level of surrounding hillslopes. Highly performant graph algorithms facilitate efficient updates of the flow directions to account for planform changes in the river network and the calculation of flow-related terrain attributes. We implement the model using an implicit-explicit (IMEX) scheme, i.e. different integrators are used for different terms in the diffusion-incision equation. While linear diffusion is solved using an implicit scheme, we calculate incision explicitly. Contrary to previously published LEMS, however, river incision is solved using a total volume method which is total variation diminishing in order to prevent numerical diffusion when solving the stream power law (Campforts and Govers, 2015). We show that the use of this updated numerical scheme alters both landscape topography and catchment wide erosion rates at a geological time scale. Finally, the availability of a graphical user interface facilitates user interaction, making the tool very useful both for research and didactical purposes. References Campforts, B., Govers, G., 2015. Keeping the edge: A numerical method that avoids knickpoint smearing when solving the stream power law. J. Geophys. Res. Earth Surf. 120, 1189-1205. doi:10.1002/2014JF003376 Schwanghart, W., Scherler, D., 2014. TopoToolbox 2 - MATLAB-based software for topographic analysis and modeling in Earth surface sciences. Earth Surf. Dyn. 2, 1-7. doi:10.5194/esurf-2-1-2014

Technical Feasibility of Centrifugal Techniques for Evaluating Hazardous Waste Migration

DTIC Science & Technology

1987-12-01

direct evaluation of the -influence of acceleration on soil moisture movement. A fully implicit finite difference solution scheme was used. The...using the finite difference scheme mentioned earlier. 2. The soil test apparatus for the centrifuge tests was designed and constructed. 110 3...npcr3 f~nJPX 115 S.. 0i U 4 I3 u cc/ U) C~j tC LL~~*- Lý u ’ uiu ’ 4-’ Uju x~j~r3np~~r~tj~jpU W3= 116 Finite Difference Model The finite difference

Large eddy simulation of incompressible turbulent channel flow

NASA Technical Reports Server (NTRS)

Moin, P.; Reynolds, W. C.; Ferziger, J. H.

1978-01-01

The three-dimensional, time-dependent primitive equations of motion were numerically integrated for the case of turbulent channel flow. A partially implicit numerical method was developed. An important feature of this scheme is that the equation of continuity is solved directly. The residual field motions were simulated through an eddy viscosity model, while the large-scale field was obtained directly from the solution of the governing equations. An important portion of the initial velocity field was obtained from the solution of the linearized Navier-Stokes equations. The pseudospectral method was used for numerical differentiation in the horizontal directions, and second-order finite-difference schemes were used in the direction normal to the walls. The large eddy simulation technique is capable of reproducing some of the important features of wall-bounded turbulent flows. The resolvable portions of the root-mean square wall pressure fluctuations, pressure velocity-gradient correlations, and velocity pressure-gradient correlations are documented.

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

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

NASA Technical Reports Server (NTRS)

Swanson, R. C.

2004-01-01

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

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.

Robust Integration Schemes for Generalized Viscoplasticity with Internal-State Variables

NASA Technical Reports Server (NTRS)

Saleeb, Atef F.; Li, W.; Wilt, Thomas E.

1997-01-01

The scope of the work in this presentation focuses on the development of algorithms for the integration of rate dependent constitutive equations. In view of their robustness; i.e., their superior stability and convergence properties for isotropic and anisotropic coupled viscoplastic-damage models, implicit integration schemes have been selected. This is the simplest in its class and is one of the most widely used implicit integrators at present.

Multidimensional, fully implicit, exactly conserving electromagnetic particle-in-cell simulations

NASA Astrophysics Data System (ADS)

Chacon, Luis

2015-09-01

We discuss a new, conservative, fully implicit 2D-3V particle-in-cell algorithm for non-radiative, electromagnetic kinetic plasma simulations, based on the Vlasov-Darwin model. Unlike earlier linearly implicit PIC schemes and standard explicit PIC schemes, fully implicit PIC algorithms are unconditionally stable and allow exact discrete energy and charge conservation. This has been demonstrated in 1D electrostatic and electromagnetic contexts. In this study, we build on these recent algorithms to develop an implicit, orbit-averaged, time-space-centered finite difference scheme for the Darwin field and particle orbit equations for multiple species in multiple dimensions. The Vlasov-Darwin model is very attractive for PIC simulations because it avoids radiative noise issues in non-radiative electromagnetic regimes. The algorithm conserves global energy, local charge, and particle canonical-momentum exactly, even with grid packing. The nonlinear iteration is effectively accelerated with a fluid preconditioner, 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 and 2D. Support from the LANL LDRD program and the DOE-SC ASCR office.

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.

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

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

Liu, Xiaodong; Xia, Yidong; Luo, Hong

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

A comparative study of Rosenbrock-type and implicit Runge-Kutta time integration for discontinuous Galerkin method for unsteady 3D compressible Navier-Stokes equations

DOE PAGES

Liu, Xiaodong; Xia, Yidong; Luo, Hong; ...

2016-10-05

A comparative study of two classes of third-order implicit time integration schemes is presented for a third-order hierarchical WENO reconstructed discontinuous Galerkin (rDG) method to solve the 3D unsteady compressible Navier-Stokes equations: — 1) the explicit first stage, single diagonally implicit Runge-Kutta (ESDIRK3) scheme, and 2) the Rosenbrock-Wanner (ROW) schemes based on the differential algebraic equations (DAEs) of Index-2. Compared with the ESDIRK3 scheme, a remarkable feature of the ROW schemes is that, they only require one approximate Jacobian matrix calculation every time step, thus considerably reducing the overall computational cost. A variety of test cases, ranging from inviscid flowsmore » to DNS of turbulent flows, are presented to assess the performance of these schemes. Here, numerical experiments demonstrate that the third-order ROW scheme for the DAEs of index-2 can not only achieve the designed formal order of temporal convergence accuracy in a benchmark test, but also require significantly less computing time than its ESDIRK3 counterpart to converge to the same level of discretization errors in all of the flow simulations in this study, indicating that the ROW methods provide an attractive alternative for the higher-order time-accurate integration of the unsteady compressible Navier-Stokes equations.« less

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.

Implicit high-order discontinuous Galerkin method with HWENO type limiters for steady viscous flow simulations

NASA Astrophysics Data System (ADS)

Jiang, Zhen-Hua; Yan, Chao; Yu, Jian

2013-08-01

Two types of implicit algorithms have been improved for high order discontinuous Galerkin (DG) method to solve compressible Navier-Stokes (NS) equations on triangular grids. A block lower-upper symmetric Gauss-Seidel (BLU-SGS) approach is implemented as a nonlinear iterative scheme. And a modified LU-SGS (LLU-SGS) approach is suggested to reduce the memory requirements while retain the good convergence performance of the original LU-SGS approach. Both implicit schemes have the significant advantage that only the diagonal block matrix is stored. The resulting implicit high-order DG methods are applied, in combination with Hermite weighted essentially non-oscillatory (HWENO) limiters, to solve viscous flow problems. Numerical results demonstrate that the present implicit methods are able to achieve significant efficiency improvements over explicit counterparts and for viscous flows with shocks, and the HWENO limiters can be used to achieve the desired essentially non-oscillatory shock transition and the designed high-order accuracy simultaneously.

Viscous compressible flow direct and inverse computation and illustrations

NASA Technical Reports Server (NTRS)

Yang, T. T.; Ntone, F.

1986-01-01

An algorithm for laminar and turbulent viscous compressible two dimensional flows is presented. For the application of precise boundary conditions over an arbitrary body surface, a body-fitted coordinate system is used in the physical plane. A thin-layer approximation of tne Navier-Stokes equations is introduced to keep the viscous terms relatively simple. The flow field computation is performed in the transformed plane. A factorized, implicit scheme is used to facilitate the computation. Sample calculations, for Couette flow, developing pipe flow, an isolated airflow, two dimensional compressor cascade flow, and segmental compressor blade design are presented. To a certain extent, the effective use of the direct solver depends on the user's skill in setting up the gridwork, the time step size and the choice of the artificial viscosity. The design feature of the algorithm, an iterative scheme to correct geometry for a specified surface pressure distribution, works well for subsonic flows. A more elaborate correction scheme is required in treating transonic flows where local shock waves may be involved.

Transonic small disturbances equation applied to the solution of two-dimensional nonsteady flows

NASA Technical Reports Server (NTRS)

Couston, M.; Angelini, J. J.; Mulak, P.

1980-01-01

Transonic nonsteady flows are of large practical interest. Aeroelastic instability prediction, control figured vehicle techniques or rotary wings in forward flight are some examples justifying the effort undertaken to improve knowledge of these problems is described. The numerical solution of these problems under the potential flow hypothesis is described. The use of an alternating direction implicit scheme allows the efficient resolution of the two dimensional transonic small perturbations equation.

Implicit time accurate simulation of unsteady flow

NASA Astrophysics Data System (ADS)

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

2001-03-01

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

On the solution of evolution equations based on multigrid and explicit iterative methods

NASA Astrophysics Data System (ADS)

Zhukov, V. T.; Novikova, N. D.; Feodoritova, O. B.

2015-08-01

Two schemes for solving initial-boundary value problems for three-dimensional parabolic equations are studied. One is implicit and is solved using the multigrid method, while the other is explicit iterative and is based on optimal properties of the Chebyshev polynomials. In the explicit iterative scheme, the number of iteration steps and the iteration parameters are chosen as based on the approximation and stability conditions, rather than on the optimization of iteration convergence to the solution of the implicit scheme. The features of the multigrid scheme include the implementation of the intergrid transfer operators for the case of discontinuous coefficients in the equation and the adaptation of the smoothing procedure to the spectrum of the difference operators. The results produced by these schemes as applied to model problems with anisotropic discontinuous coefficients are compared.

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.

Small-Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers

DOE PAGES

Goodman, Jonathan; Lin, Kevin K.; Morzfeld, Matthias

2015-07-06

Implicit samplers are algorithms for producing independent, weighted samples from multivariate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algorithms that leads to improved implicit sampling schemes at a relatively small additional cost. Here, computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems.

On the properties of energy stable flux reconstruction schemes for implicit large eddy simulation

NASA Astrophysics Data System (ADS)

Vermeire, B. C.; Vincent, P. E.

2016-12-01

We begin by investigating the stability, order of accuracy, and dispersion and dissipation characteristics of the extended range of energy stable flux reconstruction (E-ESFR) schemes in the context of implicit large eddy simulation (ILES). We proceed to demonstrate that subsets of the E-ESFR schemes are more stable than collocation nodal discontinuous Galerkin methods recovered with the flux reconstruction approach (FRDG) for marginally-resolved ILES simulations of the Taylor-Green vortex. These schemes are shown to have reduced dissipation and dispersion errors relative to FRDG schemes of the same polynomial degree and, simultaneously, have increased Courant-Friedrichs-Lewy (CFL) limits. Finally, we simulate turbulent flow over an SD7003 aerofoil using two of the most stable E-ESFR schemes identified by the aforementioned Taylor-Green vortex experiments. Results demonstrate that subsets of E-ESFR schemes appear more stable than the commonly used FRDG method, have increased CFL limits, and are suitable for ILES of complex turbulent flows on unstructured grids.

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

NASA Astrophysics Data System (ADS)

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

2017-05-01

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

Finite time step and spatial grid effects in δf simulation of warm plasmas

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

Sturdevant, Benjamin J., E-mail: benjamin.j.sturdevant@gmail.com; Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309; Parker, Scott E.

2016-01-15

This paper introduces a technique for analyzing time integration methods used with the particle weight equations in δf method particle-in-cell (PIC) schemes. The analysis applies to the simulation of warm, uniform, periodic or infinite plasmas in the linear regime and considers the collective behavior similar to the analysis performed by Langdon for full-f PIC schemes [1,2]. We perform both a time integration analysis and spatial grid analysis for a kinetic ion, adiabatic electron model of ion acoustic waves. An implicit time integration scheme is studied in detail for δf simulations using our weight equation analysis and for full-f simulations usingmore » the method of Langdon. It is found that the δf method exhibits a CFL-like stability condition for low temperature ions, which is independent of the parameter characterizing the implicitness of the scheme. The accuracy of the real frequency and damping rate due to the discrete time and spatial schemes is also derived using a perturbative method. The theoretical analysis of numerical error presented here may be useful for the verification of simulations and for providing intuition for the design of new implicit time integration schemes for the δf method, as well as understanding differences between δf and full-f approaches to plasma simulation.« less

Nonequilibrium thermo-chemical calculations using a diagonal implicit scheme

NASA Technical Reports Server (NTRS)

Imlay, Scott T.; Roberts, Donald W.; Soetrisno, Moeljo; Eberhardt, Scott

1991-01-01

A recently developed computer program for hypersonic vehicle flow analysis is described. The program uses a diagonal implicit algorithm to solve the equations of viscous flow for a gas in thermochemical nonequilibrium. The diagonal scheme eliminates the expense of inverting large block matrices that arise when species conservation equations are introduced. The program uses multiple zones of grids patched together and includes radiation wall and rarefied gas boundary conditions. Solutions are presented for hypersonic flows of air and hydrogen air mixtures.

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.

Implicit Block ACK Scheme for IEEE 802.11 WLANs

PubMed Central

Sthapit, Pranesh; Pyun, Jae-Young

2016-01-01

The throughput of IEEE 802.11 standard is significantly bounded by the associated Medium Access Control (MAC) overhead. Because of the overhead, an upper limit exists for throughput, which is bounded, including situations where data rates are extremely high. Therefore, an overhead reduction is necessary to achieve higher throughput. The IEEE 802.11e amendment introduced the block ACK mechanism, to reduce the number of control messages in MAC. Although the block ACK scheme greatly reduces overhead, further improvements are possible. In this letter, we propose an implicit block ACK method that further reduces the overhead associated with IEEE 802.11e’s block ACK scheme. The mathematical analysis results are presented for both the original protocol and the proposed scheme. A performance improvement of greater than 10% was achieved with the proposed implementation.

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

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1992-01-01

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

Time-asymptotic solutions of the Navier-Stokes equation for free shear flows using an alternating-direction implicit method

NASA Technical Reports Server (NTRS)

Rudy, D. H.; Morris, D. J.

1976-01-01

An uncoupled time asymptotic alternating direction implicit method for solving the Navier-Stokes equations was tested on two laminar parallel mixing flows. A constant total temperature was assumed in order to eliminate the need to solve the full energy equation; consequently, static temperature was evaluated by using algebraic relationship. For the mixing of two supersonic streams at a Reynolds number of 1,000, convergent solutions were obtained for a time step 5 times the maximum allowable size for an explicit method. The solution diverged for a time step 10 times the explicit limit. Improved convergence was obtained when upwind differencing was used for convective terms. Larger time steps were not possible with either upwind differencing or the diagonally dominant scheme. Artificial viscosity was added to the continuity equation in order to eliminate divergence for the mixing of a subsonic stream with a supersonic stream at a Reynolds number of 1,000.

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

NASA Astrophysics Data System (ADS)

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

2018-01-01

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

Binding free energy prediction in strongly hydrophobic biomolecular systems.

PubMed

Charlier, Landry; Nespoulous, Claude; Fiorucci, Sébastien; Antonczak, Serge; Golebiowski, Jérome

2007-11-21

We present a comparison of various computational approaches aiming at predicting the binding free energy in ligand-protein systems where the ligand is located within a highly hydrophobic cavity. The relative binding free energy between similar ligands is obtained by means of the thermodynamic integration (TI) method and compared to experimental data obtained through isothermal titration calorimetry measurements. The absolute free energy of binding prediction was obtained on a similar system (a pyrazine derivative bound to a lipocalin) by TI, potential of mean force (PMF) and also by means of the MMPBSA protocols. Although the TI protocol performs poorly either with an explicit or an implicit solvation scheme, the PMF calculation using an implicit solvation scheme leads to encouraging results, with a prediction of the binding affinity being 2 kcal mol(-1) lower than the experimental value. The use of an implicit solvation scheme appears to be well suited for the study of such hydrophobic systems, due to the lack of water molecules within the binding site.

A multigrid LU-SSOR scheme for approximate Newton iteration applied to the Euler equations

NASA Technical Reports Server (NTRS)

Yoon, Seokkwan; Jameson, Antony

1986-01-01

A new efficient relaxation scheme in conjunction with a multigrid method is developed for the Euler equations. The LU SSOR scheme is based on a central difference scheme and does not need flux splitting for Newton iteration. Application to transonic flow shows that the new method surpasses the performance of the LU implicit scheme.

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

Patched-grid calculations with the Euler and Navier-Stokes equations: Theory and applications

NASA Technical Reports Server (NTRS)

Rai, M. M.

1986-01-01

A patched-grid approach is one in which the flow region of interest is divided into subregions which are then discretized independently using existing grid generator. The equations of motion are integrated in each subregion in conjunction with patch-boundary schemes which allow proper information transfer across interfaces that separate subregions. The patched-grid approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. A conservative patch-boundary condition that can be used with explicit, implicit factored and implicit relaxation schemes is described. Several example calculations that demonstrate the capabilities of the patched-grid scheme are also included.

A splitting scheme based on the space-time CE/SE method for solving multi-dimensional hydrodynamical models of semiconductor devices

NASA Astrophysics Data System (ADS)

Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul

2016-08-01

Numerical solutions of the hydrodynamical model of semiconductor devices are presented in one and two-space dimension. The model describes the charge transport in semiconductor devices. Mathematically, the models can be written as a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the conservation element and solution element (CE/SE) method for hyperbolic step, and a semi-implicit scheme for the relaxation step. The numerical results of the suggested scheme are compared with the splitting scheme based on Nessyahu-Tadmor (NT) central scheme for convection step and the same semi-implicit scheme for the relaxation step. The effects of various parameters such as low field mobility, device length, lattice temperature and voltages for one-space dimensional hydrodynamic model are explored to further validate the generic applicability of the CE/SE method for the current model equations. A two dimensional simulation is also performed by CE/SE method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

Salt-water-freshwater transient upconing - An implicit boundary-element solution

USGS Publications Warehouse

Kemblowski, M.

1985-01-01

The boundary-element method is used to solve the set of partial differential equations describing the flow of salt water and fresh water separated by a sharp interface in the vertical plane. In order to improve the accuracy and stability of the numerical solution, a new implicit scheme was developed for calculating the motion of the interface. The performance of this scheme was tested by means of numerical simulation. The numerical results are compared to experimental results for a salt-water upconing under a drain problem. ?? 1985.

An efficient mode-splitting method for a curvilinear nearshore circulation model

USGS Publications Warehouse

Shi, Fengyan; Kirby, James T.; Hanes, Daniel M.

2007-01-01

A mode-splitting method is applied to the quasi-3D nearshore circulation equations in generalized curvilinear coordinates. The gravity wave mode and the vorticity wave mode of the equations are derived using the two-step projection method. Using an implicit algorithm for the gravity mode and an explicit algorithm for the vorticity mode, we combine the two modes to derive a mixed difference–differential equation with respect to surface elevation. McKee et al.'s [McKee, S., Wall, D.P., and Wilson, S.K., 1996. An alternating direction implicit scheme for parabolic equations with mixed derivative and convective terms. J. Comput. Phys., 126, 64–76.] ADI scheme is then used to solve the parabolic-type equation in dealing with the mixed derivative and convective terms from the curvilinear coordinate transformation. Good convergence rates are found in two typical cases which represent respectively the motions dominated by the gravity mode and the vorticity mode. Time step limitations imposed by the vorticity convective Courant number in vorticity-mode-dominant cases are discussed. Model efficiency and accuracy are verified in model application to tidal current simulations in San Francisco Bight.

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.

Construction of Three Dimensional Solutions for the Maxwell Equations

NASA Technical Reports Server (NTRS)

Yefet, A.; Turkel, E.

1998-01-01

We consider numerical solutions for the three dimensional time dependent Maxwell equations. We construct a fourth order accurate compact implicit scheme and compare it to the Yee scheme for free space in a box.

Implicit Kalman filtering

NASA Technical Reports Server (NTRS)

Skliar, M.; Ramirez, W. F.

1997-01-01

For an implicitly defined discrete system, a new algorithm for Kalman filtering is developed and an efficient numerical implementation scheme is proposed. Unlike the traditional explicit approach, the implicit filter can be readily applied to ill-conditioned systems and allows for generalization to descriptor systems. The implementation of the implicit filter depends on the solution of the congruence matrix equation (A1)(Px)(AT1) = Py. We develop a general iterative method for the solution of this equation, and prove necessary and sufficient conditions for convergence. It is shown that when the system matrices of an implicit system are sparse, the implicit Kalman filter requires significantly less computer time and storage to implement as compared to the traditional explicit Kalman filter. Simulation results are presented to illustrate and substantiate the theoretical developments.

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

NASA Astrophysics Data System (ADS)

Cox, Christopher

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

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

NASA Astrophysics Data System (ADS)

Basson, Anton Herman

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

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.

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

NASA Technical Reports Server (NTRS)

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

1995-01-01

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

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.

Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

NASA Technical Reports Server (NTRS)

Helenbrook, B. T.; Atkins, H. L.

2006-01-01

We investigate p-multigrid as a solution method for several different discontinuous Galerkin (DG) formulations of the Poisson equation. Different combinations of relaxation schemes and basis sets have been combined with the DG formulations to find the best performing combination. The damping factors of the schemes have been determined using Fourier analysis for both one and two-dimensional problems. One important finding is that when using DG formulations, the standard approach of forming the coarse p matrices separately for each level of multigrid is often unstable. To ensure stability the coarse p matrices must be constructed from the fine grid matrices using algebraic multigrid techniques. Of the relaxation schemes, we find that the combination of Jacobi relaxation with the spectral element basis is fairly effective. The results using this combination are p sensitive in both one and two dimensions, but reasonable convergence rates can still be achieved for moderate values of p and isotropic meshes. A competitive alternative is a block Gauss-Seidel relaxation. This actually out performs a more expensive line relaxation when the mesh is isotropic. When the mesh becomes highly anisotropic, the implicit line method and the Gauss-Seidel implicit line method are the only effective schemes. Adding the Gauss-Seidel terms to the implicit line method gives a significant improvement over the line relaxation method.

On Richardson extrapolation for low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes

NASA Astrophysics Data System (ADS)

Havasi, Ágnes; Kazemi, Ehsan

2018-04-01

In the modeling of wave propagation phenomena it is necessary to use time integration methods which are not only sufficiently accurate, but also properly describe the amplitude and phase of the propagating waves. It is not clear if amending the developed schemes by extrapolation methods to obtain a high order of accuracy preserves the qualitative properties of these schemes in the perspective of dissipation, dispersion and stability analysis. It is illustrated that the combination of various optimized schemes with Richardson extrapolation is not optimal for minimal dissipation and dispersion errors. Optimized third-order and fourth-order methods are obtained, and it is shown that the proposed methods combined with Richardson extrapolation result in fourth and fifth orders of accuracy correspondingly, while preserving optimality and stability. The numerical applications include the linear wave equation, a stiff system of reaction-diffusion equations and the nonlinear Euler equations with oscillatory initial conditions. It is demonstrated that the extrapolated third-order scheme outperforms the recently developed fourth-order diagonally implicit Runge-Kutta scheme in terms of accuracy and stability.

Transient analysis of a thermal storage unit involving a phase change material

NASA Technical Reports Server (NTRS)

Griggs, E. I.; Pitts, D. R.; Humphries, W. R.

1974-01-01

The transient response of a single cell of a typical phase change material type thermal capacitor has been modeled using numerical conductive heat transfer techniques. The cell consists of a base plate, an insulated top, and two vertical walls (fins) forming a two-dimensional cavity filled with a phase change material. Both explicit and implicit numerical formulations are outlined. A mixed explicit-implicit scheme which treats the fin implicity while treating the phase change material explicitly is discussed. A band algorithmic scheme is used to reduce computer storage requirements for the implicit approach while retaining a relatively fine grid. All formulations are presented in dimensionless form thereby enabling application to geometrically similar problems. Typical parametric results are graphically presented for the case of melting with constant heat input to the base of the cell.

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

NASA Astrophysics Data System (ADS)

Kifonidis, K.; Müller, E.

2012-08-01

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

An Algebraic Implicitization and Specialization of Minimum KL-Divergence Models

NASA Astrophysics Data System (ADS)

Dukkipati, Ambedkar; Manathara, Joel George

In this paper we study representation of KL-divergence minimization, in the cases where integer sufficient statistics exists, using tools from polynomial algebra. We show that the estimation of parametric statistical models in this case can be transformed to solving a system of polynomial equations. In particular, we also study the case of Kullback-Csisźar iteration scheme. We present implicit descriptions of these models and show that implicitization preserves specialization of prior distribution. This result leads us to a Gröbner bases method to compute an implicit representation of minimum KL-divergence models.

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.

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.

A class of the van Leer-type transport schemes and its application to the moisture transport in a general circulation model

NASA Technical Reports Server (NTRS)

Lin, Shian-Jiann; Chao, Winston C.; Sud, Y. C.; Walker, G. K.

1994-01-01

A generalized form of the second-order van Leer transport scheme is derived. Several constraints to the implied subgrid linear distribution are discussed. A very simple positive-definite scheme can be derived directly from the generalized form. A monotonic version of the scheme is applied to the Goddard Laboratory for Atmospheres (GLA) general circulation model (GCM) for the moisture transport calculations, replacing the original fourth-order center-differencing scheme. Comparisons with the original scheme are made in idealized tests as well as in a summer climate simulation using the full GLA GCM. A distinct advantage of the monotonic transport scheme is its ability to transport sharp gradients without producing spurious oscillations and unphysical negative mixing ratio. Within the context of low-resolution climate simulations, the aforementioned characteristics are demonstrated to be very beneficial in regions where cumulus convection is active. The model-produced precipitation pattern using the new transport scheme is more coherently organized both in time and in space, and correlates better with observations. The side effect of the filling algorithm used in conjunction with the original scheme is also discussed, in the context of idealized tests. The major weakness of the proposed transport scheme with a local monotonic constraint is its substantial implicit diffusion at low resolution. Alternative constraints are discussed to counter this problem.

Effective Social Relationship Measurement and Cluster Based Routing in Mobile Opportunistic Networks †

PubMed Central

Zeng, Feng; Zhao, Nan; Li, Wenjia

2017-01-01

In mobile opportunistic networks, the social relationship among nodes has an important impact on data transmission efficiency. Motivated by the strong share ability of “circles of friends” in communication networks such as Facebook, Twitter, Wechat and so on, we take a real-life example to show that social relationships among nodes consist of explicit and implicit parts. The explicit part comes from direct contact among nodes, and the implicit part can be measured through the “circles of friends”. We present the definitions of explicit and implicit social relationships between two nodes, adaptive weights of explicit and implicit parts are given according to the contact feature of nodes, and the distributed mechanism is designed to construct the “circles of friends” of nodes, which is used for the calculation of the implicit part of social relationship between nodes. Based on effective measurement of social relationships, we propose a social-based clustering and routing scheme, in which each node selects the nodes with close social relationships to form a local cluster, and the self-control method is used to keep all cluster members always having close relationships with each other. A cluster-based message forwarding mechanism is designed for opportunistic routing, in which each node only forwards the copy of the message to nodes with the destination node as a member of the local cluster. Simulation results show that the proposed social-based clustering and routing outperforms the other classic routing algorithms. PMID:28498309

Effective Social Relationship Measurement and Cluster Based Routing in Mobile Opportunistic Networks.

PubMed

Zeng, Feng; Zhao, Nan; Li, Wenjia

2017-05-12

In mobile opportunistic networks, the social relationship among nodes has an important impact on data transmission efficiency. Motivated by the strong share ability of "circles of friends" in communication networks such as Facebook, Twitter, Wechat and so on, we take a real-life example to show that social relationships among nodes consist of explicit and implicit parts. The explicit part comes from direct contact among nodes, and the implicit part can be measured through the "circles of friends". We present the definitions of explicit and implicit social relationships between two nodes, adaptive weights of explicit and implicit parts are given according to the contact feature of nodes, and the distributed mechanism is designed to construct the "circles of friends" of nodes, which is used for the calculation of the implicit part of social relationship between nodes. Based on effective measurement of social relationships, we propose a social-based clustering and routing scheme, in which each node selects the nodes with close social relationships to form a local cluster, and the self-control method is used to keep all cluster members always having close relationships with each other. A cluster-based message forwarding mechanism is designed for opportunistic routing, in which each node only forwards the copy of the message to nodes with the destination node as a member of the local cluster. Simulation results show that the proposed social-based clustering and routing outperforms the other classic routing algorithms.

A numerical method for simulating the dynamics of 3D axisymmetric vesicles suspended in viscous flows

NASA Astrophysics Data System (ADS)

Veerapaneni, Shravan K.; Gueyffier, Denis; Biros, George; Zorin, Denis

2009-10-01

We extend [Shravan K. Veerapaneni, Denis Gueyffier, Denis Zorin, George Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, Journal of Computational Physics 228(7) (2009) 2334-2353] to the case of three-dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows. Although the main components of the algorithm are similar in spirit to the 2D case—spectral approximation in space, semi-implicit time-stepping scheme—the main differences are that the bending and viscous force require new analysis, the linearization for the semi-implicit schemes must be rederived, a fully implicit scheme must be used for the toroidal topology to eliminate a CFL-type restriction and a novel numerical scheme for the evaluation of the 3D Stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations. By introducing these novel components, we obtain a time-scheme that experimentally is unconditionally stable, has low cost per time step, and is third-order accurate in time. We present numerical results to analyze the cost and convergence rates of the scheme. To verify the solver, we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid. To illustrate the applicability of method, we consider a few vesicle-flow interaction problems: the sedimentation of a vesicle, interactions of one and three vesicles with a background Poiseuille flow.

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.

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.

Chemistry-split techniques for viscous reactive blunt body flow computations

NASA Technical Reports Server (NTRS)

Li, C. P.

1987-01-01

The weak-coupling structure between the fluid and species equations has been exploited and resulted in three, closely related, time-iterative implicit techniques. While the primitive variables are solved in two separated groups and each by an Alternating Direction Implicit (ADI) factorization scheme, the rate-species Jacobian can be treated in either full or diagonal matrix form, or simply ignored. The latter two versions render the split technique to solving for species as scalar rather than vector variables. The solution is completed at the end of each iteration after determining temperature and pressure from the flow density, energy and species concentrations. Numerical experimentation has shown that the split scalar technique, using partial rate Jacobian, yields the best overall stability and consistency. Satisfactory viscous solutions were obtained for an ellipsoidal body of axis ratio 3:1 at Mach 35 and an angle of attack of 20 degrees.

Implicit flux-split schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Thomas, J. L.; Walters, R. W.; Van Leer, B.

1985-01-01

Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.

Fisher's method of scoring in statistical image reconstruction: comparison of Jacobi and Gauss-Seidel iterative schemes.

PubMed

Hudson, H M; Ma, J; Green, P

1994-01-01

Many algorithms for medical image reconstruction adopt versions of the expectation-maximization (EM) algorithm. In this approach, parameter estimates are obtained which maximize a complete data likelihood or penalized likelihood, in each iteration. Implicitly (and sometimes explicitly) penalized algorithms require smoothing of the current reconstruction in the image domain as part of their iteration scheme. In this paper, we discuss alternatives to EM which adapt Fisher's method of scoring (FS) and other methods for direct maximization of the incomplete data likelihood. Jacobi and Gauss-Seidel methods for non-linear optimization provide efficient algorithms applying FS in tomography. One approach uses smoothed projection data in its iterations. We investigate the convergence of Jacobi and Gauss-Seidel algorithms with clinical tomographic projection data.

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.

A new heterogeneous asynchronous explicit-implicit time integrator for nonsmooth dynamics

NASA Astrophysics Data System (ADS)

Fekak, Fatima-Ezzahra; Brun, Michael; Gravouil, Anthony; Depale, Bruno

2017-07-01

In computational structural dynamics, particularly in the presence of nonsmooth behavior, the choice of the time-step and the time integrator has a critical impact on the feasibility of the simulation. Furthermore, in some cases, as in the case of a bridge crane under seismic loading, multiple time-scales coexist in the same problem. In that case, the use of multi-time scale methods is suitable. Here, we propose a new explicit-implicit heterogeneous asynchronous time integrator (HATI) for nonsmooth transient dynamics with frictionless unilateral contacts and impacts. Furthermore, we present a new explicit time integrator for contact/impact problems where the contact constraints are enforced using a Lagrange multiplier method. In other words, the aim of this paper consists in using an explicit time integrator with a fine time scale in the contact area for reproducing high frequency phenomena, while an implicit time integrator is adopted in the other parts in order to reproduce much low frequency phenomena and to optimize the CPU time. In a first step, the explicit time integrator is tested on a one-dimensional example and compared to Moreau-Jean's event-capturing schemes. The explicit algorithm is found to be very accurate and the scheme has generally a higher order of convergence than Moreau-Jean's schemes and provides also an excellent energy behavior. Then, the two time scales explicit-implicit HATI is applied to the numerical example of a bridge crane under seismic loading. The results are validated in comparison to a fine scale full explicit computation. The energy dissipated in the implicit-explicit interface is well controlled and the computational time is lower than a full-explicit simulation.

Particle-laden Thin Film Flow: An Alternating Direction Implicit Scheme and Comparison between Theory, Numerical Simulations, and Experiments

DTIC Science & Technology

2011-01-01

instability and a dark particle-rich ridge at the front of the fluid can be observed. Figure 5.3 contains a series of plots each taken two minutes into... dark ridge at the front. However, it is also clear that the model does not quantita- tively reproduce this departure from self-similarity of the fluid...behaviors cluster in these diagrams, forming distinct bands. We use color to label these regime bands: white for settled, light for well-mixed, and dark

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

NASA Technical Reports Server (NTRS)

Fatoohi, Rod; Yoon, Seokkwan

1991-01-01

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

Development of the general interpolants method for the CYBER 200 series of supercomputers

NASA Technical Reports Server (NTRS)

Stalnaker, J. F.; Robinson, M. A.; Spradley, L. W.; Kurzius, S. C.; Thoenes, J.

1988-01-01

The General Interpolants Method (GIM) is a 3-D, time-dependent, hybrid procedure for generating numerical analogs of the conservation laws. This study is directed toward the development and application of the GIM computer code for fluid dynamic research applications as implemented for the Cyber 200 series of supercomputers. An elliptic and quasi-parabolic version of the GIM code are discussed. Turbulence models, algebraic and differential equations, were added to the basic viscous code. An equilibrium reacting chemistry model and an implicit finite difference scheme are also included.

Implicit gas-kinetic unified algorithm based on multi-block docking grid for multi-body reentry flows covering all flow regimes

NASA Astrophysics Data System (ADS)

Peng, Ao-Ping; Li, Zhi-Hui; Wu, Jun-Lin; Jiang, Xin-Yu

2016-12-01

Based on the previous researches of the Gas-Kinetic Unified Algorithm (GKUA) for flows from highly rarefied free-molecule transition to continuum, a new implicit scheme of cell-centered finite volume method is presented for directly solving the unified Boltzmann model equation covering various flow regimes. In view of the difficulty in generating the single-block grid system with high quality for complex irregular bodies, a multi-block docking grid generation method is designed on the basis of data transmission between blocks, and the data structure is constructed for processing arbitrary connection relations between blocks with high efficiency and reliability. As a result, the gas-kinetic unified algorithm with the implicit scheme and multi-block docking grid has been firstly established and used to solve the reentry flow problems around the multi-bodies covering all flow regimes with the whole range of Knudsen numbers from 10 to 3.7E-6. The implicit and explicit schemes are applied to computing and analyzing the supersonic flows in near-continuum and continuum regimes around a circular cylinder with careful comparison each other. It is shown that the present algorithm and modelling possess much higher computational efficiency and faster converging properties. The flow problems including two and three side-by-side cylinders are simulated from highly rarefied to near-continuum flow regimes, and the present computed results are found in good agreement with the related DSMC simulation and theoretical analysis solutions, which verify the good accuracy and reliability of the present method. It is observed that the spacing of the multi-body is smaller, the cylindrical throat obstruction is greater with the flow field of single-body asymmetrical more obviously and the normal force coefficient bigger. While in the near-continuum transitional flow regime of near-space flying surroundings, the spacing of the multi-body increases to six times of the diameter of the single-body, the interference effects of the multi-bodies tend to be negligible. The computing practice has confirmed that it is feasible for the present method to compute the aerodynamics and reveal flow mechanism around complex multi-body vehicles covering all flow regimes from the gas-kinetic point of view of solving the unified Boltzmann model velocity distribution function equation.

Comparison of Implicit Schemes for the Incompressible Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Rogers, Stuart E.

1995-01-01

For a computational flow simulation tool to be useful in a design environment, it must be very robust and efficient. To develop such a tool for incompressible flow applications, a number of different implicit schemes are compared for several two-dimensional flow problems in the current study. The schemes include Point-Jacobi relaxation, Gauss-Seidel line relaxation, incomplete lower-upper decomposition, and the generalized minimum residual method preconditioned with each of the three other schemes. The efficiency of the schemes is measured in terms of the computing time required to obtain a steady-state solution for the laminar flow over a backward-facing step, the flow over a NACA 4412 airfoil, and the flow over a three-element airfoil using overset grids. The flow solver used in the study is the INS2D code that solves the incompressible Navier-Stokes equations using the method of artificial compressibility and upwind differencing of the convective terms. The results show that the generalized minimum residual method preconditioned with the incomplete lower-upper factorization outperforms all other methods by at least a factor of 2.

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.

Stabilized linear semi-implicit schemes for the nonlocal Cahn-Hilliard equation

NASA Astrophysics Data System (ADS)

Du, Qiang; Ju, Lili; Li, Xiao; Qiao, Zhonghua

2018-06-01

Comparing with the well-known classic Cahn-Hilliard equation, the nonlocal Cahn-Hilliard equation is equipped with a nonlocal diffusion operator and can describe more practical phenomena for modeling phase transitions of microstructures in materials. On the other hand, it evidently brings more computational costs in numerical simulations, thus efficient and accurate time integration schemes are highly desired. In this paper, we propose two energy-stable linear semi-implicit methods with first and second order temporal accuracies respectively for solving the nonlocal Cahn-Hilliard equation. The temporal discretization is done by using the stabilization technique with the nonlocal diffusion term treated implicitly, while the spatial discretization is carried out by the Fourier collocation method with FFT-based fast implementations. The energy stabilities are rigorously established for both methods in the fully discrete sense. Numerical experiments are conducted for a typical case involving Gaussian kernels. We test the temporal convergence rates of the proposed schemes and make a comparison of the nonlocal phase transition process with the corresponding local one. In addition, long-time simulations of the coarsening dynamics are also performed to predict the power law of the energy decay.

An Exact Integration Scheme for Radiative Cooling in Hydrodynamical Simulations

NASA Astrophysics Data System (ADS)

Townsend, R. H. D.

2009-04-01

A new scheme for incorporating radiative cooling in hydrodynamical codes is presented, centered around exact integration of the governing semidiscrete cooling equation. Using benchmark calculations based on the cooling downstream of a radiative shock, I demonstrate that the new scheme outperforms traditional explicit and implicit approaches in terms of accuracy, while remaining competitive in terms of execution speed.

A circular median filter approach for resolving directional ambiguities in wind fields retrieved from spaceborne scatterometer data

NASA Technical Reports Server (NTRS)

Schultz, Howard

1990-01-01

The retrieval algorithm for spaceborne scatterometry proposed by Schultz (1985) is extended. A circular median filter (CMF) method is presented, which operates on wind directions independently of wind speed, removing any implicit wind speed dependence. A cell weighting scheme is included in the algorithm, permitting greater weights to be assigned to more reliable data. The mathematical properties of the ambiguous solutions to the wind retrieval problem are reviewed. The CMF algorithm is tested on twelve simulated data sets. The effects of spatially correlated likelihood assignment errors on the performance of the CMF algorithm are examined. Also, consideration is given to a wind field smoothing technique that uses a CMF.

A group electronegativity equalization scheme including external potential effects.

PubMed

Leyssens, Tom; Geerlings, Paul; Peeters, Daniel

2006-07-20

By calculating the electron affinity and ionization energy of different functional groups, CCSD electronegativity values are obtained, which implicitly account for the effect of the molecular environment. This latter is approximated using a chemically justified point charge model. On the basis of Sanderson's electronegativity equalization principle, this approach is shown to lead to reliable "group in molecule" electronegativities. Using a slight adjustment of the modeled environment and first-order principles, an electronegativity equalization scheme is obtained, which implicitly accounts for the major part of the external potential effect. This scheme can be applied in a predictive manner to estimate the charge transfer between two functional groups, without having to rely on cumbersome calibrations. A very satisfactory correlation is obtained between these charge transfers and those obtained from an ab initio calculation of the entire molecule.

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.

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

Perfectly matched layers in a divergence preserving ADI scheme for electromagnetics

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

Kraus, C.; ETH Zurich, Chair of Computational Science, 8092 Zuerich; Adelmann, A., E-mail: andreas.adelmann@psi.ch

For numerical simulations of highly relativistic and transversely accelerated charged particles including radiation fast algorithms are needed. While the radiation in particle accelerators has wavelengths in the order of 100 {mu}m the computational domain has dimensions roughly five orders of magnitude larger resulting in very large mesh sizes. The particles are confined to a small area of this domain only. To resolve the smallest scales close to the particles subgrids are envisioned. For reasons of stability the alternating direction implicit (ADI) scheme by Smithe et al. [D.N. Smithe, J.R. Cary, J.A. Carlsson, Divergence preservation in the ADI algorithms for electromagnetics,more » J. Comput. Phys. 228 (2009) 7289-7299] for Maxwell equations has been adopted. At the boundary of the domain absorbing boundary conditions have to be employed to prevent reflection of the radiation. In this paper we show how the divergence preserving ADI scheme has to be formulated in perfectly matched layers (PML) and compare the performance in several scenarios.« less

Multiple burn fuel-optimal orbit transfers: Numerical trajectory computation and neighboring optimal feedback guidance

NASA Technical Reports Server (NTRS)

Chuang, C.-H.; Goodson, Troy D.; Ledsinger, Laura A.

1995-01-01

This report describes current work in the numerical computation of multiple burn, fuel-optimal orbit transfers and presents an analysis of the second variation for extremal multiple burn orbital transfers as well as a discussion of a guidance scheme which may be implemented for such transfers. The discussion of numerical computation focuses on the use of multivariate interpolation to aid the computation in the numerical optimization. The second variation analysis includes the development of the conditions for the examination of both fixed and free final time transfers. Evaluations for fixed final time are presented for extremal one, two, and three burn solutions of the first variation. The free final time problem is considered for an extremal two burn solution. In addition, corresponding changes of the second variation formulation over thrust arcs and coast arcs are included. The guidance scheme discussed is an implicit scheme which implements a neighboring optimal feedback guidance strategy to calculate both thrust direction and thrust on-off times.

Heating 7.2 user`s manual

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

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Heating 7. 2 user's manual

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

Childs, K.W.

1993-02-01

HEATING is a general-purpose conduction heat transfer program written in Fortran 77. HEATING can solve steady-state and/or transient heat conduction problems in one-, two-, or three-dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may also be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heat-generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- andmore » position-dependent. The boundary conditions, which may be surface-to-environment or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General gray-body radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING uses a runtime memory allocation scheme to avoid having to recompile to match memory requirements for each specific problem. HEATING utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution, and conjugate gradient. Transient problems may be solved using any one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method. The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Tensor-product preconditioners for higher-order space-time discontinuous Galerkin methods

NASA Astrophysics Data System (ADS)

Diosady, Laslo T.; Murman, Scott M.

2017-02-01

A space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equations. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high-order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Tensor-Product Preconditioners for Higher-Order Space-Time Discontinuous Galerkin Methods

NASA Technical Reports Server (NTRS)

Diosady, Laslo T.; Murman, Scott M.

2016-01-01

space-time discontinuous-Galerkin spectral-element discretization is presented for direct numerical simulation of the compressible Navier-Stokes equat ions. An efficient solution technique based on a matrix-free Newton-Krylov method is developed in order to overcome the stiffness associated with high solution order. The use of tensor-product basis functions is key to maintaining efficiency at high order. Efficient preconditioning methods are presented which can take advantage of the tensor-product formulation. A diagonalized Alternating-Direction-Implicit (ADI) scheme is extended to the space-time discontinuous Galerkin discretization. A new preconditioner for the compressible Euler/Navier-Stokes equations based on the fast-diagonalization method is also presented. Numerical results demonstrate the effectiveness of these preconditioners for the direct numerical simulation of subsonic turbulent flows.

Hyperbolic Prismatic Grid Generation and Solution of Euler Equations on Prismatic Grids

NASA Technical Reports Server (NTRS)

Pandya, S. A.; Chattot, JJ; Hafez, M. M.; Kutler, Paul (Technical Monitor)

1994-01-01

A hyperbolic grid generation method is used to generate prismatic grids and an approach using prismatic grids to solve the Euler equations is presented. The theory of the stability and feasibility of the hyperbolic grid generation method is presented. The hyperbolic grid generation method of Steger et al for structured grids is applied to a three dimensional triangularized surface definition to generate a grid that is unstructured on each successive layer. The grid, however, retains structure in the body-normal direction and has a computational cell shaped like a triangular prism. In order to take advantage of the structure in the normal direction, a finite-volume scheme that treats the unknowns along the normal direction implicitly is introduced and the flow over a sphere is simulated.

Transport on Riemannian manifold for functional connectivity-based classification.

PubMed

Ng, Bernard; Dressler, Martin; Varoquaux, Gaël; Poline, Jean Baptiste; Greicius, Michael; Thirion, Bertrand

2014-01-01

We present a Riemannian approach for classifying fMRI connectivity patterns before and after intervention in longitudinal studies. A fundamental difficulty with using connectivity as features is that covariance matrices live on the positive semi-definite cone, which renders their elements inter-related. The implicit independent feature assumption in most classifier learning algorithms is thus violated. In this paper, we propose a matrix whitening transport for projecting the covariance estimates onto a common tangent space to reduce the statistical dependencies between their elements. We show on real data that our approach provides significantly higher classification accuracy than directly using Pearson's correlation. We further propose a non-parametric scheme for identifying significantly discriminative connections from classifier weights. Using this scheme, a number of neuroanatomically meaningful connections are found, whereas no significant connections are detected with pure permutation testing.

Highly Parallel Alternating Directions Algorithm for Time Dependent Problems

NASA Astrophysics Data System (ADS)

Ganzha, M.; Georgiev, K.; Lirkov, I.; Margenov, S.; Paprzycki, M.

2011-11-01

In our work, we consider the time dependent Stokes equation on a finite time interval and on a uniform rectangular mesh, written in terms of velocity and pressure. For this problem, a parallel algorithm based on a novel direction splitting approach is developed. Here, the pressure equation is derived from a perturbed form of the continuity equation, in which the incompressibility constraint is penalized in a negative norm induced by the direction splitting. The scheme used in the algorithm is composed of two parts: (i) velocity prediction, and (ii) pressure correction. This is a Crank-Nicolson-type two-stage time integration scheme for two and three dimensional parabolic problems in which the second-order derivative, with respect to each space variable, is treated implicitly while the other variable is made explicit at each time sub-step. In order to achieve a good parallel performance the solution of the Poison problem for the pressure correction is replaced by solving a sequence of one-dimensional second order elliptic boundary value problems in each spatial direction. The parallel code is implemented using the standard MPI functions and tested on two modern parallel computer systems. The performed numerical tests demonstrate good level of parallel efficiency and scalability of the studied direction-splitting-based algorithm.

Application of kinetic flux vector splitting scheme for solving multi-dimensional hydrodynamical models of semiconductor devices

NASA Astrophysics Data System (ADS)

Nisar, Ubaid Ahmed; Ashraf, Waqas; Qamar, Shamsul

In this article, one and two-dimensional hydrodynamical models of semiconductor devices are numerically investigated. The models treat the propagation of electrons in a semiconductor device as the flow of a charged compressible fluid. It plays an important role in predicting the behavior of electron flow in semiconductor devices. Mathematically, the governing equations form a convection-diffusion type system with a right hand side describing the relaxation effects and interaction with a self consistent electric field. The proposed numerical scheme is a splitting scheme based on the kinetic flux-vector splitting (KFVS) method for the hyperbolic step, and a semi-implicit Runge-Kutta method for the relaxation step. The KFVS method is based on the direct splitting of macroscopic flux functions of the system on the cell interfaces. The second order accuracy of the scheme is achieved by using MUSCL-type initial reconstruction and Runge-Kutta time stepping method. Several case studies are considered. For validation, the results of current scheme are compared with those obtained from the splitting scheme based on the NT central scheme. The effects of various parameters such as low field mobility, device length, lattice temperature and voltage are analyzed. The accuracy, efficiency and simplicity of the proposed KFVS scheme validates its generic applicability to the given model equations. A two dimensional simulation is also performed by KFVS method for a MESFET device, producing results in good agreement with those obtained by NT-central scheme.

Calculation of the recirculating compressible flow downstream a sudden axisymmetric expansion

NASA Technical Reports Server (NTRS)

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

1988-01-01

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

Numerical developments for short-pulsed Near Infra-Red laser spectroscopy. Part I: direct treatment

NASA Astrophysics Data System (ADS)

Boulanger, Joan; Charette, André

2005-03-01

This two part study is devoted to the numerical treatment of short-pulsed laser near infra-red spectroscopy. The overall goal is to address the possibility of numerical inverse treatment based on a recently developed direct model to solve the transient radiative transfer equation. This model has been constructed in order to incorporate the last improvements in short-pulsed laser interaction with semi-transparent media and combine a discrete ordinates computing of the implicit source term appearing in the radiative transfer equation with an explicit treatment of the transport of the light intensity using advection schemes, a method encountered in reactive flow dynamics. The incident collimated beam is analytically solved through Bouger Beer Lambert extinction law. In this first part, the direct model is extended to fully non-homogeneous materials and tested with two different spatial schemes in order to be adapted to the inversion methods presented in the following second part. As a first point, fundamental methods and schemes used in the direct model are presented. Then, tests are conducted by comparison with numerical simulations given as references. In a third and last part, multi-dimensional extensions of the code are provided. This allows presentation of numerical results of short pulses propagation in 1, 2 and 3D homogeneous and non-homogeneous materials given some parametrical studies on medium properties and pulse shape. For comparison, an integral method adapted to non-homogeneous media irradiated by a pulsed laser beam is also developed for the 3D case.

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.

Implicit preconditioned WENO scheme for steady viscous flow computation

NASA Astrophysics Data System (ADS)

Huang, Juan-Chen; Lin, Herng; Yang, Jaw-Yen

2009-02-01

A class of lower-upper symmetric Gauss-Seidel implicit weighted essentially nonoscillatory (WENO) schemes is developed for solving the preconditioned Navier-Stokes equations of primitive variables with Spalart-Allmaras one-equation turbulence model. The numerical flux of the present preconditioned WENO schemes consists of a first-order part and high-order part. For first-order part, we adopt the preconditioned Roe scheme and for the high-order part, we employ preconditioned WENO methods. For comparison purpose, a preconditioned TVD scheme is also given and tested. A time-derivative preconditioning algorithm is devised and a discriminant is devised for adjusting the preconditioning parameters at low Mach numbers and turning off the preconditioning at intermediate or high Mach numbers. The computations are performed for the two-dimensional lid driven cavity flow, low subsonic viscous flow over S809 airfoil, three-dimensional low speed viscous flow over 6:1 prolate spheroid, transonic flow over ONERA-M6 wing and hypersonic flow over HB-2 model. The solutions of the present algorithms are in good agreement with the experimental data. The application of the preconditioned WENO schemes to viscous flows at all speeds not only enhances the accuracy and robustness of resolving shock and discontinuities for supersonic flows, but also improves the accuracy of low Mach number flow with complicated smooth solution structures.

Comparative evaluation of direct plating and most probable number for enumeration of low levels of Listeria monocytogenes in naturally contaminated ice cream products.

PubMed

Chen, Yi; Pouillot, Régis; S Burall, Laurel; Strain, Errol A; Van Doren, Jane M; De Jesus, Antonio J; Laasri, Anna; Wang, Hua; Ali, Laila; Tatavarthy, Aparna; Zhang, Guodong; Hu, Lijun; Day, James; Sheth, Ishani; Kang, Jihun; Sahu, Surasri; Srinivasan, Devayani; Brown, Eric W; Parish, Mickey; Zink, Donald L; Datta, Atin R; Hammack, Thomas S; Macarisin, Dumitru

2017-01-16

A precise and accurate method for enumeration of low level of Listeria monocytogenes in foods is critical to a variety of studies. In this study, paired comparison of most probable number (MPN) and direct plating enumeration of L. monocytogenes was conducted on a total of 1730 outbreak-associated ice cream samples that were naturally contaminated with low level of L. monocytogenes. MPN was performed on all 1730 samples. Direct plating was performed on all samples using the RAPID'L.mono (RLM) agar (1600 samples) and agar Listeria Ottaviani and Agosti (ALOA; 130 samples). Probabilistic analysis with Bayesian inference model was used to compare paired direct plating and MPN estimates of L. monocytogenes in ice cream samples because assumptions implicit in ordinary least squares (OLS) linear regression analyses were not met for such a comparison. The probabilistic analysis revealed good agreement between the MPN and direct plating estimates, and this agreement showed that the MPN schemes and direct plating schemes using ALOA or RLM evaluated in the present study were suitable for enumerating low levels of L. monocytogenes in these ice cream samples. The statistical analysis further revealed that OLS linear regression analyses of direct plating and MPN data did introduce bias that incorrectly characterized systematic differences between estimates from the two methods. Published by Elsevier B.V.

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

Unified implicit kinetic scheme for steady multiscale heat transfer based on the phonon Boltzmann transport equation

NASA Astrophysics Data System (ADS)

Zhang, Chuang; Guo, Zhaoli; Chen, Songze

2017-12-01

An implicit kinetic scheme is proposed to solve the stationary phonon Boltzmann transport equation (BTE) for multiscale heat transfer problem. Compared to the conventional discrete ordinate method, the present method employs a macroscopic equation to accelerate the convergence in the diffusive regime. The macroscopic equation can be taken as a moment equation for phonon BTE. The heat flux in the macroscopic equation is evaluated from the nonequilibrium distribution function in the BTE, while the equilibrium state in BTE is determined by the macroscopic equation. These two processes exchange information from different scales, such that the method is applicable to the problems with a wide range of Knudsen numbers. Implicit discretization is implemented to solve both the macroscopic equation and the BTE. In addition, a memory reduction technique, which is originally developed for the stationary kinetic equation, is also extended to phonon BTE. Numerical comparisons show that the present scheme can predict reasonable results both in ballistic and diffusive regimes with high efficiency, while the memory requirement is on the same order as solving the Fourier law of heat conduction. The excellent agreement with benchmark and the rapid converging history prove that the proposed macro-micro coupling is a feasible solution to multiscale heat transfer problems.

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

NASA Astrophysics Data System (ADS)

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

2017-12-01

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

Numerical boundary condition procedures and multigrid methods; Proceedings of the Symposium, NASA Ames Research Center, Moffett Field, CA, October 19-22, 1981

NASA Technical Reports Server (NTRS)

1982-01-01

Papers presented in this volume provide an overview of recent work on numerical boundary condition procedures and multigrid methods. The topics discussed include implicit boundary conditions for the solution of the parabolized Navier-Stokes equations for supersonic flows; far field boundary conditions for compressible flows; and influence of boundary approximations and conditions on finite-difference solutions. Papers are also presented on fully implicit shock tracking and on the stability of two-dimensional hyperbolic initial boundary value problems for explicit and implicit schemes.

An impulsive receptance technique for the time domain computation of the vibration of a whole aero-engine model with nonlinear bearings

NASA Astrophysics Data System (ADS)

Hai, Pham Minh; Bonello, Philip

2008-12-01

The direct study of the vibration of real engine structures with nonlinear bearings, particularly aero-engines, has been severely limited by the fact that current nonlinear computational techniques are not well-suited for complex large-order systems. This paper introduces a novel implicit "impulsive receptance method" (IRM) for the time domain analysis of such structures. The IRM's computational efficiency is largely immune to the number of modes used and dependent only on the number of nonlinear elements. This means that, apart from retaining numerical accuracy, a much more physically accurate solution is achievable within a short timeframe. Simulation tests on a realistically sized representative twin-spool aero-engine showed that the new method was around 40 times faster than a conventional implicit integration scheme. Preliminary results for a given rotor unbalance distribution revealed the varying degree of journal lift, orbit size and shape at the example engine's squeeze-film damper bearings, and the effect of end-sealing at these bearings.

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

NASA Astrophysics Data System (ADS)

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

2016-06-01

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

A splitting integration scheme for the SPH simulation of concentrated particle suspensions

NASA Astrophysics Data System (ADS)

Bian, Xin; Ellero, Marco

2014-01-01

Simulating nearly contacting solid particles in suspension is a challenging task due to the diverging behavior of short-range lubrication forces, which pose a serious time-step limitation for explicit integration schemes. This general difficulty limits severely the total duration of simulations of concentrated suspensions. Inspired by the ideas developed in [S. Litvinov, M. Ellero, X.Y. Hu, N.A. Adams, J. Comput. Phys. 229 (2010) 5457-5464] for the simulation of highly dissipative fluids, we propose in this work a splitting integration scheme for the direct simulation of solid particles suspended in a Newtonian liquid. The scheme separates the contributions of different forces acting on the solid particles. In particular, intermediate- and long-range multi-body hydrodynamic forces, which are computed from the discretization of the Navier-Stokes equations using the smoothed particle hydrodynamics (SPH) method, are taken into account using an explicit integration; for short-range lubrication forces, velocities of pairwise interacting solid particles are updated implicitly by sweeping over all the neighboring pairs iteratively, until convergence in the solution is obtained. By using the splitting integration, simulations can be run stably and efficiently up to very large solid particle concentrations. Moreover, the proposed scheme is not limited to the SPH method presented here, but can be easily applied to other simulation techniques employed for particulate suspensions.

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

DTIC Science & Technology

2015-06-22

Galerkin methodology formulated in the framework of the residual-distribution method. For both second- and third- 1. REPORT DATE (DD-MM-YYYY) 4. TITLE AND...construct these schemes based on the Low-Diffusion-A and the Streamwise-Upwind-Petrov-Galerkin methodology formulated in the framework of the residual...methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit

An Analysis of an Implicit Factored Scheme for Simulating Shock Waves

DTIC Science & Technology

1988-05-01

can cope with a wide range of boundary conditions and equations of state, For modelling -( shock waves in solids, elastic- plastic terms must also be...positive caracteristic speeds. One-sided schemes have superior dissipative and dispersive properties compared to those of centered schemes (Steger and...Elastic- plastic con. ditions must be- incorporated into the problem and usually the addition of suitable bource or sink terms to c-’ustion (1

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-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.

A Least-Squares Finite Element Method for Electromagnetic Scattering Problems

NASA Technical Reports Server (NTRS)

Wu, Jie; Jiang, Bo-nan

1996-01-01

The least-squares finite element method (LSFEM) is applied to electromagnetic scattering and radar cross section (RCS) calculations. In contrast to most existing numerical approaches, in which divergence-free constraints are omitted, the LSFF-M directly incorporates two divergence equations in the discretization process. The importance of including the divergence equations is demonstrated by showing that otherwise spurious solutions with large divergence occur near the scatterers. The LSFEM is based on unstructured grids and possesses full flexibility in handling complex geometry and local refinement Moreover, the LSFEM does not require any special handling, such as upwinding, staggered grids, artificial dissipation, flux-differencing, etc. Implicit time discretization is used and the scheme is unconditionally stable. By using a matrix-free iterative method, the computational cost and memory requirement for the present scheme is competitive with other approaches. The accuracy of the LSFEM is verified by several benchmark test problems.

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

NASA Technical Reports Server (NTRS)

Nielsen, Eric J.; Lu, James; Park, Michael A.; Darmofal, David L.

2003-01-01

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Multigrid methods for numerical simulation of laminar diffusion flames

NASA Technical Reports Server (NTRS)

Liu, C.; Liu, Z.; Mccormick, S.

1993-01-01

This paper documents the result of a computational study of multigrid methods for numerical simulation of 2D diffusion flames. The focus is on a simplified combustion model, which is assumed to be a single step, infinitely fast and irreversible chemical reaction with five species (C3H8, O2, N2, CO2 and H2O). A fully-implicit second-order hybrid scheme is developed on a staggered grid, which is stretched in the streamwise coordinate direction. A full approximation multigrid scheme (FAS) based on line distributive relaxation is developed as a fast solver for the algebraic equations arising at each time step. Convergence of the process for the simplified model problem is more than two-orders of magnitude faster than other iterative methods, and the computational results show good grid convergence, with second-order accuracy, as well as qualitatively agreement with the results of other researchers.

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

Smoothing and the second law

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1987-01-01

The technique of obtaining second-order oscillation-free total -variation-diminishing (TVD), scalar difference schemes by adding a limited diffusive flux ('smoothing') to a second-order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell-by-cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second-order spatial accuracy was found to have extremely restrictive time-step limitation. Switching to an implicit scheme removed the time-step limitation.

Numerical solution of the stochastic parabolic equation with the dependent operator coefficient

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

Ashyralyev, Allaberen; Department of Mathematics, ITTU, Ashgabat; Okur, Ulker

2015-09-18

In the present paper, a single step implicit difference scheme for the numerical solution of the stochastic parabolic equation with the dependent operator coefficient is presented. Theorem on convergence estimates for the solution of this difference scheme is established. In applications, this abstract result permits us to obtain the convergence estimates for the solution of difference schemes for the numerical solution of initial boundary value problems for parabolic equations. The theoretical statements for the solution of this difference scheme are supported by the results of numerical experiments.

Outcomes of Quality Assurance: A Discussion of Knowledge, Methodology and Validity

ERIC Educational Resources Information Center

Stensaker, Bjorn

2008-01-01

A common characteristic in many quality assurance schemes around the world is their implicit and often narrowly formulated understanding of how organisational change is to take place as a result of the process. By identifying some of the underlying assumptions related to organisational change in current quality assurance schemes, the aim of this…

Three-Dimensional Navier-Stokes Method with Two-Equation Turbulence Models for Efficient Numerical Simulation of Hypersonic Flows

NASA Technical Reports Server (NTRS)

Bardina, J. E.

1994-01-01

A new computational efficient 3-D compressible Reynolds-averaged implicit Navier-Stokes method with advanced two equation turbulence models for high speed flows is presented. All convective terms are modeled using an entropy satisfying higher-order Total Variation Diminishing (TVD) scheme based on implicit upwind flux-difference split approximations and arithmetic averaging procedure of primitive variables. This method combines the best features of data management and computational efficiency of space marching procedures with the generality and stability of time dependent Navier-Stokes procedures to solve flows with mixed supersonic and subsonic zones, including streamwise separated flows. Its robust stability derives from a combination of conservative implicit upwind flux-difference splitting with Roe's property U to provide accurate shock capturing capability that non-conservative schemes do not guarantee, alternating symmetric Gauss-Seidel 'method of planes' relaxation procedure coupled with a three-dimensional two-factor diagonal-dominant approximate factorization scheme, TVD flux limiters of higher-order flux differences satisfying realizability, and well-posed characteristic-based implicit boundary-point a'pproximations consistent with the local characteristics domain of dependence. The efficiency of the method is highly increased with Newton Raphson acceleration which allows convergence in essentially one forward sweep for supersonic flows. The method is verified by comparing with experiment and other Navier-Stokes methods. Here, results of adiabatic and cooled flat plate flows, compression corner flow, and 3-D hypersonic shock-wave/turbulent boundary layer interaction flows are presented. The robust 3-D method achieves a better computational efficiency of at least one order of magnitude over the CNS Navier-Stokes code. It provides cost-effective aerodynamic predictions in agreement with experiment, and the capability of predicting complex flow structures in complex geometries with good accuracy.

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

NASA Astrophysics Data System (ADS)

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

2018-04-01

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

Drag reduction strategies

NASA Technical Reports Server (NTRS)

Hill, D. Christopher

1994-01-01

previously a description was given of an active control scheme using wall transpiration that leads to a 15% reduction in surface skin friction beneath a turbulent boundary layer, according to direct numerical simulation. In this research brief further details of that scheme and its variants are given together with some suggestions as to how sensor/actuator arrays could be configured to reduce surface drag. The research which is summarized here was performed during the first half of 1994. This research is motivated by the need to understand better how the dynamics of near-wall turbulent flow can be modified so that skin friction is reduced. The reduction of turbulent skin friction is highly desirable in many engineering applications. Experiments and direct numerical simulations have led to an increased understanding of the cycle of turbulence production and transport in the boundary layer and raised awareness of the possibility of disrupting the process with a subsequent reduction in turbulent skin friction. The implementation of active feedback control in a computational setting is a viable approach for the investigation of the modifications to the flow physics that can be achieved. Bewley et al. and Hill describe how ideas from optimal control theory are employed to give 'sub-optimal' drag reduction schemes. The objectives of the work reported here is to investigate in greater detail the assumptions implicit within such schemes and their limitations. It is also our objective to describe how an array of sensors and actuators could be arranged and interconnected to form a 'smart' surface which has low skin friction.

Vectorized schemes for conical potential flow using the artificial density method

NASA Technical Reports Server (NTRS)

Bradley, P. F.; Dwoyer, D. L.; South, J. C., Jr.; Keen, J. M.

1984-01-01

A method is developed to determine solutions to the full-potential equation for steady supersonic conical flow using the artificial density method. Various update schemes used generally for transonic potential solutions are investigated. The schemes are compared for speed and robustness. All versions of the computer code have been vectorized and are currently running on the CYBER-203 computer. The update schemes are vectorized, where possible, either fully (explicit schemes) or partially (implicit schemes). Since each version of the code differs only by the update scheme and elements other than the update scheme are completely vectorizable, comparisons of computational effort and convergence rate among schemes are a measure of the specific scheme's performance. Results are presented for circular and elliptical cones at angle of attack for subcritical and supercritical crossflows.

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

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

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

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.

An analytical particle mover for the charge- and energy-conserving, nonlinearly implicit, electrostatic particle-in-cell algorithm

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.

2013-08-01

We propose a 1D analytical particle mover for the recent charge- and energy-conserving electrostatic particle-in-cell (PIC) algorithm in Ref. [G. Chen, L. Chacón, D.C. Barnes, An energy- and charge-conserving, implicit, electrostatic particle-in-cell algorithm, Journal of Computational Physics 230 (2011) 7018-7036]. The approach computes particle orbits exactly for a given piece-wise linear electric field. The resulting PIC algorithm maintains the exact charge and energy conservation properties of the original algorithm, but with improved performance (both in efficiency and robustness against the number of particles and timestep). We demonstrate the advantageous properties of the scheme with a challenging multiscale numerical test case, the ion acoustic wave. Using the analytical mover as a reference, we demonstrate that the choice of error estimator in the Crank-Nicolson mover has significant impact on the overall performance of the implicit PIC algorithm. The generalization of the approach to the multi-dimensional case is outlined, based on a novel and simple charge conserving interpolation scheme.

Three-Dimensional Flow of Nanofluid Induced by an Exponentially Stretching Sheet: An Application to Solar Energy

PubMed Central

Khan, Junaid Ahmad; Mustafa, M.; Hayat, T.; Sheikholeslami, M.; Alsaedi, A.

2015-01-01

This work deals with the three-dimensional flow of nanofluid over a bi-directional exponentially stretching sheet. The effects of Brownian motion and thermophoretic diffusion of nanoparticles are considered in the mathematical model. The temperature and nanoparticle volume fraction at the sheet are also distributed exponentially. Local similarity solutions are obtained by an implicit finite difference scheme known as Keller-box method. The results are compared with the existing studies in some limiting cases and found in good agreement. The results reveal the existence of interesting Sparrow-Gregg-type hills for temperature distribution corresponding to some range of parametric values. PMID:25785857

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.

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.

Efficient parallel implicit methods for rotary-wing aerodynamics calculations

NASA Astrophysics Data System (ADS)

Wissink, Andrew M.

Euler/Navier-Stokes Computational Fluid Dynamics (CFD) methods are commonly used for prediction of the aerodynamics and aeroacoustics of modern rotary-wing aircraft. However, their widespread application to large complex problems is limited lack of adequate computing power. Parallel processing offers the potential for dramatic increases in computing power, but most conventional implicit solution methods are inefficient in parallel and new techniques must be adopted to realize its potential. This work proposes alternative implicit schemes for Euler/Navier-Stokes rotary-wing calculations which are robust and efficient in parallel. The first part of this work proposes an efficient parallelizable modification of the Lower Upper-Symmetric Gauss Seidel (LU-SGS) implicit operator used in the well-known Transonic Unsteady Rotor Navier Stokes (TURNS) code. The new hybrid LU-SGS scheme couples a point-relaxation approach of the Data Parallel-Lower Upper Relaxation (DP-LUR) algorithm for inter-processor communication with the Symmetric Gauss Seidel algorithm of LU-SGS for on-processor computations. With the modified operator, TURNS is implemented in parallel using Message Passing Interface (MPI) for communication. Numerical performance and parallel efficiency are evaluated on the IBM SP2 and Thinking Machines CM-5 multi-processors for a variety of steady-state and unsteady test cases. The hybrid LU-SGS scheme maintains the numerical performance of the original LU-SGS algorithm in all cases and shows a good degree of parallel efficiency. It experiences a higher degree of robustness than DP-LUR for third-order upwind solutions. The second part of this work examines use of Krylov subspace iterative solvers for the nonlinear CFD solutions. The hybrid LU-SGS scheme is used as a parallelizable preconditioner. Two iterative methods are tested, Generalized Minimum Residual (GMRES) and Orthogonal s-Step Generalized Conjugate Residual (OSGCR). The Newton method demonstrates good parallel performance on the IBM SP2, with OS-GCR giving slightly better performance than GMRES on large numbers of processors. For steady and quasi-steady calculations, the convergence rate is accelerated but the overall solution time remains about the same as the standard hybrid LU-SGS scheme. For unsteady calculations, however, the Newton method maintains a higher degree of time-accuracy which allows tbe use of larger timesteps and results in CPU savings of 20-35%.

Smoothing and the second law

NASA Technical Reports Server (NTRS)

Merriam, Marshal L.

1986-01-01

The technique of obtaining second order, oscillation free, total variation diminishing (TVD), scalar difference schemes by adding a limited diffusion flux (smoothing) to a second order centered scheme is explored. It is shown that such schemes do not always converge to the correct physical answer. The approach presented here is to construct schemes that numerically satisfy the second law of thermodynamics on a cell by cell basis. Such schemes can only converge to the correct physical solution and in some cases can be shown to be TVD. An explicit scheme with this property and second order spatial accuracy was found to have an extremely restrictive time step limitation (Delta t less than Delta x squared). Switching to an implicit scheme removed the time step limitation.

Estimating the implicit component of visuomotor rotation learning by constraining movement preparation time.

PubMed

Leow, Li-Ann; Gunn, Reece; Marinovic, Welber; Carroll, Timothy J

2017-08-01

When sensory feedback is perturbed, accurate movement is restored by a combination of implicit processes and deliberate reaiming to strategically compensate for errors. Here, we directly compare two methods used previously to dissociate implicit from explicit learning on a trial-by-trial basis: 1 ) asking participants to report the direction that they aim their movements, and contrasting this with the directions of the target and the movement that they actually produce, and 2 ) manipulating movement preparation time. By instructing participants to reaim without a sensory perturbation, we show that reaiming is possible even with the shortest possible preparation times, particularly when targets are narrowly distributed. Nonetheless, reaiming is effortful and comes at the cost of increased variability, so we tested whether constraining preparation time is sufficient to suppress strategic reaiming during adaptation to visuomotor rotation with a broad target distribution. The rate and extent of error reduction under preparation time constraints were similar to estimates of implicit learning obtained from self-report without time pressure, suggesting that participants chose not to apply a reaiming strategy to correct visual errors under time pressure. Surprisingly, participants who reported aiming directions showed less implicit learning according to an alternative measure, obtained during trials performed without visual feedback. This suggests that the process of reporting can affect the extent or persistence of implicit learning. The data extend existing evidence that restricting preparation time can suppress explicit reaiming and provide an estimate of implicit visuomotor rotation learning that does not require participants to report their aiming directions. NEW & NOTEWORTHY During sensorimotor adaptation, implicit error-driven learning can be isolated from explicit strategy-driven reaiming by subtracting self-reported aiming directions from movement directions, or by restricting movement preparation time. Here, we compared the two methods. Restricting preparation times did not eliminate reaiming but was sufficient to suppress reaiming during adaptation with widely distributed targets. The self-report method produced a discrepancy in implicit learning estimated by subtracting aiming directions and implicit learning measured in no-feedback trials. Copyright © 2017 the American Physiological Society.

Accelerating NLTE radiative transfer by means of the Forth-and-Back Implicit Lambda Iteration: A two-level atom line formation in 2D Cartesian coordinates

NASA Astrophysics Data System (ADS)

Milić, Ivan; Atanacković, Olga

2014-10-01

State-of-the-art methods in multidimensional NLTE radiative transfer are based on the use of local approximate lambda operator within either Jacobi or Gauss-Seidel iterative schemes. Here we propose another approach to the solution of 2D NLTE RT problems, Forth-and-Back Implicit Lambda Iteration (FBILI), developed earlier for 1D geometry. In order to present the method and examine its convergence properties we use the well-known instance of the two-level atom line formation with complete frequency redistribution. In the formal solution of the RT equation we employ short characteristics with two-point algorithm. Using an implicit representation of the source function in the computation of the specific intensities, we compute and store the coefficients of the linear relations J=a+bS between the mean intensity J and the corresponding source function S. The use of iteration factors in the ‘local’ coefficients of these implicit relations in two ‘inward’ sweeps of 2D grid, along with the update of the source function in other two ‘outward’ sweeps leads to four times faster solution than the Jacobi’s one. Moreover, the update made in all four consecutive sweeps of the grid leads to an acceleration by a factor of 6-7 compared to the Jacobi iterative scheme.

A semi-implicit finite difference model for three-dimensional tidal circulation,

USGS Publications Warehouse

Casulli, V.; Cheng, R.T.

1992-01-01

A semi-implicit finite difference formulation for the numerical solution of three-dimensional tidal circulation is presented. 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 in the absence of horizontal viscosity the resulting algorithm is unconditionally stable at a minimal computational cost. When only one vertical layer is specified this method reduces, as a particular case, to a semi-implicit scheme for the solutions of the corresponding two-dimensional shallow water equations. The resulting two- and three-dimensional algorithm is fast, accurate and mass conservative. This formulation includes the simulation of flooding and drying of tidal flats, and is fully vectorizable for an efficient implementation on modern vector computers.

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

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Weed, Richard A.

1995-01-01

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

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

NASA Astrophysics Data System (ADS)

Sankar, Lakshmi N.; Weed, Richard A.

1995-08-01

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

Adaptive Numerical Algorithms in Space Weather Modeling

NASA Technical Reports Server (NTRS)

Toth, Gabor; vanderHolst, Bart; Sokolov, Igor V.; DeZeeuw, Darren; Gombosi, Tamas I.; Fang, Fang; Manchester, Ward B.; Meng, Xing; Nakib, Dalal; Powell, Kenneth G.;

Direct speech quotations promote low relative-clause attachment in silent reading of English.

PubMed

Yao, Bo; Scheepers, Christoph

2018-07-01

The implicit prosody hypothesis (Fodor, 1998, 2002) proposes that silent reading coincides with a default, implicit form of prosody to facilitate sentence processing. Recent research demonstrated that a more vivid form of implicit prosody is mentally simulated during silent reading of direct speech quotations (e.g., Mary said, "This dress is beautiful"), with neural and behavioural consequences (e.g., Yao, Belin, & Scheepers, 2011; Yao & Scheepers, 2011). Here, we explored the relation between 'default' and 'simulated' implicit prosody in the context of relative-clause (RC) attachment in English. Apart from confirming a general low RC-attachment preference in both production (Experiment 1) and comprehension (Experiments 2 and 3), we found that during written sentence completion (Experiment 1) or when reading silently (Experiment 2), the low RC-attachment preference was reliably enhanced when the critical sentences were embedded in direct speech quotations as compared to indirect speech or narrative sentences. However, when reading aloud (Experiment 3), direct speech did not enhance the general low RC-attachment preference. The results from Experiments 1 and 2 suggest a quantitative boost to implicit prosody (via auditory perceptual simulation) during silent production/comprehension of direct speech. By contrast, when reading aloud (Experiment 3), prosody becomes equally salient across conditions due to its explicit nature; indirect speech and narrative sentences thus become as susceptible to prosody-induced syntactic biases as direct speech. The present findings suggest a shared cognitive basis between default implicit prosody and simulated implicit prosody, providing a new platform for studying the effects of implicit prosody on sentence processing. Copyright © 2018 Elsevier B.V. All rights reserved.

Network discovery with DCM

PubMed Central

Friston, Karl J.; Li, Baojuan; Daunizeau, Jean; Stephan, Klaas E.

2011-01-01

This paper is about inferring or discovering the functional architecture of distributed systems using Dynamic Causal Modelling (DCM). We describe a scheme that recovers the (dynamic) Bayesian dependency graph (connections in a network) using observed network activity. This network discovery uses Bayesian model selection to identify the sparsity structure (absence of edges or connections) in a graph that best explains observed time-series. The implicit adjacency matrix specifies the form of the network (e.g., cyclic or acyclic) and its graph-theoretical attributes (e.g., degree distribution). The scheme is illustrated using functional magnetic resonance imaging (fMRI) time series to discover functional brain networks. Crucially, it can be applied to experimentally evoked responses (activation studies) or endogenous activity in task-free (resting state) fMRI studies. Unlike conventional approaches to network discovery, DCM permits the analysis of directed and cyclic graphs. Furthermore, it eschews (implausible) Markovian assumptions about the serial independence of random fluctuations. The scheme furnishes a network description of distributed activity in the brain that is optimal in the sense of having the greatest conditional probability, relative to other networks. The networks are characterised in terms of their connectivity or adjacency matrices and conditional distributions over the directed (and reciprocal) effective connectivity between connected nodes or regions. We envisage that this approach will provide a useful complement to current analyses of functional connectivity for both activation and resting-state studies. PMID:21182971

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

PubMed Central

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

2012-01-01

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

A nearly-linear computational-cost scheme for the forward dynamics of an N-body pendulum

NASA Technical Reports Server (NTRS)

Chou, Jack C. K.

1989-01-01

The dynamic equations of motion of an n-body pendulum with spherical joints are derived to be a mixed system of differential and algebraic equations (DAE's). The DAE's are kept in implicit form to save arithmetic and preserve the sparsity of the system and are solved by the robust implicit integration method. At each solution point, the predicted solution is corrected to its exact solution within given tolerance using Newton's iterative method. For each iteration, a linear system of the form J delta X = E has to be solved. The computational cost for solving this linear system directly by LU factorization is O(n exp 3), and it can be reduced significantly by exploring the structure of J. It is shown that by recognizing the recursive patterns and exploiting the sparsity of the system the multiplicative and additive computational costs for solving J delta X = E are O(n) and O(n exp 2), respectively. The formulation and solution method for an n-body pendulum is presented. The computational cost is shown to be nearly linearly proportional to the number of bodies.

Treecode-based generalized Born method

NASA Astrophysics Data System (ADS)

Xu, Zhenli; Cheng, Xiaolin; Yang, Haizhao

2011-02-01

We have developed a treecode-based O(Nlog N) algorithm for the generalized Born (GB) implicit solvation model. Our treecode-based GB (tGB) is based on the GBr6 [J. Phys. Chem. B 111, 3055 (2007)], an analytical GB method with a pairwise descreening approximation for the R6 volume integral expression. The algorithm is composed of a cutoff scheme for the effective Born radii calculation, and a treecode implementation of the GB charge-charge pair interactions. Test results demonstrate that the tGB algorithm can reproduce the vdW surface based Poisson solvation energy with an average relative error less than 0.6% while providing an almost linear-scaling calculation for a representative set of 25 proteins with different sizes (from 2815 atoms to 65456 atoms). For a typical system of 10k atoms, the tGB calculation is three times faster than the direct summation as implemented in the original GBr6 model. Thus, our tGB method provides an efficient way for performing implicit solvent GB simulations of larger biomolecular systems at longer time scales.

An Implicit Finite Difference Solution to the Viscous Radiating Shock Layer with Strong Blowing. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Garrett, L. B.

1971-01-01

An implicit finite difference scheme is developed for the fully coupled solution of the viscous radiating stagnation line equations, including strong blowing. Solutions are presented for both air injection and carbon phenolic ablation products injection 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.

Implicit and Explicit Representations of Hand Position in Tool Use

PubMed Central

Rand, Miya K.; Heuer, Herbert

2013-01-01

Understanding the interactions of visual and proprioceptive information in tool use is important as it is the basis for learning of the tool's kinematic transformation and thus skilled performance. This study investigated how the CNS combines seen cursor positions and felt hand positions under a visuo-motor rotation paradigm. Young and older adult participants performed aiming movements on a digitizer while looking at rotated visual feedback on a monitor. After each movement, they judged either the proprioceptively sensed hand direction or the visually sensed cursor direction. We identified asymmetric mutual biases with a strong visual dominance. Furthermore, we found a number of differences between explicit and implicit judgments of hand directions. The explicit judgments had considerably larger variability than the implicit judgments. The bias toward the cursor direction for the explicit judgments was about twice as strong as for the implicit judgments. The individual biases of explicit and implicit judgments were uncorrelated. Biases of these judgments exhibited opposite sequential effects. Moreover, age-related changes were also different between these judgments. The judgment variability was decreased and the bias toward the cursor direction was increased with increasing age only for the explicit judgments. These results indicate distinct explicit and implicit neural representations of hand direction, similar to the notion of distinct visual systems. PMID:23894307

Engine dynamic analysis with general nonlinear finite element codes. II - Bearing element implementation, overall numerical characteristics and benchmarking

NASA Technical Reports Server (NTRS)

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

1982-01-01

Second-year efforts within a three-year study to develop and extend finite element (FE) methodology to efficiently handle the transient/steady state response of rotor-bearing-stator structure associated with gas turbine engines are outlined. The two main areas aim at (1) implanting the squeeze film damper element into a general purpose FE code for testing and evaluation; and (2) determining the numerical characteristics of the FE-generated rotor-bearing-stator simulation scheme. The governing FE field equations are set out and the solution methodology is presented. The choice of ADINA as the general-purpose FE code is explained, and the numerical operational characteristics of the direct integration approach of FE-generated rotor-bearing-stator simulations is determined, including benchmarking, comparison of explicit vs. implicit methodologies of direct integration, and demonstration problems.

Comparing implicit and explicit semantic access of direct and indirect word pairs in schizophrenia to evaluate models of semantic memory.

PubMed

Neill, Erica; Rossell, Susan Lee

2013-02-28

Semantic memory deficits in schizophrenia (SZ) are profound, yet there is no research comparing implicit and explicit semantic processing in the same participant sample. In the current study, both implicit and explicit priming are investigated using direct (LION-TIGER) and indirect (LION-STRIPES; where tiger is not displayed) stimuli comparing SZ to healthy controls. Based on a substantive review (Rossell and Stefanovic, 2007) and meta-analysis (Pomarol-Clotet et al., 2008), it was predicted that SZ would be associated with increased indirect priming implicitly. Further, it was predicted that SZ would be associated with abnormal indirect priming explicitly, replicating earlier work (Assaf et al., 2006). No specific hypotheses were made for implicit direct priming due to the heterogeneity of the literature. It was hypothesised that explicit direct priming would be intact based on the structured nature of this task. The pattern of results suggests (1) intact reaction time (RT) and error performance implicitly in the face of abnormal direct priming and (2) impaired RT and error performance explicitly. This pattern confirms general findings regarding implicit/explicit memory impairments in SZ whilst highlighting the unique pattern of performance specific to semantic priming. Finally, priming performance is discussed in relation to thought disorder and length of illness. Copyright © 2012 Elsevier Ireland Ltd. All rights reserved.

Generation of a composite grid for turbine flows and consideration of a numerical scheme

NASA Technical Reports Server (NTRS)

Choo, Y.; Yoon, S.; Reno, C.

1986-01-01

A composite grid was generated for flows in turbines. It consisted of the C-grid (or O-grid) in the immediate vicinity of the blade and the H-grid in the middle of the blade passage between the C-grids and in the upstream region. This new composite grid provides better smoothness, resolution, and orthogonality than any single grid for a typical turbine blade with a large camber and rounded leading and trailing edges. The C-H (or O-H) composite grid has an unusual grid point that is connected to more than four neighboring nodes in two dimensions (more than six neighboring nodes in three dimensions). A finite-volume lower-upper (LU) implicit scheme to be used on this grid poses no problem and requires no special treatment because each interior cell of this composite grid has only four neighboring cells in two dimensions (six cells in three dimensions). The LU implicit scheme was demonstrated to be efficient and robust for external flows in a broad flow regime and can be easily applied to internal flows and extended from two to three dimensions.

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.

An Implicit Upwind Algorithm for Computing Turbulent Flows on Unstructured Grids

NASA Technical Reports Server (NTRS)

Anerson, W. Kyle; Bonhaus, Daryl L.

1994-01-01

An implicit, Navier-Stokes solution algorithm is presented for the computation of turbulent flow on unstructured grids. The inviscid fluxes are computed using an upwind algorithm and the solution is advanced in time using a backward-Euler time-stepping scheme. At each time step, the linear system of equations is approximately solved with a point-implicit relaxation scheme. This methodology provides a viable and robust algorithm for computing turbulent flows on unstructured meshes. Results are shown for subsonic flow over a NACA 0012 airfoil and for transonic flow over a RAE 2822 airfoil exhibiting a strong upper-surface shock. In addition, results are shown for 3 element and 4 element airfoil configurations. For the calculations, two one equation turbulence models are utilized. For the NACA 0012 airfoil, a pressure distribution and force data are compared with other computational results as well as with experiment. Comparisons of computed pressure distributions and velocity profiles with experimental data are shown for the RAE airfoil and for the 3 element configuration. For the 4 element case, comparisons of surface pressure distributions with experiment are made. In general, the agreement between the computations and the experiment is good.

On a comparison of two schemes in sequential data assimilation

NASA Astrophysics Data System (ADS)

Grishina, Anastasiia A.; Penenko, Alexey V.

2017-11-01

This paper is focused on variational data assimilation as an approach to mathematical modeling. Realization of the approach requires a sequence of connected inverse problems with different sets of observational data to be solved. Two variational data assimilation schemes, "implicit" and "explicit", are considered in the article. Their equivalence is shown and the numerical results are given on a basis of non-linear Robertson system. To avoid the "inverse problem crime" different schemes were used to produce synthetic measurement and to solve the data assimilation problem.

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

NASA Astrophysics Data System (ADS)

Belli, Emily Ann

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

An efficient three-dimensional Poisson solver for SIMD high-performance-computing architectures

NASA Technical Reports Server (NTRS)

Cohl, H.

1994-01-01

We present an algorithm that solves the three-dimensional Poisson equation on a cylindrical grid. The technique uses a finite-difference scheme with operator splitting. This splitting maps the banded structure of the operator matrix into a two-dimensional set of tridiagonal matrices, which are then solved in parallel. Our algorithm couples FFT techniques with the well-known ADI (Alternating Direction Implicit) method for solving Elliptic PDE's, and the implementation is extremely well suited for a massively parallel environment like the SIMD architecture of the MasPar MP-1. Due to the highly recursive nature of our problem, we believe that our method is highly efficient, as it avoids excessive interprocessor communication.

Solution of Poisson equations for 3-dimensional grid generations. [computations of a flow field over a thin delta wing

NASA Technical Reports Server (NTRS)

Fujii, K.

1983-01-01

A method for generating three dimensional, finite difference grids about complicated geometries by using Poisson equations is developed. The inhomogenous terms are automatically chosen such that orthogonality and spacing restrictions at the body surface are satisfied. Spherical variables are used to avoid the axis singularity, and an alternating-direction-implicit (ADI) solution scheme is used to accelerate the computations. Computed results are presented that show the capability of the method. Since most of the results presented have been used as grids for flow-field computations, this is indicative that the method is a useful tool for generating three-dimensional grids about complicated geometries.

A global multilevel atmospheric model using a vector semi-Lagrangian finite-difference scheme. I - Adiabatic formulation

NASA Technical Reports Server (NTRS)

Bates, J. R.; Moorthi, S.; Higgins, R. W.

1993-01-01

An adiabatic global multilevel primitive equation model using a two time-level, semi-Lagrangian semi-implicit finite-difference integration scheme is presented. A Lorenz grid is used for vertical discretization and a C grid for the horizontal discretization. The momentum equation is discretized in vector form, thus avoiding problems near the poles. The 3D model equations are reduced by a linear transformation to a set of 2D elliptic equations, whose solution is found by means of an efficient direct solver. The model (with minimal physics) is integrated for 10 days starting from an initialized state derived from real data. A resolution of 16 levels in the vertical is used, with various horizontal resolutions. The model is found to be stable and efficient, and to give realistic output fields. Integrations with time steps of 10 min, 30 min, and 1 h are compared, and the differences are found to be acceptable.

A family of compact high order coupled time-space unconditionally stable vertical advection schemes

NASA Astrophysics Data System (ADS)

Lemarié, Florian; Debreu, Laurent

2016-04-01

Recent papers by Shchepetkin (2015) and Lemarié et al. (2015) have emphasized that the time-step of an oceanic model with an Eulerian vertical coordinate and an explicit time-stepping scheme is very often restricted by vertical advection in a few hot spots (i.e. most of the grid points are integrated with small Courant numbers, compared to the Courant-Friedrichs-Lewy (CFL) condition, except just few spots where numerical instability of the explicit scheme occurs first). The consequence is that the numerics for vertical advection must have good stability properties while being robust to changes in Courant number in terms of accuracy. An other constraint for oceanic models is the strict control of numerical mixing imposed by the highly adiabatic nature of the oceanic interior (i.e. mixing must be very small in the vertical direction below the boundary layer). We examine in this talk the possibility of mitigating vertical Courant-Friedrichs-Lewy (CFL) restriction, while avoiding numerical inaccuracies associated with standard implicit advection schemes (i.e. large sensitivity of the solution on Courant number, large phase delay, and possibly excess of numerical damping with unphysical orientation). Most regional oceanic models have been successfully using fourth order compact schemes for vertical advection. In this talk we present a new general framework to derive generic expressions for (one-step) coupled time and space high order compact schemes (see Daru & Tenaud (2004) for a thorough description of coupled time and space schemes). Among other properties, we show that those schemes are unconditionally stable and have very good accuracy properties even for large Courant numbers while having a very reasonable computational cost.

Reconstruction of fluorescence molecular tomography with a cosinoidal level set method.

PubMed

Zhang, Xuanxuan; Cao, Xu; Zhu, Shouping

2017-06-27

Implicit shape-based reconstruction method in fluorescence molecular tomography (FMT) is capable of achieving higher image clarity than image-based reconstruction method. However, the implicit shape method suffers from a low convergence speed and performs unstably due to the utilization of gradient-based optimization methods. Moreover, the implicit shape method requires priori information about the number of targets. A shape-based reconstruction scheme of FMT with a cosinoidal level set method is proposed in this paper. The Heaviside function in the classical implicit shape method is replaced with a cosine function, and then the reconstruction can be accomplished with the Levenberg-Marquardt method rather than gradient-based methods. As a result, the priori information about the number of targets is not required anymore and the choice of step length is avoided. Numerical simulations and phantom experiments were carried out to validate the proposed method. Results of the proposed method show higher contrast to noise ratios and Pearson correlations than the implicit shape method and image-based reconstruction method. Moreover, the number of iterations required in the proposed method is much less than the implicit shape method. The proposed method performs more stably, provides a faster convergence speed than the implicit shape method, and achieves higher image clarity than the image-based reconstruction method.

Direct comparison of four implicit memory tests.

PubMed

Rajaram, S; Roediger, H L

1993-07-01

Four verbal implicit memory tests, word identification, word stem completion, word fragment completion, and anagram solution, were directly compared in one experiment and were contrasted with free recall. On all implicit tests, priming was greatest from prior visual presentation of words, less (but significant) from auditory presentation, and least from pictorial presentations. Typefont did not affect priming. In free recall, pictures were recalled better than words. The four implicit tests all largely index perceptual (lexical) operations in recognizing words, or visual word form representations.

Comment on "An improved gray Lattice Boltzmann model for simulating fluid flow in multi-scale porous media": Intrinsic links between LBE Brinkman schemes

NASA Astrophysics Data System (ADS)

Ginzburg, Irina

2016-02-01

In this Comment on the recent work (Zhu and Ma, 2013) [11] by Zhu and Ma (ZM) we first show that all three local gray Lattice Boltzmann (GLB) schemes in the form (Zhu and Ma, 2013) [11]: GS (Chen and Zhu, 2008; Gao and Sharma, 1994) [1,4], WBS (Walsh et al., 2009) [12] and ZM, fail to get constant Darcy's velocity in series of porous blocks. This inconsistency is because of their incorrect definition of the macroscopic velocity in the presence of the heterogeneous momentum exchange, while the original WBS model (Walsh et al., 2009) [12] does this properly. We improve the GS and ZM schemes for this and other related deficiencies. Second, we show that the ;discontinuous velocity; they recover on the stratified interfaces with their WBS scheme is inherent, in different degrees, to all LBE Brinkman schemes, including ZM scheme. None of them guarantees the stress and the velocity continuity by their implicit interface conditions, even in the frame of the two-relaxation-times (TRT) collision operator where these two properties are assured in stratified Stokes flow, Ginzburg (2007) [5]. Third, the GLB schemes are presented in work (Zhu and Ma, 2013) [11] as the alternative ones to direct, Brinkman-force based (BF) schemes (Freed, 1998; Nie and Martys, 2007) [3,8]. Yet, we show that the BF-TRT scheme (Ginzburg, 2008) [6] gets the solutions of any of the improved GLB schemes for specific, viscosity-dependent choice of its one or two local relaxation rates. This provides the principal difference between the GLB and BF: while the BF may respect the linearity of the Stokes-Brinkman equation rigorously, the GLB-TRT cannot, unless it reduces to the BF via the inverse transform of the relaxation rates. Furthermore, we show that, in limited parameter space, ;gray; schemes may run one another. From the practical point of view, permeability values obtained with the GLB are viscosity-dependent, unlike with the BF. Finally, the GLB shares with the BF a so-called anisotropy (Ginzburg, 2008; Nie and Martys, 2007) [6,8], that is, flow-direction-dependency in their effective viscosity corrections, related to the discretized spatial variation of the resistance forcing.

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.

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.

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.

Direct numerical simulation of laminar-turbulent flow over a flat plate at hypersonic flow speeds

NASA Astrophysics Data System (ADS)

Egorov, I. V.; Novikov, A. V.

2016-06-01

A method for direct numerical simulation of a laminar-turbulent flow around bodies at hypersonic flow speeds is proposed. The simulation is performed by solving the full three-dimensional unsteady Navier-Stokes equations. The method of calculation is oriented to application of supercomputers and is based on implicit monotonic approximation schemes and a modified Newton-Raphson method for solving nonlinear difference equations. By this method, the development of three-dimensional perturbations in the boundary layer over a flat plate and in a near-wall flow in a compression corner is studied at the Mach numbers of the free-stream of M = 5.37. In addition to pulsation characteristic, distributions of the mean coefficients of the viscous flow in the transient section of the streamlined surface are obtained, which enables one to determine the beginning of the laminar-turbulent transition and estimate the characteristics of the turbulent flow in the boundary layer.

Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints.

PubMed

Chen, Weisheng

2009-07-01

This paper focuses on the problem of adaptive neural network tracking control for a class of discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints. Two novel state-feedback and output-feedback dynamic control laws are established where the function tanh(.) is employed to solve the saturation constraint problem. Implicit function theorem and mean value theorem are exploited to deal with non-affine variables that are used as actual control. Radial basis function neural networks are used to approximate the desired input function. Discrete Nussbaum gain is used to estimate the unknown sign of control gain. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of control schemes proposed in this paper.

Direct numerical simulation of the laminar-turbulent transition at hypersonic flow speeds on a supercomputer

NASA Astrophysics Data System (ADS)

Egorov, I. V.; Novikov, A. V.; Fedorov, A. V.

2017-08-01

A method for direct numerical simulation of three-dimensional unsteady disturbances leading to a laminar-turbulent transition at hypersonic flow speeds is proposed. The simulation relies on solving the full three-dimensional unsteady Navier-Stokes equations. The computational technique is intended for multiprocessor supercomputers and is based on a fully implicit monotone approximation scheme and the Newton-Raphson method for solving systems of nonlinear difference equations. This approach is used to study the development of three-dimensional unstable disturbances in a flat-plate and compression-corner boundary layers in early laminar-turbulent transition stages at the free-stream Mach number M = 5.37. The three-dimensional disturbance field is visualized in order to reveal and discuss features of the instability development at the linear and nonlinear stages. The distribution of the skin friction coefficient is used to detect laminar and transient flow regimes and determine the onset of the laminar-turbulent transition.

A three dimensional multigrid multiblock multistage time stepping scheme for the Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Elmiligui, Alaa; Cannizzaro, Frank; Melson, N. D.

1991-01-01

A general multiblock method for the solution of the three-dimensional, unsteady, compressible, thin-layer Navier-Stokes equations has been developed. The convective and pressure terms are spatially discretized using Roe's flux differencing technique while the viscous terms are centrally differenced. An explicit Runge-Kutta method is used to advance the solution in time. Local time stepping, adaptive implicit residual smoothing, and the Full Approximation Storage (FAS) multigrid scheme are added to the explicit time stepping scheme to accelerate convergence to steady state. Results for three-dimensional test cases are presented and discussed.

A New Family of Compact High Order Coupled Time-Space Unconditionally Stable Vertical Advection Schemes

NASA Astrophysics Data System (ADS)

Lemarié, F.; Debreu, L.

2016-02-01

Recent papers by Shchepetkin (2015) and Lemarié et al. (2015) have emphasized that the time-step of an oceanic model with an Eulerian vertical coordinate and an explicit time-stepping scheme is very often restricted by vertical advection in a few hot spots (i.e. most of the grid points are integrated with small Courant numbers, compared to the Courant-Friedrichs-Lewy (CFL) condition, except just few spots where numerical instability of the explicit scheme occurs first). The consequence is that the numerics for vertical advection must have good stability properties while being robust to changes in Courant number in terms of accuracy. An other constraint for oceanic models is the strict control of numerical mixing imposed by the highly adiabatic nature of the oceanic interior (i.e. mixing must be very small in the vertical direction below the boundary layer). We examine in this talk the possibility of mitigating vertical Courant-Friedrichs-Lewy (CFL) restriction, while avoiding numerical inaccuracies associated with standard implicit advection schemes (i.e. large sensitivity of the solution on Courant number, large phase delay, and possibly excess of numerical damping with unphysical orientation). Most regional oceanic models have been successfully using fourth order compact schemes for vertical advection. In this talk we present a new general framework to derive generic expressions for (one-step) coupled time and space high order compact schemes (see Daru & Tenaud (2004) for a thorough description of coupled time and space schemes). Among other properties, we show that those schemes are unconditionally stable and have very good accuracy properties even for large Courant numbers while having a very reasonable computational cost. To our knowledge no unconditionally stable scheme with such high order accuracy in time and space have been presented so far in the literature. Furthermore, we show how those schemes can be made monotonic without compromising their stability properties.

Oxygen Vacancy Linear Clustering in a Perovskite Oxide

DOE PAGES

Eom, Kitae; Choi, Euiyoung; Choi, Minsu; ...

2017-07-14

Oxygen vacancies have been implicitly assumed isolated ones, and understanding oxide materials possibly containing oxygen vacancies remains elusive within the scheme of the isolated vacancies, although the oxygen vacancies have been playing a decisive role in oxide materials. We report the presence of oxygen vacancy linear clusters and their orientation along a specific crystallographic direction in SrTiO 3, a representative of a perovskite oxide. The presence of the linear clusters and associated electron localization was revealed by an electronic structure represented in the increase in the Ti 2+ valence state or corresponding Ti 3d 2 electronic configuration along with divacancymore » cluster model analysis and transport measurement. The orientation of the linear clusters along the [001] direction in perovskite SrTiO 3 was verified by further X-ray diffuse scattering analysis. And because SrTiO 3 is an archetypical perovskite oxide, the vacancy linear clustering with the specific aligned direction and electron localization can be extended to a wide variety of the perovskite oxides.« less

Oxygen Vacancy Linear Clustering in a Perovskite Oxide

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

Eom, Kitae; Choi, Euiyoung; Choi, Minsu

Oxygen vacancies have been implicitly assumed isolated ones, and understanding oxide materials possibly containing oxygen vacancies remains elusive within the scheme of the isolated vacancies, although the oxygen vacancies have been playing a decisive role in oxide materials. We report the presence of oxygen vacancy linear clusters and their orientation along a specific crystallographic direction in SrTiO 3, a representative of a perovskite oxide. The presence of the linear clusters and associated electron localization was revealed by an electronic structure represented in the increase in the Ti 2+ valence state or corresponding Ti 3d 2 electronic configuration along with divacancymore » cluster model analysis and transport measurement. The orientation of the linear clusters along the [001] direction in perovskite SrTiO 3 was verified by further X-ray diffuse scattering analysis. And because SrTiO 3 is an archetypical perovskite oxide, the vacancy linear clustering with the specific aligned direction and electron localization can be extended to a wide variety of the perovskite oxides.« less

Universal block diagram based modeling and simulation schemes for fractional-order control systems.

PubMed

Bai, Lu; Xue, Dingyü

2017-05-08

Universal block diagram based schemes are proposed for modeling and simulating the fractional-order control systems in this paper. A fractional operator block in Simulink is designed to evaluate the fractional-order derivative and integral. Based on the block, the fractional-order control systems with zero initial conditions can be modeled conveniently. For modeling the system with nonzero initial conditions, the auxiliary signal is constructed in the compensation scheme. Since the compensation scheme is very complicated, therefore the integrator chain scheme is further proposed to simplify the modeling procedures. The accuracy and effectiveness of the schemes are assessed in the examples, the computation results testify the block diagram scheme is efficient for all Caputo fractional-order ordinary differential equations (FODEs) of any complexity, including the implicit Caputo FODEs. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

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.

The Pivotal Role of Effort Beliefs in Mediating Implicit Theories of Intelligence and Achievement Goals and Academic Motivations

ERIC Educational Resources Information Center

Tempelaar, Dirk T.; Rienties, Bart; Giesbers, Bas; Gijselaers, Wim H.

2015-01-01

Empirical studies into meaning systems surrounding implicit theories of intelligence typically entail two stringent assumptions: that different implicit theories and different effort beliefs represent opposite poles on a single scale, and that implicit theories directly impact the constructs as achievement goals and academic motivations. Through…

Geometric multigrid for an implicit-time immersed boundary method

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

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

2014-10-12

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

Implicit continuum mechanics approach to heat conduction in granular materials

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

Massoudi, M.; Mehrabadi, M.

In this paper, we derive a properly frame-invariant implicit constitutive relationship for the heat flux vector for a granular medium (or a density-gradient-type fluid). The heat flux vector is commonly modeled by Fourier’s law of heat conduction, and for complex materials such as nonlinear fluids, porous media, or granular materials, the coefficient of thermal conductivity is generalized by assuming that it would depend on a host of material and kinematic parameters such as temperature, shear rate, porosity, concentration, etc. In this paper, we extend the approach of Massoudi [Massoudi, M. Math. Methods Appl. Sci. 2006, 29, 1585; Massoudi, M. Math.more » Methods Appl. Sci. 2006, 29, 1599], who provided explicit constitutive relations for the heat flux vector for flowing granular materials; in order to do so, we use the implicit scheme suggested by Fox [Fox, N. Int. J. Eng. Sci. 1969, 7, 437], who obtained implicit relations in thermoelasticity.« less

An Unsteady Preconditioning Scheme Based on Convective-Upwind Split-Pressure (CUSP) Artificial Dissipation

DTIC Science & Technology

2014-01-07

this can have a disastrous effect on convergence rate. Even if steady state is obtained for low Mach number flows (after many iterations ), the results...rally lead do a diagonally dominant left-hand-side matrix, which causes stability problems for implicit Gauss - Seidel schemes. For this reason, matrix... convergence at the stagnation point. The iterations for each airfoil is also reported in Fig. 2. Without preconditioning, dramatic efficiency problems are seen

Application of CFD to aerothermal heating problems

NASA Technical Reports Server (NTRS)

Macaraeg, M. G.

1986-01-01

Numerical solutions of the compressible Navier-Stokes equations by an alternating direction implicit scheme, applied to two experimental investigations are presented. The first is cooling by injection of a gas jet through the nose of an ogive-cone, and the second is the aerothermal environment in the gap formed by the wing and elevon section of a test model of the space shuttle. The simulations demonstrate that accurate pressure calculations are easily obtained on a coarse grid, while convergence is obtained after the residual reduces by four orders of magnitude. Accurate heating rates, however, require a fine grid solution, with convergence requiring at least a reduction of six orders of magnitude in the residual. The effect of artificial dissipation on numerical results is also assessed.

Consider the source: persuasion of implicit evaluations is moderated by source credibility.

PubMed

Smith, Colin Tucker; De Houwer, Jan; Nosek, Brian A

2013-02-01

The long history of persuasion research shows how to change explicit, self-reported evaluations through direct appeals. At the same time, research on how to change implicit evaluations has focused almost entirely on techniques of retraining existing evaluations or manipulating contexts. In five studies, we examined whether direct appeals can change implicit evaluations in the same way as they do explicit evaluations. In five studies, both explicit and implicit evaluations showed greater evidence of persuasion following information presented by a highly credible source than a source low in credibility. Whereas cognitive load did not alter the effect of source credibility on explicit evaluations, source credibility had an effect on the persuasion of implicit evaluations only when participants were encouraged and able to consider information about the source. Our findings reveal the relevance of persuasion research for changing implicit evaluations and provide new ideas about the processes underlying both types of evaluation.

Source-to-Sink: An implicit and O(n) landscape evolution model and its application to the Ogooue Delta, Gabon

NASA Astrophysics Data System (ADS)

Yuan, X.; Braun, J.; Guerit, L.; Simon, B.

2017-12-01

Limited attention has been given to linking continental erosion to transport and deposition of sediments in the marine environment in large-scale landscape evolution models. Although both environments have been thoroughly investigated, the details of how erosional or climatic events are recorded in the sedimentary and stratigraphic records have not been studied in a consistent quantitative manner. Here we propose a new numerical model for marine multi-lithology (sand and silt) coupling transport and deposition that is directly coupled to FastScape, a landscape evolution model that solves the continental stream power law and hillslope diffusion equation using implicit and O(n) algorithms. Marine transport and deposition is simulated by a nonlinear 2D diffusion model that incorporates a dual lithology (sand and slit) and where source terms represent the sediment flux from continental river erosion. Sediment compaction effects are also incorporated, taking into account the dual lithology, and are important to properly compute the details of the synthetic stratigraphic record. The algorithm used to represent marine transport and deposition is also implicit and O(n). The main purpose of our work is to invert stratigraphic data from offshore marginal basins to provide constraints on the tectonic, climatic and sea-level conditions that have affected the adjacent continental areas. In order to do so, we have incorporated the new model into a Bayesian inversion and optimisation scheme and tested and validated the approach with synthetic data. This is made possible due to the high efficient of the forward model. We are in the process of applying the inversion scheme to stratigraphic data from the Ogooue Delta (Gabon). By comparing real and synthetic stratigraphic geometries along cross-section of the delta, the shape and slope of seismic/time markers, and the sand to silt fraction in wells, we hope to obtain good constraints, not only of the value of the transport coefficients for sand and silt in the marine environment, but also of the uplift, erosional and climate history of the adjacent continental areas, as well as the amplitude of sea level variations.

Parallelizing alternating direction implicit solver on GPUs

USDA-ARS?s Scientific Manuscript database

We present a parallel Alternating Direction Implicit (ADI) solver on GPUs. Our implementation significantly improves existing implementations in two aspects. First, we address the scalability issue of existing Parallel Cyclic Reduction (PCR) implementations by eliminating their hardware resource con...

Issues associated with Galilean invariance on a moving solid boundary in the lattice Boltzmann method

NASA Astrophysics Data System (ADS)

Peng, Cheng; Geneva, Nicholas; Guo, Zhaoli; Wang, Lian-Ping

2017-01-01

In lattice Boltzmann simulations involving moving solid boundaries, the momentum exchange between the solid and fluid phases was recently found to be not fully consistent with the principle of local Galilean invariance (GI) when the bounce-back schemes (BBS) and the momentum exchange method (MEM) are used. In the past, this inconsistency was resolved by introducing modified MEM schemes so that the overall moving-boundary algorithm could be more consistent with GI. However, in this paper we argue that the true origin of this violation of Galilean invariance (VGI) in the presence of a moving solid-fluid interface is due to the BBS itself, as the VGI error not only exists in the hydrodynamic force acting on the solid phase, but also in the boundary force exerted on the fluid phase, according to Newton's Third Law. The latter, however, has so far gone unnoticed in previously proposed modified MEM schemes. Based on this argument, we conclude that the previous modifications to the momentum exchange method are incomplete solutions to the VGI error in the lattice Boltzmann method (LBM). An implicit remedy to the VGI error in the LBM and its limitation is then revealed. To address the VGI error for a case when this implicit remedy does not exist, a bounce-back scheme based on coordinate transformation is proposed. Numerical tests in both laminar and turbulent flows show that the proposed scheme can effectively eliminate the errors associated with the usual bounce-back implementations on a no-slip solid boundary, and it can maintain an accurate momentum exchange calculation with minimal computational overhead.

Fractional Steps methods for transient problems on commodity computer architectures

NASA Astrophysics Data System (ADS)

Krotkiewski, M.; Dabrowski, M.; Podladchikov, Y. Y.

2008-12-01

Fractional Steps methods are suitable for modeling transient processes that are central to many geological applications. Low memory requirements and modest computational complexity facilitates calculations on high-resolution three-dimensional models. An efficient implementation of Alternating Direction Implicit/Locally One-Dimensional schemes for an Opteron-based shared memory system is presented. The memory bandwidth usage, the main bottleneck on modern computer architectures, is specially addressed. High efficiency of above 2 GFlops per CPU is sustained for problems of 1 billion degrees of freedom. The optimized sequential implementation of all 1D sweeps is comparable in execution time to copying the used data in the memory. Scalability of the parallel implementation on up to 8 CPUs is close to perfect. Performing one timestep of the Locally One-Dimensional scheme on a system of 1000 3 unknowns on 8 CPUs takes only 11 s. We validate the LOD scheme using a computational model of an isolated inclusion subject to a constant far field flux. Next, we study numerically the evolution of a diffusion front and the effective thermal conductivity of composites consisting of multiple inclusions and compare the results with predictions based on the differential effective medium approach. Finally, application of the developed parabolic solver is suggested for a real-world problem of fluid transport and reactions inside a reservoir.

Newton-like methods for Navier-Stokes solution

NASA Astrophysics Data System (ADS)

Qin, N.; Xu, X.; Richards, B. E.

1992-12-01

The paper reports on Newton-like methods called SFDN-alpha-GMRES and SQN-alpha-GMRES methods that have been devised and proven as powerful schemes for large nonlinear problems typical of viscous compressible Navier-Stokes solutions. They can be applied using a partially converged solution from a conventional explicit or approximate implicit method. Developments have included the efficient parallelization of the schemes on a distributed memory parallel computer. The methods are illustrated using a RISC workstation and a transputer parallel system respectively to solve a hypersonic vortical flow.

Global Asymptotic Behavior of Iterative Implicit Schemes

NASA Technical Reports Server (NTRS)

Yee, H. C.; Sweby, P. K.

1994-01-01

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

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).

A new uniformly valid asymptotic integration algorithm for elasto-plastic creep and unified viscoplastic theories including continuum damage

NASA Technical Reports Server (NTRS)

Chulya, Abhisak; Walker, Kevin P.

1991-01-01

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

A new uniformly valid asymptotic integration algorithm for elasto-plastic-creep and unified viscoplastic theories including continuum damage

NASA Technical Reports Server (NTRS)

Chulya, A.; Walker, K. P.

1989-01-01

A new scheme to integrate a system of stiff differential equations for both the elasto-plastic creep and the unified viscoplastic theories is presented. The method has high stability, allows large time increments, and is implicit and iterative. It is suitable for use with continuum damage theories. The scheme was incorporated into MARC, a commercial finite element code through a user subroutine called HYPELA. Results from numerical problems under complex loading histories are presented for both small and large scale analysis. To demonstrate the scheme's accuracy and efficiency, comparisons to a self-adaptive forward Euler method are made.

High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition

NASA Astrophysics Data System (ADS)

Zhong, Xiaolin

1998-08-01

Direct numerical simulation (DNS) has become a powerful tool in studying fundamental phenomena of laminar-turbulent transition of high-speed boundary layers. Previous DNS studies of supersonic and hypersonic boundary layer transition have been limited to perfect-gas flow over flat-plate boundary layers without shock waves. For hypersonic boundary layers over realistic blunt bodies, DNS studies of transition need to consider the effects of bow shocks, entropy layers, surface curvature, and finite-rate chemistry. It is necessary that numerical methods for such studies are robust and high-order accurate both in resolving wide ranges of flow time and length scales and in resolving the interaction between the bow shocks and flow disturbance waves. This paper presents a new high-order shock-fitting finite-difference method for the DNS of the stability and transition of hypersonic boundary layers over blunt bodies with strong bow shocks and with (or without) thermo-chemical nonequilibrium. The proposed method includes a set of new upwind high-order finite-difference schemes which are stable and are less dissipative than a straightforward upwind scheme using an upwind-bias grid stencil, a high-order shock-fitting formulation, and third-order semi-implicit Runge-Kutta schemes for temporal discretization of stiff reacting flow equations. The accuracy and stability of the new schemes are validated by numerical experiments of the linear wave equation and nonlinear Navier-Stokes equations. The algorithm is then applied to the DNS of the receptivity of hypersonic boundary layers over a parabolic leading edge to freestream acoustic disturbances.

An improved semi-implicit method for structural dynamics analysis

NASA Technical Reports Server (NTRS)

Park, K. C.

1982-01-01

A semi-implicit algorithm is presented for direct time integration of the structural dynamics equations. The algorithm avoids the factoring of the implicit difference solution matrix and mitigates the unacceptable accuracy losses which plagued previous semi-implicit algorithms. This substantial accuracy improvement is achieved by augmenting the solution matrix with two simple diagonal matrices of the order of the integration truncation error.

Haptics-based dynamic implicit solid modeling.

PubMed

Hua, Jing; Qin, Hong

2004-01-01

This paper systematically presents a novel, interactive solid modeling framework, Haptics-based Dynamic Implicit Solid Modeling, which is founded upon volumetric implicit functions and powerful physics-based modeling. In particular, we augment our modeling framework with a haptic mechanism in order to take advantage of additional realism associated with a 3D haptic interface. Our dynamic implicit solids are semi-algebraic sets of volumetric implicit functions and are governed by the principles of dynamics, hence responding to sculpting forces in a natural and predictable manner. In order to directly manipulate existing volumetric data sets as well as point clouds, we develop a hierarchical fitting algorithm to reconstruct and represent discrete data sets using our continuous implicit functions, which permit users to further design and edit those existing 3D models in real-time using a large variety of haptic and geometric toolkits, and visualize their interactive deformation at arbitrary resolution. The additional geometric and physical constraints afford more sophisticated control of the dynamic implicit solids. The versatility of our dynamic implicit modeling enables the user to easily modify both the geometry and the topology of modeled objects, while the inherent physical properties can offer an intuitive haptic interface for direct manipulation with force feedback.

u-w formulation for dynamic problems in large deformation regime solved through an implicit meshfree scheme

NASA Astrophysics Data System (ADS)

Navas, Pedro; Sanavia, Lorenzo; López-Querol, Susana; Yu, Rena C.

2017-12-01

Solving dynamic problems for fluid saturated porous media at large deformation regime is an interesting but complex issue. An implicit time integration scheme is herein developed within the framework of the u-w (solid displacement-relative fluid displacement) formulation for the Biot's equations. In particular, liquid water saturated porous media is considered and the linearization of the linear momentum equations taking into account all the inertia terms for both solid and fluid phases is for the first time presented. The spatial discretization is carried out through a meshfree method, in which the shape functions are based on the principle of local maximum entropy LME. The current methodology is firstly validated with the dynamic consolidation of a soil column and the plastic shear band formulation of a square domain loaded by a rigid footing. The feasibility of this new numerical approach for solving large deformation dynamic problems is finally demonstrated through the application to an embankment problem subjected to an earthquake.

Parallel Computing of Upwelling in a Rotating Stratified Flow

NASA Astrophysics Data System (ADS)

Cui, A.; Street, R. L.

1997-11-01

A code for the three-dimensional, unsteady, incompressible, and turbulent flow has been implemented on the IBM SP2, using message passing. The effects of rotation and variable density are included. A finite volume method is used to discretize the Navier-Stokes equations in general curvilinear coordinates on a non-staggered grid. All the spatial derivatives are approximated using second-order central differences with the exception of the convection terms, which are handled with special upwind-difference schemes. The semi-implicit, second-order accurate, time-advancement scheme employs the Adams-Bashforth method for the explicit terms and Crank-Nicolson for the implicit terms. A multigrid method, with the four-color ZEBRA as smoother, is used to solve the Poisson equation for pressure, while the momentum equations are solved with an approximate factorization technique. The code was successfully validated for a variety test cases. Simulations of a laboratory model of coastal upwelling in a rotating annulus are in progress and will be presented.

IMEX HDG-DG: A coupled implicit hybridized discontinuous Galerkin and explicit discontinuous Galerkin approach for Euler systems on cubed sphere.

NASA Astrophysics Data System (ADS)

Kang, S.; Muralikrishnan, S.; Bui-Thanh, T.

2017-12-01

We propose IMEX HDG-DG schemes for Euler systems on cubed sphere. Of interest is subsonic flow, where the speed of the acoustic wave is faster than that of the nonlinear advection. In order to simulate these flows efficiently, we split the governing system into stiff part describing the fast waves and non-stiff part associated with nonlinear advection. The former is discretized implicitly with HDG method while explicit Runge-Kutta DG discretization is employed for the latter. The proposed IMEX HDG-DG framework: 1) facilitates high-order solution both in time and space; 2) avoids overly small time stepsizes; 3) requires only one linear system solve per time step; and 4) relatively to DG generates smaller and sparser linear system while promoting further parallelism owing to HDG discretization. Numerical results for various test cases demonstrate that our methods are comparable to explicit Runge-Kutta DG schemes in terms of accuracy, while allowing for much larger time stepsizes.

Non-hydrostatic semi-elastic hybrid-coordinate SISL extension of HIRLAM. Part II: numerical testing

NASA Astrophysics Data System (ADS)

Rõõm, Rein; Männik, Aarne; Luhamaa, Andres; Zirk, Marko

2007-10-01

The semi-implicit semi-Lagrangian (SISL), two-time-level, non-hydrostatic numerical scheme, based on the non-hydrostatic, semi-elastic pressure-coordinate equations, is tested in model experiments with flow over given orography (elliptical hill, mountain ridge, system of successive ridges) in a rectangular domain with emphasis on the numerical accuracy and non-hydrostatic effect presentation capability. Comparison demonstrates good (in strong primary wave generation) to satisfactory (in weak secondary wave reproduction in some cases) consistency of the numerical modelling results with known stationary linear test solutions. Numerical stability of the developed model is investigated with respect to the reference state choice, modelling dynamics of a stationary front. The horizontally area-mean reference temperature proves to be the optimal stability warrant. The numerical scheme with explicit residual in the vertical forcing term becomes unstable for cross-frontal temperature differences exceeding 30 K. Stability is restored, if the vertical forcing is treated implicitly, which enables to use time steps, comparable with the hydrostatic SISL.

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

NASA Astrophysics Data System (ADS)

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

2018-07-01

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

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.

A multigrid nonoscillatory method for computing high speed flows

NASA Technical Reports Server (NTRS)

Li, C. P.; Shieh, T. H.

1993-01-01

A multigrid method using different smoothers has been developed to solve the Euler equations discretized by a nonoscillatory scheme up to fourth order accuracy. The best smoothing property is provided by a five-stage Runge-Kutta technique with optimized coefficients, yet the most efficient smoother is a backward Euler technique in factored and diagonalized form. The singlegrid solution for a hypersonic, viscous conic flow is in excellent agreement with the solution obtained by the third order MUSCL and Roe's method. Mach 8 inviscid flow computations for a complete entry probe have shown that the accuracy is at least as good as the symmetric TVD scheme of Yee and Harten. The implicit multigrid method is four times more efficient than the explicit multigrid technique and 3.5 times faster than the single-grid implicit technique. For a Mach 8.7 inviscid flow over a blunt delta wing at 30 deg incidence, the CPU reduction factor from the three-level multigrid computation is 2.2 on a grid of 37 x 41 x 73 nodes.

Multistage Schemes with Multigrid for Euler and Navier-Strokes Equations: Components and Analysis

NASA Technical Reports Server (NTRS)

Swanson, R. C.; Turkel, Eli

1997-01-01

A class of explicit multistage time-stepping schemes with centered spatial differencing and multigrids are considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs (flow codes with multigrid (FLOMG) series) currently used to solve a wide range of fluid dynamics problems, including internal and external flows. In this paper, the components of these multistage time-stepping schemes are defined, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.

Efficient and accurate numerical schemes for a hydro-dynamically coupled phase field diblock copolymer model

NASA Astrophysics Data System (ADS)

Cheng, Qing; Yang, Xiaofeng; Shen, Jie

2017-07-01

In this paper, we consider numerical approximations of a hydro-dynamically coupled phase field diblock copolymer model, in which the free energy contains a kinetic potential, a gradient entropy, a Ginzburg-Landau double well potential, and a long range nonlocal type potential. We develop a set of second order time marching schemes for this system using the "Invariant Energy Quadratization" approach for the double well potential, the projection method for the Navier-Stokes equation, and a subtle implicit-explicit treatment for the stress and convective term. The resulting schemes are linear and lead to symmetric positive definite systems at each time step, thus they can be efficiently solved. We further prove that these schemes are unconditionally energy stable. Various numerical experiments are performed to validate the accuracy and energy stability of the proposed schemes.

Differential geometry based solvation model I: Eulerian formulation

NASA Astrophysics Data System (ADS)

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-11-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the solvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By optimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second-order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature.

Differential geometry based solvation model I: Eulerian formulation

PubMed Central

Chen, Zhan; Baker, Nathan A.; Wei, G. W.

2010-01-01

This paper presents a differential geometry based model for the analysis and computation of the equilibrium property of solvation. Differential geometry theory of surfaces is utilized to define and construct smooth interfaces with good stability and differentiability for use in characterizing the solvent-solute boundaries and in generating continuous dielectric functions across the computational domain. A total free energy functional is constructed to couple polar and nonpolar contributions to the salvation process. Geometric measure theory is employed to rigorously convert a Lagrangian formulation of the surface energy into an Eulerian formulation so as to bring all energy terms into an equal footing. By minimizing the total free energy functional, we derive coupled generalized Poisson-Boltzmann equation (GPBE) and generalized geometric flow equation (GGFE) for the electrostatic potential and the construction of realistic solvent-solute boundaries, respectively. By solving the coupled GPBE and GGFE, we obtain the electrostatic potential, the solvent-solute boundary profile, and the smooth dielectric function, and thereby improve the accuracy and stability of implicit solvation calculations. We also design efficient second order numerical schemes for the solution of the GPBE and GGFE. Matrix resulted from the discretization of the GPBE is accelerated with appropriate preconditioners. An alternative direct implicit (ADI) scheme is designed to improve the stability of solving the GGFE. Two iterative approaches are designed to solve the coupled system of nonlinear partial differential equations. Extensive numerical experiments are designed to validate the present theoretical model, test computational methods, and optimize numerical algorithms. Example solvation analysis of both small compounds and proteins are carried out to further demonstrate the accuracy, stability, efficiency and robustness of the present new model and numerical approaches. Comparison is given to both experimental and theoretical results in the literature. PMID:20938489

Kinematic Structural Modelling in Bayesian Networks

NASA Astrophysics Data System (ADS)

Schaaf, Alexander; de la Varga, Miguel; Florian Wellmann, J.

2017-04-01

We commonly capture our knowledge about the spatial distribution of distinct geological lithologies in the form of 3-D geological models. Several methods exist to create these models, each with its own strengths and limitations. We present here an approach to combine the functionalities of two modeling approaches - implicit interpolation and kinematic modelling methods - into one framework, while explicitly considering parameter uncertainties and thus model uncertainty. In recent work, we proposed an approach to implement implicit modelling algorithms into Bayesian networks. This was done to address the issues of input data uncertainty and integration of geological information from varying sources in the form of geological likelihood functions. However, one general shortcoming of implicit methods is that they usually do not take any physical constraints into consideration, which can result in unrealistic model outcomes and artifacts. On the other hand, kinematic structural modelling intends to reconstruct the history of a geological system based on physically driven kinematic events. This type of modelling incorporates simplified, physical laws into the model, at the cost of a substantial increment of usable uncertain parameters. In the work presented here, we show an integration of these two different modelling methodologies, taking advantage of the strengths of both of them. First, we treat the two types of models separately, capturing the information contained in the kinematic models and their specific parameters in the form of likelihood functions, in order to use them in the implicit modelling scheme. We then go further and combine the two modelling approaches into one single Bayesian network. This enables the direct flow of information between the parameters of the kinematic modelling step and the implicit modelling step and links the exclusive input data and likelihoods of the two different modelling algorithms into one probabilistic inference framework. In addition, we use the capabilities of Noddy to analyze the topology of structural models to demonstrate how topological information, such as the connectivity of two layers across an unconformity, can be used as a likelihood function. In an application to a synthetic case study, we show that our approach leads to a successful combination of the two different modelling concepts. Specifically, we show that we derive ensemble realizations of implicit models that now incorporate the knowledge of the kinematic aspects, representing an important step forward in the integration of knowledge and a corresponding estimation of uncertainties in structural geological models.

Positivity-preserving dual time stepping schemes for gas dynamics

NASA Astrophysics Data System (ADS)

Parent, Bernard

2018-05-01

A new approach at discretizing the temporal derivative of the Euler equations is here presented which can be used with dual time stepping. The temporal discretization stencil is derived along the lines of the Cauchy-Kowalevski procedure resulting in cross differences in spacetime but with some novel modifications which ensure the positivity of the discretization coefficients. It is then shown that the so-obtained spacetime cross differences result in changes to the wave speeds and can thus be incorporated within Roe or Steger-Warming schemes (with and without reconstruction-evolution) simply by altering the eigenvalues. The proposed approach is advantaged over alternatives in that it is positivity-preserving for the Euler equations. Further, it yields monotone solutions near discontinuities while exhibiting a truncation error in smooth regions less than the one of the second- or third-order accurate backward-difference-formula (BDF) for either small or large time steps. The high resolution and positivity preservation of the proposed discretization stencils are independent of the convergence acceleration technique which can be set to multigrid, preconditioning, Jacobian-free Newton-Krylov, block-implicit, etc. Thus, the current paper also offers the first implicit integration of the time-accurate Euler equations that is positivity-preserving in the strict sense (that is, the density and temperature are guaranteed to remain positive). This is in contrast to all previous positivity-preserving implicit methods which only guaranteed the positivity of the density, not of the temperature or pressure. Several stringent reacting and inert test cases confirm the positivity-preserving property of the proposed method as well as its higher resolution and higher computational efficiency over other second-order and third-order implicit temporal discretization strategies.

An online-coupled NWP/ACT model with conserved Lagrangian levels

NASA Astrophysics Data System (ADS)

Sørensen, B.; Kaas, E.; Lauritzen, P. H.

2012-04-01

Numerical weather and climate modelling is under constant development. Semi-implicit semi-Lagrangian (SISL) models have proven to be numerically efficient in both short-range weather forecasts and climate models, due to the ability to use long time steps. Chemical/aerosol feedback mechanism are becoming more and more relevant in NWP as well as climate models, since the biogenic and anthropogenic emissions can have a direct effect on the dynamics and radiative properties of the atmosphere. To include chemical feedback mechanisms in the NWP models, on-line coupling is crucial. In 3D semi-Lagrangian schemes with quasi-Lagrangian vertical coordinates the Lagrangian levels are remapped to Eulerian model levels each time step. This remapping introduces an undesirable tendency to smooth sharp gradients and creates unphysical numerical diffusion in the vertical distribution. A semi-Lagrangian advection method is introduced, it combines an inherently mass conserving 2D semi-Lagrangian scheme, with a SISL scheme employing both hybrid vertical coordinates and a fully Lagrangian vertical coordinate. This minimizes the vertical diffusion and thus potentially improves the simulation of the vertical profiles of moisture, clouds, and chemical constituents. Since the Lagrangian levels suffer from traditional Lagrangian limitations caused by the convergence and divergence of the flow, remappings to the Eulerian model levels are generally still required - but this need only be applied after a number of time steps - unless dynamic remapping methods are used. For this several different remapping methods has been implemented. The combined scheme is mass conserving, consistent, and multi-tracer efficient.

Evidence for Implicit Learning in Syntactic Comprehension

ERIC Educational Resources Information Center

Fine, Alex B.; Jaeger, T. Florian

2013-01-01

This study provides evidence for implicit learning in syntactic comprehension. By reanalyzing data from a syntactic priming experiment (Thothathiri & Snedeker, 2008), we find that the error signal associated with a syntactic prime influences comprehenders' subsequent syntactic expectations. This follows directly from error-based implicit learning…

What Do Lead and Copper Sampling Protocols Mean, and Which Is Right for You?

EPA Science Inventory

this presentation will provide a short review of the explicit and implicit concepts behind most of the currently-used regulatory and diagnostic sampling schemes for lead, such as: random daytime sampling; automated proportional sampler; 30 minute first draw stagnation; Sequential...

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

NASA Astrophysics Data System (ADS)

Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko

2017-11-01

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

Implicit solution of three-dimensional internal turbulent flows

NASA Technical Reports Server (NTRS)

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

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

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

2002-01-01

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

HEATING 7. 1 user's manual

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

Childs, K.W.

1991-07-01

HEATING is a FORTRAN program designed to solve steady-state and/or transient heat conduction problems in one-, two-, or three- dimensional Cartesian, cylindrical, or spherical coordinates. A model may include multiple materials, and the thermal conductivity, density, and specific heat of each material may be both time- and temperature-dependent. The thermal conductivity may be anisotropic. Materials may undergo change of phase. Thermal properties of materials may be input or may be extracted from a material properties library. Heating generation rates may be dependent on time, temperature, and position, and boundary temperatures may be time- and position-dependent. The boundary conditions, which maymore » be surface-to-boundary or surface-to-surface, may be specified temperatures or any combination of prescribed heat flux, forced convection, natural convection, and radiation. The boundary condition parameters may be time- and/or temperature-dependent. General graybody radiation problems may be modeled with user-defined factors for radiant exchange. The mesh spacing may be variable along each axis. HEATING is variably dimensioned and utilizes free-form input. Three steady-state solution techniques are available: point-successive-overrelaxation iterative method with extrapolation, direct-solution (for one-dimensional or two-dimensional problems), and conjugate gradient. Transient problems may be solved using one of several finite-difference schemes: Crank-Nicolson implicit, Classical Implicit Procedure (CIP), Classical Explicit Procedure (CEP), or Levy explicit method (which for some circumstances allows a time step greater than the CEP stability criterion). The solution of the system of equations arising from the implicit techniques is accomplished by point-successive-overrelaxation iteration and includes procedures to estimate the optimum acceleration parameter.« less

Estimation of Surface Temperature and Heat Flux by Inverse Heat Transfer Methods Using Internal Temperatures Measured While Radiantly Heating a Carbon/Carbon Specimen up to 1920 F

NASA Technical Reports Server (NTRS)

Pizzo, Michelle; Daryabeigi, Kamran; Glass, David

2015-01-01

The ability to solve the heat conduction equation is needed when designing materials to be used on vehicles exposed to extremely high temperatures; e.g. vehicles used for atmospheric entry or hypersonic flight. When using test and flight data, computational methods such as finite difference schemes may be used to solve for both the direct heat conduction problem, i.e., solving between internal temperature measurements, and the inverse heat conduction problem, i.e., using the direct solution to march forward in space to the surface of the material to estimate both surface temperature and heat flux. The completed research first discusses the methods used in developing a computational code to solve both the direct and inverse heat transfer problems using one dimensional, centered, implicit finite volume schemes and one dimensional, centered, explicit space marching techniques. The developed code assumed the boundary conditions to be specified time varying temperatures and also considered temperature dependent thermal properties. The completed research then discusses the results of analyzing temperature data measured while radiantly heating a carbon/carbon specimen up to 1920 F. The temperature was measured using thermocouple (TC) plugs (small carbon/carbon material specimens) with four embedded TC plugs inserted into the larger carbon/carbon specimen. The purpose of analyzing the test data was to estimate the surface heat flux and temperature values from the internal temperature measurements using direct and inverse heat transfer methods, thus aiding in the thermal and structural design and analysis of high temperature vehicles.

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

On the effect of using the Shapiro filter to smooth winds on a sphere

NASA Technical Reports Server (NTRS)

Takacs, L. L.; Balgovind, R. C.

1984-01-01

Spatial differencing schemes which are not enstrophy conserving nor implicitly damping require global filtering of short waves to eliminate the build-up of energy in the shortest wavelengths due to aliasing. Takacs and Balgovind (1983) have shown that filtering on a sphere with a latitude dependent damping function will cause spurious vorticity and divergence source terms to occur if care is not taken to ensure the irrotationality of the gradients of the stream function and velocity potential. Using a shallow water model with fourth-order energy-conserving spatial differencing, it is found that using a 16th-order Shapiro (1979) filter on the winds and heights to control nonlinear instability also creates spurious source terms when the winds are filtered in the meridional direction.

Multi-partitioning for ADI-schemes on message passing architectures

NASA Technical Reports Server (NTRS)

Vanderwijngaart, Rob F.

1994-01-01

A kind of discrete-operator splitting called Alternating Direction Implicit (ADI) has been found to be useful in simulating fluid flow problems. In particular, it is being used to study the effects of hot exhaust jets from high performance aircraft on landing surfaces. Decomposition techniques that minimize load imbalance and message-passing frequency are described. Three strategies that are investigated for implementing the NAS Scalar Penta-diagonal Parallel Benchmark (SP) are transposition, pipelined Gaussian elimination, and multipartitioning. The multipartitioning strategy, which was used on Ethernet, was found to be the most efficient, although it was considered only a moderate success because of Ethernet's limited communication properties. The efficiency derived largely from the coarse granularity of the strategy, which reduced latencies and allowed overlap of communication and computation.

Development of upwind schemes for the Euler equations

NASA Technical Reports Server (NTRS)

Chakravarthy, Sukumar R.

1987-01-01

Described are many algorithmic and computational aspects of upwind schemes and their second-order accurate formulations based on Total-Variation-Diminishing (TVD) approaches. An operational unification of the underlying first-order scheme is first presented encompassing Godunov's, Roe's, Osher's, and Split-Flux methods. For higher order versions, the preprocessing and postprocessing approaches to constructing TVD discretizations are considered. TVD formulations can be used to construct relaxation methods for unfactored implicit upwind schemes, which in turn can be exploited to construct space-marching procedures for even the unsteady Euler equations. A major part of the report describes time- and space-marching procedures for solving the Euler equations in 2-D, 3-D, Cartesian, and curvilinear coordinates. Along with many illustrative examples, several results of efficient computations on 3-D supersonic flows with subsonic pockets are presented.

A fully-implicit high-order system thermal-hydraulics model for advanced non-LWR safety analyses

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

Hu, Rui

An advanced system analysis tool is being developed for advanced reactor safety analysis. This paper describes the underlying physics and numerical models used in the code, including the governing equations, the stabilization schemes, the high-order spatial and temporal discretization schemes, and the Jacobian Free Newton Krylov solution method. The effects of the spatial and temporal discretization schemes are investigated. Additionally, a series of verification test problems are presented to confirm the high-order schemes. Furthermore, it is demonstrated that the developed system thermal-hydraulics model can be strictly verified with the theoretical convergence rates, and that it performs very well for amore » wide range of flow problems with high accuracy, efficiency, and minimal numerical diffusions.« less

A fully-implicit high-order system thermal-hydraulics model for advanced non-LWR safety analyses

DOE PAGES

Hu, Rui

2016-11-19

An advanced system analysis tool is being developed for advanced reactor safety analysis. This paper describes the underlying physics and numerical models used in the code, including the governing equations, the stabilization schemes, the high-order spatial and temporal discretization schemes, and the Jacobian Free Newton Krylov solution method. The effects of the spatial and temporal discretization schemes are investigated. Additionally, a series of verification test problems are presented to confirm the high-order schemes. Furthermore, it is demonstrated that the developed system thermal-hydraulics model can be strictly verified with the theoretical convergence rates, and that it performs very well for amore » wide range of flow problems with high accuracy, efficiency, and minimal numerical diffusions.« less

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Resonance in the dynamics of chemical systems simulated by the implicit midpoint scheme

NASA Astrophysics Data System (ADS)

Mandziuk, Margaret; Schlick, Tamar

1995-05-01

The numerical behavior of the symplectic, implicit midpoint method with a wide range of integration timesteps is examined through an application to a diatomic molecule governed by a Morse potential. Our oscillator with a 12.6 fs period exhibits notable, integrator induced, timestep- ( Δt) dependent resonances and we predict approximate values of Δt where they will occur. The particular case of a third-order resonance ( Δt ≈ 7 fs here) leads to instability, and higher-order resonances ( n = 4, 5) to large energetic fluctuations and/or corrupted phase diagrams. Significantly, for Δt > 10 fs the energy errors remain bound.

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.

The Implicit Learning of Mappings between Forms and Contextually Derived Meanings

ERIC Educational Resources Information Center

Leung, Janny H. C.; Williams, John N.

2011-01-01

The traditional implicit learning literature has focused primarily on the abstraction of statistical regularities in form-form connections. More attention has been recently directed toward the implicit learning of form-meaning connections, which might be crucial in the acquisition of natural languages. The current article reports evidence for…

Parallelized CCHE2D flow model with CUDA Fortran on Graphics Process Units

USDA-ARS?s Scientific Manuscript database

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

A Pseudo-Temporal Multi-Grid Relaxation Scheme for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

White, J. A.; Morrison, J. H.

1999-01-01

A multi-grid, flux-difference-split, finite-volume code, VULCAN, is presented for solving the elliptic and parabolized form of the equations governing three-dimensional, turbulent, calorically perfect and non-equilibrium chemically reacting flows. The space marching algorithms developed to improve convergence rate and or reduce computational cost are emphasized. The algorithms presented are extensions to the class of implicit pseudo-time iterative, upwind space-marching schemes. A full approximate storage, full multi-grid scheme is also described which is used to accelerate the convergence of a Gauss-Seidel relaxation method. The multi-grid algorithm is shown to significantly improve convergence on high aspect ratio grids.

Numerical solution of the wave equation with variable wave speed on nonconforming domains by high-order difference potentials

NASA Astrophysics Data System (ADS)

Britt, S.; Tsynkov, S.; Turkel, E.

2018-02-01

We solve the wave equation with variable wave speed on nonconforming domains with fourth order accuracy in both space and time. This is accomplished using an implicit finite difference (FD) scheme for the wave equation and solving an elliptic (modified Helmholtz) equation at each time step with fourth order spatial accuracy by the method of difference potentials (MDP). High-order MDP utilizes compact FD schemes on regular structured grids to efficiently solve problems on nonconforming domains while maintaining the design convergence rate of the underlying FD scheme. Asymptotically, the computational complexity of high-order MDP scales the same as that for FD.

Implicit cognitive processes in psychopathology: an introduction.

PubMed

Wiers, Reinout W; Teachman, Bethany A; De Houwer, Jan

2007-06-01

Implicit or automatic processes are important in understanding the etiology and maintenance of psychopathological problems. In order to study implicit processes in psychopathology, measures are needed that are valid and reliable when applied to clinical problems. One of the main topics in this special issue concerns the development and validation of new or modified implicit tests in different domains of psychopathology. The other main topic concerns the prediction of clinical outcomes and new ways to directly influence implicit processes in psychopathology. We summarize the contributions to this special issue and discuss how they further our knowledge of implicit processes in psychopathology and how to measure them.

Examining the Presence, Consequences, and Reduction of Implicit Bias in Health Care: A Narrative Review

PubMed Central

Zestcott, Colin A.; Blair, Irene V.; Stone, Jeff

2016-01-01

Recent evidence suggests that one possible cause of disparities in health outcomes for stigmatized groups is the implicit biases held by health care providers. In response, several health care organizations have called for, and developed, new training in implicit bias for their providers. This review examines current evidence on the role that provider implicit bias may play in health disparities, and whether training in implicit bias can effectively reduce the biases that providers exhibit. Directions for future research on the presence and consequences of provider implicit bias, and best practices for training to reduce such bias, will be discussed. PMID:27547105

Numerical Studies of Boundary-Layer Receptivity

NASA Technical Reports Server (NTRS)

Reed, Helen L.

1995-01-01

Direct numerical simulations (DNS) of the acoustic receptivity process on a semi-infinite flat plate with a modified-super-elliptic (MSE) leading edge are performed. The incompressible Navier-Stokes equations are solved in stream-function/vorticity form in a general curvilinear coordinate system. The steady basic-state solution is found by solving the governing equations using an alternating direction implicit (ADI) procedure which takes advantage of the parallelism present in line-splitting techniques. Time-harmonic oscillations of the farfield velocity are applied as unsteady boundary conditions to the unsteady disturbance equations. An efficient time-harmonic scheme is used to produce the disturbance solutions. Buffer-zone techniques have been applied to eliminate wave reflection from the outflow boundary. The spatial evolution of Tollmien-Schlichting (T-S) waves is analyzed and compared with experiment and theory. The effects of nose-radius, frequency, Reynolds number, angle of attack, and amplitude of the acoustic wave are investigated. This work is being performed in conjunction with the experiments at the Arizona State University Unsteady Wind Tunnel under the direction of Professor William Saric. The simulations are of the same configuration and parameters used in the wind-tunnel experiments.

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

NASA Technical Reports Server (NTRS)

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

1985-01-01

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

Given a one-step numerical scheme, on which ordinary differential equations is it exact?

NASA Astrophysics Data System (ADS)

Villatoro, Francisco R.

2009-01-01

A necessary condition for a (non-autonomous) ordinary differential equation to be exactly solved by a one-step, finite difference method is that the principal term of its local truncation error be null. A procedure to determine some ordinary differential equations exactly solved by a given numerical scheme is developed. Examples of differential equations exactly solved by the explicit Euler, implicit Euler, trapezoidal rule, second-order Taylor, third-order Taylor, van Niekerk's second-order rational, and van Niekerk's third-order rational methods are presented.

An Operator-Integration-Factor Splitting (OIFS) method for Incompressible Flows in Moving Domains

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

Patel, Saumil S.; Fischer, Paul F.; Min, Misun

In this paper, we present a characteristic-based numerical procedure for simulating incompressible flows in domains with moving boundaries. Our approach utilizes an operator-integration-factor splitting technique to help produce an effcient and stable numerical scheme. Using the spectral element method and an arbitrary Lagrangian-Eulerian formulation, we investigate flows where the convective acceleration effects are non-negligible. Several examples, ranging from laminar to turbulent flows, are considered. Comparisons with a standard, semi-implicit time-stepping procedure illustrate the improved performance of the scheme.

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 Parallel Implicit Reconstructed Discontinuous Galerkin Method for Compressible Flows on Hybrid Grids

NASA Astrophysics Data System (ADS)

Xia, Yidong

The objective this work is to develop a parallel, implicit reconstructed discontinuous Galerkin (RDG) method using Taylor basis for the solution of the compressible Navier-Stokes equations on 3D hybrid grids. This third-order accurate RDG method is based on a hierarchical weighed essentially non- oscillatory reconstruction scheme, termed as HWENO(P1P 2) to indicate that a quadratic polynomial solution is obtained from the underlying linear polynomial DG solution via a hierarchical WENO reconstruction. The HWENO(P1P2) is designed not only to enhance the accuracy of the underlying DG(P1) method but also to ensure non-linear stability of the RDG method. In this reconstruction scheme, a quadratic polynomial (P2) solution is first reconstructed using a least-squares approach from the underlying linear (P1) discontinuous Galerkin solution. The final quadratic solution is then obtained using a Hermite WENO reconstruction, which is necessary to ensure the linear stability of the RDG method on 3D unstructured grids. The first derivatives of the quadratic polynomial solution are then reconstructed using a WENO reconstruction in order to eliminate spurious oscillations in the vicinity of strong discontinuities, thus ensuring the non-linear stability of the RDG method. The parallelization in the RDG method is based on a message passing interface (MPI) programming paradigm, where the METIS library is used for the partitioning of a mesh into subdomain meshes of approximately the same size. Both multi-stage explicit Runge-Kutta and simple implicit backward Euler methods are implemented for time advancement in the RDG method. In the implicit method, three approaches: analytical differentiation, divided differencing (DD), and automatic differentiation (AD) are developed and implemented to obtain the resulting flux Jacobian matrices. The automatic differentiation is a set of techniques based on the mechanical application of the chain rule to obtain derivatives of a function given as a computer program. By using an AD tool, the manpower can be significantly reduced for deriving the flux Jacobians, which can be quite complicated, tedious, and error-prone if done by hand or symbolic arithmetic software, depending on the complexity of the numerical flux scheme. In addition, the workload for code maintenance can also be largely reduced in case the underlying flux scheme is updated. The approximate system of linear equations arising from the Newton linearization is solved by the general minimum residual (GMRES) algorithm with lower-upper symmetric gauss-seidel (LUSGS) preconditioning. This GMRES+LU-SGS linear solver is the most robust and efficient for implicit time integration of the discretized Navier-Stokes equations when the AD-based flux Jacobians are provided other than the other two approaches. The developed HWENO(P1P2) method is used to compute a variety of well-documented compressible inviscid and viscous flow test cases on 3D hybrid grids, including some standard benchmark test cases such as the Sod shock tube, flow past a circular cylinder, and laminar flow past a at plate. The computed solutions are compared with either analytical solutions or experimental data, if available to assess the accuracy of the HWENO(P 1P2) method. Numerical results demonstrate that the HWENO(P 1P2) method is able to not only enhance the accuracy of the underlying HWENO(P1) method, but also ensure the linear and non-linear stability at the presence of strong discontinuities. An extensive study of grid convergence analysis on various types of elements: tetrahedron, prism, hexahedron, and hybrid prism/hexahedron, for a number of test cases indicates that the developed HWENO(P1P2) method is able to achieve the designed third-order accuracy of spatial convergence for smooth inviscid flows: one order higher than the underlying second-order DG(P1) method without significant increase in computing costs and storage requirements. The performance of the the developed GMRES+LU-SGS implicit method is compared with the multi-stage Runge-Kutta time stepping scheme for a number of test cases in terms of the timestep and CPU time. Numerical results indicate that the overall performance of the implicit method with AD-based Jacobians is order of magnitude better than the its explicit counterpart. Finally, a set of parallel scaling tests for both explicit and implicit methods is conducted on North Carolina State University's ARC cluster, demonstrating almost an ideal scalability of the RDG method. (Abstract shortened by UMI.)

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.

Multidimensional directional flux weighted upwind scheme for multiphase flow modeling in heterogeneous porous media

NASA Astrophysics Data System (ADS)

Jin, G.

2012-12-01

Multiphase flow modeling is an important numerical tool for a better understanding of transport processes in the fields including, but not limited to, petroleum reservoir engineering, remedy of ground water contamination, and risk evaluation of greenhouse gases such as CO2 injected into deep saline reservoirs. However, accurate numerical modeling for multiphase flow remains many challenges that arise from the inherent tight coupling and strong non-linear nature of the governing equations and the highly heterogeneous media. The existence of counter current flow which is caused by the effect of adverse relative mobility contrast and gravitational and capillary forces will introduce additional numerical instability. Recently multipoint flux approximation (MPFA) has become a subject of extensive research and has been demonstrated with great success in reducing considerable grid orientation effects compared to the conventional single point upstream (SPU) weighting scheme, especially in higher dimensions. However, the present available MPFA schemes are mathematically targeted to certain types of grids in two dimensions, a more general form of MPFA scheme is needed for both 2-D and 3-D problems. In this work a new upstream weighting scheme based on multipoint directional incoming fluxes is proposed which incorporates full permeability tensor to account for the heterogeneity of the porous media. First, the multiphase governing equations are decoupled into an elliptic pressure equation and a hyperbolic or parabolic saturation depends on whether the gravitational and capillary pressures are presented or not. Next, a dual secondary grid (called finite volume grid) is formulated from a primary grid (called finite element grid) to create interaction regions for each grid cell over the entire simulation domain. Such a discretization must ensure the conservation of mass and maintain the continuity of the Darcy velocity across the boundaries between neighboring interaction regions. The pressure field is then implicitly calculated from the pressure equation, which in turn results in the derived velocity field for directional flux calculation at each grid node. Directional flux at the center of each interaction surface is also calculated by interpolation from the element nodal fluxes using shape functions. The MPFA scheme is performed by a specific linear combination of all incoming fluxes into the upstream cell represented by either nodal fluxes or interpolated surface boundary fluxes to produce an upwind directional fluxed weighted relative mobility at the center of the interaction region boundary. Such an upwind weighted relative mobility is then used for calculating the saturations of each fluid phase explicitly. The proposed upwind weighting scheme has been implemented into a mixed finite element-finite volume (FE-FV) method, which allows for handling complex reservoir geometry with second-order accuracies in approximating primary variables. The numerical solver has been tested with several bench mark test problems. The application of the proposed scheme to migration path analysis of CO2 injected into deep saline reservoirs in 3-D has demonstrated its ability and robustness in handling multiphase flow with adverse mobility contrast in highly heterogeneous porous media.

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.

Implicit Theories of Ability in Physical Education: Current Issues and Future Directions

ERIC Educational Resources Information Center

Warburton, Victoria Emily; Spray, Christopher Mark

2017-01-01

Purpose: In light of the extensive empirical evidence that implicit theories have important motivational consequences for young people across a range of educational settings we seek to provide a summary of, and personal reflection on, implicit theory research and practice in physical education (PE). Overview: We first provide an introduction to…

The Utility of Implicit Learning in the Teaching of Rules

ERIC Educational Resources Information Center

Saetrevik, Bjorn; Reber, Rolf; Sannum, Petter

2006-01-01

The potential impact of implicit learning on education has been repeatedly stressed, though little research has examined this connection directly. The current paper describes two experiments that, inspired by artificial grammar learning experiments, examine the utility of implicit learning as a method for teaching atomic bonding rules to 11-12…

The Effect of Gender Stereotypes on Explicit and Implicit Career Preferences

ERIC Educational Resources Information Center

Gadassi, Reuma; Gati, Itamar

2009-01-01

The present study compared gender differences in directly reported and indirectly derived career preferences and tested the hypothesis that individuals' implicit preferences would show less gender-biased occupational choices than their directly elicited ones. Two hundred sixty-six visitors to a career-related Internet site were asked to (a) list 5…

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

NASA Astrophysics Data System (ADS)

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

2017-11-01

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

Thailand's Student Loans Fund: Interest Rate Subsidies and Repayment Burdens

ERIC Educational Resources Information Center

Chapman, Bruce; Lounkaew, Kiatanantha; Polsiri, Piruna; Sarachitti, Rangsit; Sitthipongpanich, Thitima

2010-01-01

Government student loan schemes typically have implicit interest rate subsidies which, while these are a cost to taxpayers, they have the benefit of diminishing repayment burdens for graduates. Our goal is to illustrate the extent of both interest rate subsidies and repayment burdens with respect to Thailand's Student Loans Fund (SLF), using…

Sketching Some Postmodern Alternatives: Beyond Paradigms and Research Programs as Referents for Science Education.

ERIC Educational Resources Information Center

Geelan, David R.

2000-01-01

Suggests that Kuhn's and Lakatos' schemes for the philosophy of science have been pervasive metaphors for conceptual change approaches to the learning and teaching of science, and have been used both implicitly and explicitly to provide an organizing framework and justification matrix for those perspectives. Describes four alternative perspectives…

Identity Bargaining: A Policy Systems Research Model of Career Development.

ERIC Educational Resources Information Center

Slawski, Carl

A detailed, general and comprehensive accounting scheme is presented, consisting of nine stages of career development, three major sets of elements contributing to career choice (in terms of personal, cultural and situational roles), and 20 hypotheses relating the separate elements. Implicit in the model is a novel procedure and method for…

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.

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.

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.

High order spectral volume and spectral difference methods on unstructured grids

NASA Astrophysics Data System (ADS)

Kannan, Ravishekar

The spectral volume (SV) and the spectral difference (SD) methods were developed by Wang and Liu and their collaborators for conservation laws on unstructured grids. They were introduced to achieve high-order accuracy in an efficient manner. Recently, these methods were extended to three-dimensional systems and to the Navier Stokes equations. The simplicity and robustness of these methods have made them competitive against other higher order methods such as the discontinuous Galerkin and residual distribution methods. Although explicit TVD Runge-Kutta schemes for the temporal advancement are easy to implement, they suffer from small time step limited by the Courant-Friedrichs-Lewy (CFL) condition. When the polynomial order is high or when the grid is stretched due to complex geometries or boundary layers, the convergence rate of explicit schemes slows down rapidly. Solution strategies to remedy this problem include implicit methods and multigrid methods. A novel implicit lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation method is employed as an iterative smoother. It is compared to the explicit TVD Runge-Kutta smoothers. For some p-multigrid calculations, combining implicit and explicit smoothers for different p-levels is also studied. The multigrid method considered is nonlinear and uses Full Approximation Scheme (FAS). An overall speed-up factor of up to 150 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Euler equations for the 3rd order SD method. A study of viscous flux formulations was carried out for the SV method. Three formulations were used to discretize the viscous fluxes: local discontinuous Galerkin (LDG), a penalty method and the 2nd method of Bassi and Rebay. Fourier analysis revealed some interesting advantages for the penalty method. These were implemented in the Navier Stokes solver. An implicit and p-multigrid method was also implemented for the above. An overall speed-up factor of up to 1500 is obtained using a three-level p-multigrid LU-SGS approach in comparison with the single level explicit method for the Navier-Stokes equations. The SV method was also extended to turbulent flows. The RANS based SA model was used to close the Reynolds stresses. The numerical results are very promising and indicate that the approaches have great potentials for 3D flow problems.

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.

Hooked on a feeling: affective anti-smoking messages are more effective than cognitive messages at changing implicit evaluations of smoking

PubMed Central

Smith, Colin Tucker; De Houwer, Jan

2015-01-01

Because implicit evaluations are thought to underlie many aspects of behavior, researchers have started looking for ways to change them. We examine whether and when persuasive messages alter strongly held implicit evaluations of smoking. In smokers, an affective anti-smoking message led to more negative implicit evaluations on four different implicit measures as compared to a cognitive anti-smoking message which seemed to backfire. Additional analyses suggested that the observed effects were mediated by the feelings and emotions raised by the messages. In non-smokers, both the affective and cognitive message engendered slightly more negative implicit evaluations. We conclude that persuasive messages change implicit evaluations in a way that depends on properties of the message and of the participant. Thus, our data open new avenues for research directed at tailoring persuasive messages to change implicit evaluations. PMID:26557099

Hooked on a feeling: affective anti-smoking messages are more effective than cognitive messages at changing implicit evaluations of smoking.

PubMed

Smith, Colin Tucker; De Houwer, Jan

2015-01-01

Because implicit evaluations are thought to underlie many aspects of behavior, researchers have started looking for ways to change them. We examine whether and when persuasive messages alter strongly held implicit evaluations of smoking. In smokers, an affective anti-smoking message led to more negative implicit evaluations on four different implicit measures as compared to a cognitive anti-smoking message which seemed to backfire. Additional analyses suggested that the observed effects were mediated by the feelings and emotions raised by the messages. In non-smokers, both the affective and cognitive message engendered slightly more negative implicit evaluations. We conclude that persuasive messages change implicit evaluations in a way that depends on properties of the message and of the participant. Thus, our data open new avenues for research directed at tailoring persuasive messages to change implicit evaluations.

Damaged Self-Esteem is Associated with Internalizing Problems.

PubMed

Creemers, Daan H M; Scholte, Ron H J; Engels, Rutger C M E; Prinstein, Mitchell J; Wiers, Reinout W

2013-01-01

Implicit and explicit self-esteem are assumed to be important factors in understanding the onset and maintenance of psychological problems. The current study aims to examine the association between implicit and explicit self-esteem and their interaction with depressive symptoms, suicidal ideation, and loneliness. Specifically, the relationship between the size and the direction of the discrepancy between implicit and explicit self-esteem with depressive symptoms, suicidal ideation, and loneliness were examined. Participants were 95 young female adults (M = 21.2 years, SD = 1.88) enrolled in higher education. We administered the IAT to assess implicit self-esteem, and the Rosenberg self-esteem scale to measure explicit self-esteem while psychological problems were assessed through self-reports. Results showed that discrepancies between implicit and explicit self-esteem were positively associated with depressive symptoms, suicidal ideation, and loneliness. In addition, the direction of the discrepancy was specifically relevant: damaged self-esteem (i.e., high implicit self-esteem and low explicit self-esteem) was consistently associated with increased levels of depressive symptoms, suicidal ideation, and loneliness. In contrast, defensive or fragile self-esteem (i.e., low implicit and high explicit self-esteem) was solely associated with loneliness. These findings provide further support that specifically damaged self-esteem is an important vulnerability marker for depressive symptoms, suicidal ideation, and loneliness.

Damaged Self-Esteem is Associated with Internalizing Problems

PubMed Central

Creemers, Daan H. M.; Scholte, Ron H. J.; Engels, Rutger C. M. E.; Prinstein, Mitchell J.; Wiers, Reinout W.

2013-01-01

Implicit and explicit self-esteem are assumed to be important factors in understanding the onset and maintenance of psychological problems. The current study aims to examine the association between implicit and explicit self-esteem and their interaction with depressive symptoms, suicidal ideation, and loneliness. Specifically, the relationship between the size and the direction of the discrepancy between implicit and explicit self-esteem with depressive symptoms, suicidal ideation, and loneliness were examined. Participants were 95 young female adults (M = 21.2 years, SD = 1.88) enrolled in higher education. We administered the IAT to assess implicit self-esteem, and the Rosenberg self-esteem scale to measure explicit self-esteem while psychological problems were assessed through self-reports. Results showed that discrepancies between implicit and explicit self-esteem were positively associated with depressive symptoms, suicidal ideation, and loneliness. In addition, the direction of the discrepancy was specifically relevant: damaged self-esteem (i.e., high implicit self-esteem and low explicit self-esteem) was consistently associated with increased levels of depressive symptoms, suicidal ideation, and loneliness. In contrast, defensive or fragile self-esteem (i.e., low implicit and high explicit self-esteem) was solely associated with loneliness. These findings provide further support that specifically damaged self-esteem is an important vulnerability marker for depressive symptoms, suicidal ideation, and loneliness. PMID:23565101

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.

Discrete unified gas kinetic scheme for all Knudsen number flows. III. Binary gas mixtures of Maxwell molecules

NASA Astrophysics Data System (ADS)

Zhang, Yue; Zhu, Lianhua; Wang, Ruijie; Guo, Zhaoli

2018-05-01

Recently a discrete unified gas kinetic scheme (DUGKS) in a finite-volume formulation based on the Boltzmann model equation has been developed for gas flows in all flow regimes. The original DUGKS is designed for flows of single-species gases. In this work, we extend the DUGKS to flows of binary gas mixtures of Maxwell molecules based on the Andries-Aoki-Perthame kinetic model [P. Andries et al., J. Stat. Phys. 106, 993 (2002), 10.1023/A:1014033703134. A particular feature of the method is that the flux at each cell interface is evaluated based on the characteristic solution of the kinetic equation itself; thus the numerical dissipation is low in comparison with that using direct reconstruction. Furthermore, the implicit treatment of the collision term enables the time step to be free from the restriction of the relaxation time. Unlike the DUGKS for single-species flows, a nonlinear system must be solved to determine the interaction parameters appearing in the equilibrium distribution function, which can be obtained analytically for Maxwell molecules. Several tests are performed to validate the scheme, including the shock structure problem under different Mach numbers and molar concentrations, the channel flow driven by a small gradient of pressure, temperature, or concentration, the plane Couette flow, and the shear driven cavity flow under different mass ratios and molar concentrations. The results are compared with those from other reliable numerical methods. The results show that the proposed scheme is an effective and reliable method for binary gas mixtures in all flow regimes.

Fitted Fourier-pseudospectral methods for solving a delayed reaction-diffusion partial differential equation in biology

NASA Astrophysics Data System (ADS)

Adam, A. M. A.; Bashier, E. B. M.; Hashim, M. H. A.; Patidar, K. C.

2017-07-01

In this work, we design and analyze a fitted numerical method to solve a reaction-diffusion model with time delay, namely, a delayed version of a population model which is an extension of the logistic growth (LG) equation for a food-limited population proposed by Smith [F.E. Smith, Population dynamics in Daphnia magna and a new model for population growth, Ecology 44 (1963) 651-663]. Seeing that the analytical solution (in closed form) is hard to obtain, we seek for a robust numerical method. The method consists of a Fourier-pseudospectral semi-discretization in space and a fitted operator implicit-explicit scheme in temporal direction. The proposed method is analyzed for convergence and we found that it is unconditionally stable. Illustrative numerical results will be presented at the conference.

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.

Analysis of operator splitting errors for near-limit flame simulations

NASA Astrophysics Data System (ADS)

Lu, Zhen; Zhou, Hua; Li, Shan; Ren, Zhuyin; Lu, Tianfeng; Law, Chung K.

2017-04-01

High-fidelity simulations of ignition, extinction and oscillatory combustion processes are of practical interest in a broad range of combustion applications. Splitting schemes, widely employed in reactive flow simulations, could fail for stiff reaction-diffusion systems exhibiting near-limit flame phenomena. The present work first employs a model perfectly stirred reactor (PSR) problem with an Arrhenius reaction term and a linear mixing term to study the effects of splitting errors on the near-limit combustion phenomena. Analysis shows that the errors induced by decoupling of the fractional steps may result in unphysical extinction or ignition. The analysis is then extended to the prediction of ignition, extinction and oscillatory combustion in unsteady PSRs of various fuel/air mixtures with a 9-species detailed mechanism for hydrogen oxidation and an 88-species skeletal mechanism for n-heptane oxidation, together with a Jacobian-based analysis for the time scales. The tested schemes include the Strang splitting, the balanced splitting, and a newly developed semi-implicit midpoint method. Results show that the semi-implicit midpoint method can accurately reproduce the dynamics of the near-limit flame phenomena and it is second-order accurate over a wide range of time step size. For the extinction and ignition processes, both the balanced splitting and midpoint method can yield accurate predictions, whereas the Strang splitting can lead to significant shifts on the ignition/extinction processes or even unphysical results. With an enriched H radical source in the inflow stream, a delay of the ignition process and the deviation on the equilibrium temperature are observed for the Strang splitting. On the contrary, the midpoint method that solves reaction and diffusion together matches the fully implicit accurate solution. The balanced splitting predicts the temperature rise correctly but with an over-predicted peak. For the sustainable and decaying oscillatory combustion from cool flames, both the Strang splitting and the midpoint method can successfully capture the dynamic behavior, whereas the balanced splitting scheme results in significant errors.

Analysis of operator splitting errors for near-limit flame simulations

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

Lu, Zhen; Zhou, Hua; Li, Shan

High-fidelity simulations of ignition, extinction and oscillatory combustion processes are of practical interest in a broad range of combustion applications. Splitting schemes, widely employed in reactive flow simulations, could fail for stiff reaction–diffusion systems exhibiting near-limit flame phenomena. The present work first employs a model perfectly stirred reactor (PSR) problem with an Arrhenius reaction term and a linear mixing term to study the effects of splitting errors on the near-limit combustion phenomena. Analysis shows that the errors induced by decoupling of the fractional steps may result in unphysical extinction or ignition. The analysis is then extended to the prediction ofmore » ignition, extinction and oscillatory combustion in unsteady PSRs of various fuel/air mixtures with a 9-species detailed mechanism for hydrogen oxidation and an 88-species skeletal mechanism for n-heptane oxidation, together with a Jacobian-based analysis for the time scales. The tested schemes include the Strang splitting, the balanced splitting, and a newly developed semi-implicit midpoint method. Results show that the semi-implicit midpoint method can accurately reproduce the dynamics of the near-limit flame phenomena and it is second-order accurate over a wide range of time step size. For the extinction and ignition processes, both the balanced splitting and midpoint method can yield accurate predictions, whereas the Strang splitting can lead to significant shifts on the ignition/extinction processes or even unphysical results. With an enriched H radical source in the inflow stream, a delay of the ignition process and the deviation on the equilibrium temperature are observed for the Strang splitting. On the contrary, the midpoint method that solves reaction and diffusion together matches the fully implicit accurate solution. The balanced splitting predicts the temperature rise correctly but with an over-predicted peak. For the sustainable and decaying oscillatory combustion from cool flames, both the Strang splitting and the midpoint method can successfully capture the dynamic behavior, whereas the balanced splitting scheme results in significant errors.« less

Multigrid for hypersonic viscous two- and three-dimensional flows

NASA Technical Reports Server (NTRS)

Turkel, E.; Swanson, R. C.; Vatsa, V. N.; White, J. A.

1991-01-01

The use of a multigrid method with central differencing to solve the Navier-Stokes equations for hypersonic flows is considered. The time dependent form of the equations is integrated with an explicit Runge-Kutta scheme accelerated by local time stepping and implicit residual smoothing. Variable coefficients are developed for the implicit process that removes the diffusion limit on the time step, producing significant improvement in convergence. A numerical dissipation formulation that provides good shock capturing capability for hypersonic flows is presented. This formulation is shown to be a crucial aspect of the multigrid method. Solutions are given for two-dimensional viscous flow over a NACA 0012 airfoil and three-dimensional flow over a blunt biconic.

Simple numerical method for predicting steady compressible flows

NASA Technical Reports Server (NTRS)

Vonlavante, Ernst; Nelson, N. Duane

1986-01-01

A numerical method for solving the isenthalpic form of the governing equations for compressible viscous and inviscid flows was developed. The method was based on the concept of flux vector splitting in its implicit form. The method was tested on several demanding inviscid and viscous configurations. Two different forms of the implicit operator were investigated. The time marching to steady state was accelerated by the implementation of the multigrid procedure. Its various forms very effectively increased the rate of convergence of the present scheme. High quality steady state results were obtained in most of the test cases; these required only short computational times due to the relative efficiency of the basic method.

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.

Implicit Learning in Science: Activating and Suppressing Scientific Intuitions to Enhance Conceptual Change

NASA Astrophysics Data System (ADS)

Wang, Jeremy Yi-Ming

This dissertation examines the thesis that implicit learning plays a role in learning about scientific phenomena, and subsequently, in conceptual change. Decades of research in learning science demonstrate that a primary challenge of science education is overcoming prior, naive knowledge of natural phenomena in order to gain scientific understanding. Until recently, a key assumption of this research has been that to develop scientific understanding, learners must abandon their prior scientific intuitions and replace them with scientific concepts. However, a growing body of research shows that scientific intuitions persist, even among science experts. This suggests that naive intuitions are suppressed, not supplanted, as learners gain scientific understanding. The current study examines two potential roles of implicit learning processes in the development of scientific knowledge. First, implicit learning is a source of cognitive structures that impede science learning. Second, tasks that engage implicit learning processes can be employed to activate and suppress prior intuitions, enhancing the likelihood that scientific concepts are adopted and applied. This second proposal is tested in two experiments that measure training-induced changes in intuitive and conceptual knowledge related to sinking and floating objects in water. In Experiment 1, an implicit learning task was developed to examine whether implicit learning can induce changes in performance on near and far transfer tasks. The results of this experiment provide evidence that implicit learning tasks activate and suppress scientific intuitions. Experiment 2 examined the effects of combining implicit learning with traditional, direct instruction to enhance explicit learning of science concepts. This experiment demonstrates that sequencing implicit learning task before and after direct instruction has different effects on intuitive and conceptual knowledge. Together, these results suggest a novel approach for enhancing learning for conceptual change in science education.

Rotor cascade shape optimization with unsteady passing wakes using implicit dual time stepping method

NASA Astrophysics Data System (ADS)

Lee, Eun Seok

2000-10-01

An improved aerodynamics performance of a turbine cascade shape can be achieved by an understanding of the flow-field associated with the stator-rotor interaction. In this research, an axial gas turbine airfoil cascade shape is optimized for improved aerodynamic performance by using an unsteady Navier-Stokes solver and a parallel genetic algorithm. The objective of the research is twofold: (1) to develop a computational fluid dynamics code having faster convergence rate and unsteady flow simulation capabilities, and (2) to optimize a turbine airfoil cascade shape with unsteady passing wakes for improved aerodynamic performance. The computer code solves the Reynolds averaged Navier-Stokes equations. It is based on the explicit, finite difference, Runge-Kutta time marching scheme and the Diagonalized Alternating Direction Implicit (DADI) scheme, with the Baldwin-Lomax algebraic and k-epsilon turbulence modeling. Improvements in the code focused on the cascade shape design capability, convergence acceleration and unsteady formulation. First, the inverse shape design method was implemented in the code to provide the design capability, where a surface transpiration concept was employed as an inverse technique to modify the geometry satisfying the user specified pressure distribution on the airfoil surface. Second, an approximation storage multigrid method was implemented as an acceleration technique. Third, the preconditioning method was adopted to speed up the convergence rate in solving the low Mach number flows. Finally, the implicit dual time stepping method was incorporated in order to simulate the unsteady flow-fields. For the unsteady code validation, the Stokes's 2nd problem and the Poiseuille flow were chosen and compared with the computed results and analytic solutions. To test the code's ability to capture the natural unsteady flow phenomena, vortex shedding past a cylinder and the shock oscillation over a bicircular airfoil were simulated and compared with experiments and other research results. The rotor cascade shape optimization with unsteady passing wakes was performed to obtain an improved aerodynamic performance using the unsteady Navier-Stokes solver. Two objective functions were defined as minimization of total pressure loss and maximization of lift, while the mass flow rate was fixed. A parallel genetic algorithm was used as an optimizer and the penalty method was introduced. Each individual's objective function was computed simultaneously by using a 32 processor distributed memory computer. One optimization took about four days.

High-Order Hyperbolic Residual-Distribution Schemes on Arbitrary Triangular Grids

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2015-01-01

In this paper, we construct high-order hyperbolic residual-distribution schemes for general advection-diffusion problems on arbitrary triangular grids. We demonstrate that the second-order accuracy of the hyperbolic schemes can be greatly improved by requiring the scheme to preserve exact quadratic solutions. We also show that the improved second-order scheme can be easily extended to third-order by further requiring the exactness for cubic solutions. We construct these schemes based on the LDA and the SUPG methodology formulated in the framework of the residual-distribution method. For both second- and third-order-schemes, we construct a fully implicit solver by the exact residual Jacobian of the second-order scheme, and demonstrate rapid convergence of 10-15 iterations to reduce the residuals by 10 orders of magnitude. We demonstrate also that these schemes can be constructed based on a separate treatment of the advective and diffusive terms, which paves the way for the construction of hyperbolic residual-distribution schemes for the compressible Navier-Stokes equations. Numerical results show that these schemes produce exceptionally accurate and smooth solution gradients on highly skewed and anisotropic triangular grids, including curved boundary problems, using linear elements. We also present Fourier analysis performed on the constructed linear system and show that an under-relaxation parameter is needed for stabilization of Gauss-Seidel relaxation.

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.

Radiation pressure driving of a dusty atmosphere

NASA Astrophysics Data System (ADS)

Tsang, Benny T.-H.; Milosavljević, Miloš

2015-10-01

Radiation pressure can be dynamically important in star-forming environments such as ultra-luminous infrared and submillimetre galaxies. Whether and how radiation drives turbulence and bulk outflows in star formation sites is still unclear. The uncertainty in part reflects the limitations of direct numerical schemes that are currently used to simulate radiation transfer and radiation-gas coupling. An idealized setup in which radiation is introduced at the base of a dusty atmosphere in a gravitational field has recently become the standard test for radiation-hydrodynamics methods in the context of star formation. To a series of treatments featuring the flux-limited diffusion approximation as well as a short-characteristics tracing and M1 closure for the variable Eddington tensor approximation, we here add another treatment that is based on the implicit Monte Carlo radiation transfer scheme. Consistent with all previous treatments, the atmosphere undergoes Rayleigh-Taylor instability and readjusts to a near-Eddington-limited state. We detect late-time net acceleration in which the turbulent velocity dispersion matches that reported previously with the short-characteristics-based radiation transport closure, the most accurate of the three preceding treatments. Our technical result demonstrates the importance of accurate radiation transfer in simulations of radiative feedback.

Multi-dimensional upwinding-based implicit LES for the vorticity transport equations

NASA Astrophysics Data System (ADS)

Foti, Daniel; Duraisamy, Karthik

2017-11-01

Complex turbulent flows such as rotorcraft and wind turbine wakes are characterized by the presence of strong coherent structures that can be compactly described by vorticity variables. The vorticity-velocity formulation of the incompressible Navier-Stokes equations is employed to increase numerical efficiency. Compared to the traditional velocity-pressure formulation, high order numerical methods and sub-grid scale models for the vorticity transport equation (VTE) have not been fully investigated. Consistent treatment of the convection and stretching terms also needs to be addressed. Our belief is that, by carefully designing sharp gradient-capturing numerical schemes, coherent structures can be more efficiently captured using the vorticity-velocity formulation. In this work, a multidimensional upwind approach for the VTE is developed using the generalized Riemann problem-based scheme devised by Parish et al. (Computers & Fluids, 2016). The algorithm obtains high resolution by augmenting the upwind fluxes with transverse and normal direction corrections. The approach is investigated with several canonical vortex-dominated flows including isolated and interacting vortices and turbulent flows. The capability of the technique to represent sub-grid scale effects is also assessed. Navy contract titled ``Turbulence Modelling Across Disparate Length Scales for Naval Computational Fluid Dynamics Applications,'' through Continuum Dynamics, Inc.

A hybrid numerical technique for predicting the aerodynamic and acoustic fields of advanced turboprops

NASA Technical Reports Server (NTRS)

Homicz, G. F.; Moselle, J. R.

1985-01-01

A hybrid numerical procedure is presented for the prediction of the aerodynamic and acoustic performance of advanced turboprops. A hybrid scheme is proposed which in principle leads to a consistent simultaneous prediction of both fields. In the inner flow a finite difference method, the Approximate-Factorization Alternating-Direction-Implicit (ADI) scheme, is used to solve the nonlinear Euler equations. In the outer flow the linearized acoustic equations are solved via a Boundary-Integral Equation (BIE) method. The two solutions are iteratively matched across a fictitious interface in the flow so as to maintain continuity. At convergence the resulting aerodynamic load prediction will automatically satisfy the appropriate free-field boundary conditions at the edge of the finite difference grid, while the acoustic predictions will reflect the back-reaction of the radiated field on the magnitude of the loading source terms, as well as refractive effects in the inner flow. The equations and logic needed to match the two solutions are developed and the computer program implementing the procedure is described. Unfortunately, no converged solutions were obtained, due to unexpectedly large running times. The reasons for this are discussed and several means to alleviate the situation are suggested.

Conservative supra-characteristics method for splitting the hyperbolic systems of gasdynamics for real and perfect gases

NASA Technical Reports Server (NTRS)

Lombard, C. K.

1982-01-01

A conservative flux difference splitting is presented for the hyperbolic systems of gasdynamics. The stable robust method is suitable for wide application in a variety of schemes, explicit or implicit, iterative or direct, for marching in either time or space. The splitting is modeled on the local quasi one dimensional characteristics system for multi-dimensional flow similar to Chakravarthy's nonconservative split coefficient matrix method; but, as the result of maintaining global conservation, the method is able to capture sharp shocks correctly. The embedded characteristics formulation is cast in a primitive variable the volumetric internal energy (rather than the pressure) that is effective for treating real as well as perfect gases. Finally the relationship of the splitting to characteristics boundary conditions is discussed and the associated conservative matrix formulation for a computed blown wall boundary condition is developed as an example. The theoretical development employs and extends the notion of Roe of constructing stable upwind difference formulae by sending split simple one sided flux difference pieces to appropriate mesh sites. The developments are also believed to have the potential for aiding in the analysis of both existing and new conservative difference schemes.

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

Implicit Bias and Mental Health Professionals: Priorities and Directions for Research.

PubMed

Merino, Yesenia; Adams, Leslie; Hall, William J

2018-06-01

This Open Forum explores the role of implicit bias along the mental health care continuum, which may contribute to mental health disparities among vulnerable populations. Emerging research shows that implicit bias is prevalent among service providers. These negative or stigmatizing attitudes toward population groups are held at a subconscious level and are automatically activated during practitioner-client encounters. The authors provide examples of how implicit bias may impede access to care, clinical screening and diagnosis, treatment processes, and crisis response. They also discuss how implicit attitudes may manifest at the intersection between mental health and criminal justice institutions. Finally, they discuss the need for more research on the impact of implicit bias on health practices throughout the mental health system, including the development of interventions to address implicit bias among mental health professionals.

The Roles of Implicit Understanding of Engineering Ethics in Student Teams' Discussion.

PubMed

Lee, Eun Ah; Grohman, Magdalena; Gans, Nicholas R; Tacca, Marco; Brown, Matthew J

2017-12-01

Following previous work that shows engineering students possess different levels of understanding of ethics-implicit and explicit-this study focuses on how students' implicit understanding of engineering ethics influences their team discussion process, in cases where there is significant divergence between their explicit and implicit understanding. We observed student teams during group discussions of the ethical issues involved in their engineering design projects. Through the micro-scale discourse analysis based on cognitive ethnography, we found two possible ways in which implicit understanding influenced the discussion. In one case, implicit understanding played the role of intuitive ethics-an intuitive judgment followed by reasoning. In the other case, implicit understanding played the role of ethical insight, emotionally guiding the direction of the discussion. In either case, however, implicit understanding did not have a strong influence, and the conclusion of the discussion reflected students' explicit understanding. Because students' implicit understanding represented broader social implication of engineering design in both cases, we suggest to take account of students' relevant implicit understanding in engineering education, to help students become more socially responsible engineers.

Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

NASA Astrophysics Data System (ADS)

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the monotone and stable discrete-analytical numerical schemes [1]-[3] conserving the positivity of the chemical substance concentrations and possessing the properties of energy and mass balance that are postulated in the general variational principle for integrated models. All algorithms for solution of transport, diffusion and transformation problems are direct (without iterations). The work is partially supported by the Programs No 4 of Presidium RAS and No 3 of Mathematical Department of RAS, by RFBR project 11-01-00187 and Integrating projects of SD RAS No 8 and 35. Our studies are in the line with the goals of COST Action ES1004. References Penenko V., Tsvetova E. Discrete-analytical methods for the implementation of variational principles in environmental applications// Journal of computational and applied mathematics, 2009, v. 226, 319-330. Penenko A.V. Discrete-analytic schemes for solving an inverse coefficient heat conduction problem in a layered medium with gradient methods// Numerical Analysis and Applications, 2012, V. 5, pp 326-341. V. Penenko, E. Tsvetova. Variational methods for constructing the monotone approximations for atmospheric chemistry models //Numerical Analysis and Applications, 2013 (in press).

The Memory of What We Do Not Recall: Dissociations and Theoretical Debates in the Study of Implicit Memory

ERIC Educational Resources Information Center

Ramos, Tania; Marques, João; Garcia-Marques, Leonel

2017-01-01

Implicit memory reflects itself on situations in which previously acquired information is expressed, without awareness or intention. The study of implicit memory has had a profound impact on how researchers have investigated the human memory. In this paper, we review the main studies which have revealed dissociations between direct and indirect…

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

Random access to mobile networks with advanced error correction

NASA Technical Reports Server (NTRS)

Dippold, Michael

1990-01-01

A random access scheme for unreliable data channels is investigated in conjunction with an adaptive Hybrid-II Automatic Repeat Request (ARQ) scheme using Rate Compatible Punctured Codes (RCPC) Forward Error Correction (FEC). A simple scheme with fixed frame length and equal slot sizes is chosen and reservation is implicit by the first packet transmitted randomly in a free slot, similar to Reservation Aloha. This allows the further transmission of redundancy if the last decoding attempt failed. Results show that a high channel utilization and superior throughput can be achieved with this scheme that shows a quite low implementation complexity. For the example of an interleaved Rayleigh channel and soft decision utilization and mean delay are calculated. A utilization of 40 percent may be achieved for a frame with the number of slots being equal to half the station number under high traffic load. The effects of feedback channel errors and some countermeasures are discussed.

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

Dyachenko, Sergey A.; Zlotnik, Anatoly; Korotkevich, Alexander O.

Here, we develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme ismore » unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.« 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.

Factor Structure, Stability, and Congruence in the Functional Movement Screen

ERIC Educational Resources Information Center

Kelleher, Leila K.; Beach, Tyson A. C.; Frost, David M.; Johnson, Andrew M.; Dickey, James P.

2018-01-01

The scoring scheme for the functional movement screen implicitly assumes that the factor structure is consistent, stable, and congruent across different populations. To determine if this is the case, we compared principal components analyses of three samples: a healthy, general population (n = 100), a group of varsity athletes (n = 101), and a…

A time-accurate implicit method for chemical non-equilibrium flows at all speeds

NASA Technical Reports Server (NTRS)

Shuen, Jian-Shun

1992-01-01

A new time accurate coupled solution procedure for solving the chemical non-equilibrium Navier-Stokes equations over a wide range of Mach numbers is described. The scheme is shown to be very efficient and robust for flows with velocities ranging from M less than or equal to 10(exp -10) to supersonic speeds.

Terror management theory and self-esteem revisited: the roles of implicit and explicit self-esteem in mortality salience effects.

PubMed

Schmeichel, Brandon J; Gailliot, Matthew T; Filardo, Emily-Ana; McGregor, Ian; Gitter, Seth; Baumeister, Roy F

2009-05-01

Three studies tested the roles of implicit and/or explicit self-esteem in reactions to mortality salience. In Study 1, writing about death versus a control topic increased worldview defense among participants low in implicit self-esteem but not among those high in implicit self-esteem. In Study 2, a manipulation to boost implicit self-esteem reduced the effect of mortality salience on worldview defense. In Study 3, mortality salience increased the endorsement of positive personality descriptions but only among participants with the combination of low implicit and high explicit self-esteem. These findings indicate that high implicit self-esteem confers resilience against the psychological threat of death, and therefore the findings provide direct support for a fundamental tenet of terror management theory regarding the anxiety-buffering role of self-esteem. Copyright (c) 2009 APA, all rights reserved.

How Explicit and Implicit Test Instructions in an Implicit Learning Task Affect Performance

PubMed Central

Witt, Arnaud; Puspitawati, Ira; Vinter, Annie

2013-01-01

Typically developing children aged 5 to 8 years were exposed to artificial grammar learning. Following an implicit exposure phase, half of the participants received neutral instructions at test while the other half received instructions making a direct, explicit reference to the training phase. We first aimed to assess whether implicit learning operated in the two test conditions. We then evaluated the differential impact of age on learning performances as a function of test instructions. The results showed that performance did not vary as a function of age in the implicit instructions condition, while age effects emerged when explicit instructions were employed at test. However, performance was affected differently by age and the instructions given at test, depending on whether the implicit learning of short or long units was assessed. These results suggest that the claim that the implicit learning process is independent of age needs to be revised. PMID:23326409

Implicit associations with popularity in early adolescence: an approach-avoidance analysis.

PubMed

Lansu, Tessa A M; Cillessen, Antonius H N; Karremans, Johan C

2012-01-01

This study examined 241 early adolescents' implicit and explicit associations with popularity. The peer status and gender of both the targets and the perceivers were considered. Explicit associations with popularity were assessed with sociometric methods. Implicit associations with popularity were assessed with an approach-avoidance task (AAT). Explicit evaluations of popularity were positive, but implicit associations were negative: Avoidance reactions to popular peers were faster than approach reactions. Interactions with the status of the perceiver indicated that unpopular participants had stronger negative implicit reactions to popular girls than did popular participants. This study demonstrated a negative reaction to popularity that cannot be revealed with explicit methods. The study of implicit processes with methods such as the AAT is a new and important direction for peer relations research.

A New Approach for Constructing Highly Stable High Order CESE Schemes

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

2010-01-01

A new approach is devised to construct high order CESE schemes which would avoid the common shortcomings of traditional high order schemes including: (a) susceptibility to computational instabilities; (b) computational inefficiency due to their local implicit nature (i.e., at each mesh points, need to solve a system of linear/nonlinear equations involving all the mesh variables associated with this mesh point); (c) use of large and elaborate stencils which complicates boundary treatments and also makes efficient parallel computing much harder; (d) difficulties in applications involving complex geometries; and (e) use of problem-specific techniques which are needed to overcome stability problems but often cause undesirable side effects. In fact it will be shown that, with the aid of a conceptual leap, one can build from a given 2nd-order CESE scheme its 4th-, 6th-, 8th-,... order versions which have the same stencil and same stability conditions of the 2nd-order scheme, and also retain all other advantages of the latter scheme. A sketch of multidimensional extensions will also be provided.

An ellipsoid-chain model for conjugated polymer solutions

NASA Astrophysics Data System (ADS)

Lee, Cheng K.; Hua, Chi C.; Chen, Show A.

2012-02-01

We propose an ellipsoid-chain model which may be routinely parameterized to capture large-scale properties of semiflexible, amphiphilic conjugated polymers in various solvent media. The model naturally utilizes the defect locations as pivotal centers connecting adjacent ellipsoids (each currently representing ten monomer units), and a variant umbrella-sampling scheme is employed to construct the potentials of mean force (PMF) for specific solvent media using atomistic dynamics data and simplex optimization. The performances, both efficacy and efficiency, of the model are thoroughly evaluated by comparing the simulation results on long, single-chain (i.e., 300-mer) structures with those from two existing, finer-grained models for a standard conjugated polymer (i.e., poly(2-methoxy-5-(2'-ethylhexyloxy)-1,4-phenylenevinylene) or MEH-PPV) in two distinct solvents (i.e., chloroform or toluene) as well as a hybrid, binary-solvent medium (i.e., chloroform/toluene = 1:1 in number density). The coarse-grained Monte Carlo (CGMC) simulation of the ellipsoid-chain model is shown to be the most efficient—about 300 times faster than the coarse-grained molecular dynamics (CGMD) simulation of the finest CG model that employs explicit solvents—in capturing elementary single-chain structures for both single-solvent media, and is a few times faster than the coarse-grained Langevin dynamics (CGLD) simulation of another implicit-solvent polymer model with a slightly greater coarse-graining level than in the CGMD simulation. For the binary-solvent system considered, however, both of the two implicit-solvent schemes (i.e., CGMC and CGLD) fail to capture the effects of conspicuous concentration fluctuations near the polymer-solvent interface, arising from a pronounced coupling between the solvent molecules and different parts of the polymer. Essential physical implications are elaborated on the success as well as the failure of the two implicit-solvent CG schemes under varying solvent conditions. Within the ellipsoid-chain model, the impact of synthesized defects on local segmental ordering as well as bulk chain conformation is also scrutinized, and essential consequences in practical applications discussed. In future perspectives, we remark on strategy that takes advantage of the coordination among various CG models and simulation schemes to warrant computational efficiency and accuracy, with the anticipated capability of simulating larger-scale, many-chain aggregate systems.

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.

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

Spectral wave dissipation by submerged aquatic vegetation in a back-barrier estuary

USGS Publications Warehouse

Nowacki, Daniel J.; Beudin, Alexis; Ganju, Neil K.

2017-01-01

Submerged aquatic vegetation is generally thought to attenuate waves, but this interaction remains poorly characterized in shallow-water field settings with locally generated wind waves. Better quantification of wave–vegetation interaction can provide insight to morphodynamic changes in a variety of environments and also is relevant to the planning of nature-based coastal protection measures. Toward that end, an instrumented transect was deployed across a Zostera marina (common eelgrass) meadow in Chincoteague Bay, Maryland/Virginia, U.S.A., to characterize wind-wave transformation within the vegetated region. Field observations revealed wave-height reduction, wave-period transformation, and wave-energy dissipation with distance into the meadow, and the data informed and calibrated a spectral wave model of the study area. The field observations and model results agreed well when local wind forcing and vegetation-induced drag were included in the model, either explicitly as rigid vegetation elements or implicitly as large bed-roughness values. Mean modeled parameters were similar for both the explicit and implicit approaches, but the spectral performance of the explicit approach was poor compared to the implicit approach. The explicit approach over-predicted low-frequency energy within the meadow because the vegetation scheme determines dissipation using mean wavenumber and frequency, in contrast to the bed-friction formulations, which dissipate energy in a variable fashion across frequency bands. Regardless of the vegetation scheme used, vegetation was the most important component of wave dissipation within much of the study area. These results help to quantify the influence of submerged aquatic vegetation on wave dynamics in future model parameterizations, field efforts, and coastal-protection measures.

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

Meng, F.; Banks, J. W.; Henshaw, W. D.

We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in a implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems togethermore » with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode the- ory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized- Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and dif- fusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. Lastly, the CHAMP scheme is also developed for general curvilinear grids and CHT ex- amples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.« less

Single-step methods for predicting orbital motion considering its periodic components

NASA Astrophysics Data System (ADS)

Lavrov, K. N.

1989-01-01

Modern numerical methods for integration of ordinary differential equations can provide accurate and universal solutions to celestial mechanics problems. The implicit single sequence algorithms of Everhart and multiple step computational schemes using a priori information on periodic components can be combined to construct implicit single sequence algorithms which combine their advantages. The construction and analysis of the properties of such algorithms are studied, utilizing trigonometric approximation of the solutions of differential equations containing periodic components. The algorithms require 10 percent more machine memory than the Everhart algorithms, but are twice as fast, and yield short term predictions valid for five to ten orbits with good accuracy and five to six times faster than algorithms using other methods.

Implicit solvers for unstructured meshes

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.; Mavriplis, Dimitri J.

1991-01-01

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

Multigrid Method for Modeling Multi-Dimensional Combustion with Detailed Chemistry

NASA Technical Reports Server (NTRS)

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

1996-01-01

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

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.

Distinguishing the affective and cognitive bases of implicit attitudes to improve prediction of food choices.

PubMed

Trendel, Olivier; Werle, Carolina O C

2016-09-01

Eating behaviors largely result from automatic processes. Yet, in existing research, automatic or implicit attitudes toward food often fail to predict eating behaviors. Applying findings in cognitive neuroscience research, we propose and find that a central reason why implicit attitudes toward food are not good predictors of eating behaviors is that implicit attitudes are driven by two distinct constructs that often have diverging evaluative consequences: the automatic affective reactions to food (e.g., tastiness; the affective basis of implicit attitudes) and the automatic cognitive reactions to food (e.g., healthiness; the cognitive basis of implicit attitudes). More importantly, we find that the affective and cognitive bases of implicit attitudes directly and uniquely influence actual food choices under different conditions. While the affective basis of implicit attitude is the main driver of food choices, it is the only driver when cognitive resources during choice are limited. The cognitive basis of implicit attitudes uniquely influences food choices when cognitive resources during choice are plentiful but only for participants low in impulsivity. Researchers interested in automatic processes in eating behaviors could thus benefit by distinguishing between the affective and cognitive bases of implicit attitudes. Copyright © 2015 Elsevier Ltd. All rights reserved.

Numerical investigation of MHD flow of blood and heat transfer in a stenosed arterial segment

NASA Astrophysics Data System (ADS)

Majee, Sreeparna; Shit, G. C.

2017-02-01

A numerical investigation of unsteady flow of blood and heat transfer has been performed with an aim to provide better understanding of blood flow through arteries under stenotic condition. The blood is treated as Newtonian fluid and the arterial wall is considered to be rigid having deposition of plaque in its lumen. The heat transfer characteristic has been analyzed by taking into consideration of the dissipation of energy due to applied magnetic field and the viscosity of blood. The vorticity-stream function formulation has been adopted to solve the problem using implicit finite difference method by developing well known Peaceman-Rachford Alternating Direction Implicit (ADI) scheme. The quantitative profile analysis of velocity, temperature and wall shear stress as well as Nusselt number is carried out over the entire arterial segment. The streamline and temperature contours have been plotted to understand the flow pattern in the diseased artery, which alters significantly in the downstream of the stenosis in the presence of magnetic field. Both the wall shear stress and Nusselt number increases with increasing magnetic field strength. However, wall shear stress decreases and Nusselt number enhances with Reynolds number. The results show that with an increase in the magnetic field strength upto 8 T, does not causes any damage to the arterial wall, but the study is significant for assessing temperature rise during hyperthermic treatment.

Numerical analysis of natural convection in liquid droplets by phase change

NASA Astrophysics Data System (ADS)

Duh, J. C.; Yang, Wen-Jei

1989-09-01

A numerical analysis is performed on thermocapillary buoyancy convection induced by phase change in a liquid droplet. A finite-difference code is developed using an alternating-direction implicit (ADI) scheme. The intercoupling relation between thermocapillary force, buoyancy force, fluid property, heat transfer, and phase change, along with their effects on the induced flow patterns, are disclosed. The flow is classified into three types: thermocapillary, buoyancy, and combined convection. Among the three mechanisms, the combined convection simulates the experimental observations quite well, and the basic mechanism of the observed convection inside evaporating sessile drops is thus identified. It is disclosed that evaporation initiates unstable convection, while condensation always brings about a stable density distribution which eventually damps out all fluid disturbances. Another numerical model is presented to study the effect of boundary recession due to evaporation, and the 'peeling-off' effect (the removal of the surface layer of fluid by evaporation) is shown to be relevant.

Simulating incompressible flow on moving meshfree grids using General Finite Differences (GFD)

NASA Astrophysics Data System (ADS)

Vasyliv, Yaroslav; Alexeev, Alexander

2016-11-01

We simulate incompressible flow around an oscillating cylinder at different Reynolds numbers using General Finite Differences (GFD) on a meshfree grid. We evolve the meshfree grid by treating each grid node as a particle. To compute velocities and accelerations, we consider the particles at a particular instance as Eulerian observation points. The incompressible Navier-Stokes equations are directly discretized using GFD with boundary conditions enforced using a sharp interface treatment. Cloud sizes are set such that the local approximations use only 16 neighbors. To enforce incompressibility, we apply a semi-implicit approximate projection method. To prevent overlapping particles and formation of voids in the grid, we propose a particle regularization scheme based on a local minimization principle. We validate the GFD results for an oscillating cylinder against the lattice Boltzmann method and find good agreement. Financial support provided by National Science Foundation (NSF) Graduate Research Fellowship, Grant No. DGE-1148903.

Implicit Large-Eddy Simulations of Zero-Pressure Gradient, Turbulent Boundary Layer

NASA Technical Reports Server (NTRS)

Sekhar, Susheel; Mansour, Nagi N.

2015-01-01

A set of direct simulations of zero-pressure gradient, turbulent boundary layer flows are conducted using various span widths (62-630 wall units), to document their influence on the generated turbulence. The FDL3DI code that solves compressible Navier-Stokes equations using high-order compact-difference scheme and filter, with the standard recycling/rescaling method of turbulence generation, is used. Results are analyzed at two different Re values (500 and 1,400), and compared with spectral DNS data. They show that a minimum span width is required for the mere initiation of numerical turbulence. Narrower domains ((is) less than 100 w.u.) result in relaminarization. Wider spans ((is) greater than 600 w.u.) are required for the turbulent statistics to match reference DNS. The upper-wall boundary condition for this setup spawns marginal deviations in the mean velocity and Reynolds stress profiles, particularly in the buffer region.

Combustion of hydrogen injected into a supersonic airstream (a guide to the HISS computer program)

NASA Technical Reports Server (NTRS)

Dyer, D. F.; Maples, G.; Spalding, D. B.

1976-01-01

A computer program based on a finite-difference, implicit numerical integration scheme is described for the prediction of hydrogen injected into a supersonic airstream at an angle ranging from normal to parallel to the airstream main flow direction. Results of calculations for flow and thermal property distributions were compared with 'cold flow data' taken by NASA/Langley and show excellent correlation. Typical results for equilibrium combustion are presented and exhibit qualitatively plausible behavior. Computer time required for a given case is approximately one minute on a CDC 7600. A discussion of the assumption of parabolic flow in the injection region is given which demonstrates that improvement in calculation in this region could be obtained by a partially-parabolic procedure which has been developed. It is concluded that the technique described provides an efficient and reliable means for analyzing hydrogen injection into supersonic airstreams and the subsequent combustion.

Efficient solutions to the Euler equations for supersonic flow with embedded subsonic regions

NASA Technical Reports Server (NTRS)

Walters, Robert W.; Dwoyer, Douglas L.

1987-01-01

A line Gauss-Seidel (LGS) relaxation algorithm in conjunction with a one-parameter family of upwind discretizations of the Euler equations in two dimensions is described. Convergence of the basic algorithm to the steady state is quadratic for fully supersonic flows and is linear for other flows. This is in contrast to the block alternating direction implicit methods (either central or upwind differenced) and the upwind biased relaxation schemes, all of which converge linearly, independent of the flow regime. Moreover, the algorithm presented herein is easily coupled with methods to detect regions of subsonic flow embedded in supersonic flow. This allows marching by lines in the supersonic regions, converging each line quadratically, and iterating in the subsonic regions, and yields a very efficient iteration strategy. Numerical results are presented for two-dimensional supersonic and transonic flows containing oblique and normal shock waves which confirm the efficiency of the iteration strategy.

Numerical analysis of natural convection in liquid droplets by phase change

NASA Technical Reports Server (NTRS)

Duh, J. C.; Yang, Wen-Jei

1989-01-01

A numerical analysis is performed on thermocapillary buoyancy convection induced by phase change in a liquid droplet. A finite-difference code is developed using an alternating-direction implicit (ADI) scheme. The intercoupling relation between thermocapillary force, buoyancy force, fluid property, heat transfer, and phase change, along with their effects on the induced flow patterns, are disclosed. The flow is classified into three types: thermocapillary, buoyancy, and combined convection. Among the three mechanisms, the combined convection simulates the experimental observations quite well, and the basic mechanism of the observed convection inside evaporating sessile drops is thus identified. It is disclosed that evaporation initiates unstable convection, while condensation always brings about a stable density distribution which eventually damps out all fluid disturbances. Another numerical model is presented to study the effect of boundary recession due to evaporation, and the 'peeling-off' effect (the removal of the surface layer of fluid by evaporation) is shown to be relevant.

Three Dimensional Solution of Pneumatic Active Control of Forebody Vortex Asymmetry

NASA Technical Reports Server (NTRS)

Kandil, Osama A.; SharafEl-Din, Hazem H.; Liu, C. H.

1995-01-01

Pneumatic active control of asymmetric vortical flows around a slender pointed forebody is investigated using the three dimensional solution for the compressible thin-layer Navier-Stokes equation. The computational applications cover the normal and tangential injection control of asymmetric flows around a 5 degree semi-apex angle cone at a 40 degree angle of attack, 1.4 freestream Mach number and 6 x 10(exp 6) freestream Reynolds number (based on the cone length). The effective tangential angle range of 67.5 approaches minus 67.5 degrees is used for both normal and tangential ports of injection. The effective axial length of injection is varied from 0.03 to 0.05. The computational solver uses the implicit, upwind, flux difference splitting finite volume scheme, and the grid consists of 161 x 55 x 65 points in the wrap around, normal and axial directions, respectively. The results show that tangential injection is more effective than normal injection.

Two-dimensional HID light source radiative transfer using discrete ordinates method

NASA Astrophysics Data System (ADS)

Ghrib, Basma; Bouaoun, Mohamed; Elloumi, Hatem

2016-08-01

This paper shows the implementation of the Discrete Ordinates Method for handling radiation problems in High Intensity Discharge (HID) lamps. Therefore, we start with presenting this rigorous method for treatment of radiation transfer in a two-dimensional, axisymmetric HID lamp. Furthermore, the finite volume method is used for the spatial discretization of the Radiative Transfer Equation. The atom and electron densities were calculated using temperature profiles established by a 2D semi-implicit finite-element scheme for the solution of conservation equations relative to energy, momentum, and mass. Spectral intensities as a function of position and direction are first calculated, and then axial and radial radiative fluxes are evaluated as well as the net emission coefficient. The results are given for a HID mercury lamp on a line-by-line basis. A particular attention is paid on the 253.7 nm resonance and 546.1 nm green lines.

LFNet: A Novel Bidirectional Recurrent Convolutional Neural Network for Light-Field Image Super-Resolution.

PubMed

Wang, Yunlong; Liu, Fei; Zhang, Kunbo; Hou, Guangqi; Sun, Zhenan; Tan, Tieniu

2018-09-01

The low spatial resolution of light-field image poses significant difficulties in exploiting its advantage. To mitigate the dependency of accurate depth or disparity information as priors for light-field image super-resolution, we propose an implicitly multi-scale fusion scheme to accumulate contextual information from multiple scales for super-resolution reconstruction. The implicitly multi-scale fusion scheme is then incorporated into bidirectional recurrent convolutional neural network, which aims to iteratively model spatial relations between horizontally or vertically adjacent sub-aperture images of light-field data. Within the network, the recurrent convolutions are modified to be more effective and flexible in modeling the spatial correlations between neighboring views. A horizontal sub-network and a vertical sub-network of the same network structure are ensembled for final outputs via stacked generalization. Experimental results on synthetic and real-world data sets demonstrate that the proposed method outperforms other state-of-the-art methods by a large margin in peak signal-to-noise ratio and gray-scale structural similarity indexes, which also achieves superior quality for human visual systems. Furthermore, the proposed method can enhance the performance of light field applications such as depth estimation.

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

NASA Technical Reports Server (NTRS)

Batina, John T.

1991-01-01

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

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

NASA Technical Reports Server (NTRS)

Batina, John T.

1990-01-01

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

Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models

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

Lester, Brian; Scherzinger, William

2017-01-19

Here, a new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, andmore » compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. Through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.« less

Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models

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

Lester, Brian T.; Scherzinger, William M.

2017-01-19

A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and comparedmore » to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.« less

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

NASA Technical Reports Server (NTRS)

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

1994-01-01

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

A pressure-based semi-implicit space-time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier-Stokes equations at all Mach numbers

NASA Astrophysics Data System (ADS)

Tavelli, Maurizio; Dumbser, Michael

2017-07-01

We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations on staggered unstructured curved meshes. The method is pressure-based and semi-implicit and is able to deal with all Mach number flows. The new DG scheme extends the seminal ideas outlined in [1], where a second order semi-implicit finite volume method for the solution of the compressible Navier-Stokes equations with a general equation of state was introduced on staggered Cartesian grids. Regarding the high order extension we follow [2], where a staggered space-time DG scheme for the incompressible Navier-Stokes equations was presented. In our scheme, the discrete pressure is defined on the primal grid, while the discrete velocity field and the density are defined on a face-based staggered dual grid. Then, the mass conservation equation, as well as the nonlinear convective terms in the momentum equation and the transport of kinetic energy in the energy equation are discretized explicitly, while the pressure terms appearing in the momentum and energy equation are discretized implicitly. Formal substitution of the discrete momentum equation into the total energy conservation equation yields a linear system for only one unknown, namely the scalar pressure. Here the equation of state is assumed linear with respect to the pressure. The enthalpy and the kinetic energy are taken explicitly and are then updated using a simple Picard procedure. Thanks to the use of a staggered grid, the final pressure system is a very sparse block five-point system for three dimensional problems and it is a block four-point system in the two dimensional case. Furthermore, for high order in space and piecewise constant polynomials in time, the system is observed to be symmetric and positive definite. This allows to use fast linear solvers such as the conjugate gradient (CG) method. In addition, all the volume and surface integrals needed by the scheme depend only on the geometry and the polynomial degree of the basis and test functions and can therefore be precomputed and stored in a preprocessing stage. This leads to significant savings in terms of computational effort for the time evolution part. In this way also the extension to a fully curved isoparametric approach becomes natural and affects only the preprocessing step. The viscous terms and the heat flux are also discretized making use of the staggered grid by defining the viscous stress tensor and the heat flux vector on the dual grid, which corresponds to the use of a lifting operator, but on the dual grid. The time step of our new numerical method is limited by a CFL condition based only on the fluid velocity and not on the sound speed. This makes the method particularly interesting for low Mach number flows. Finally, a very simple combination of artificial viscosity and the a posteriori MOOD technique allows to deal with shock waves and thus permits also to simulate high Mach number flows. We show computational results for a large set of two and three-dimensional benchmark problems, including both low and high Mach number flows and using polynomial approximation degrees up to p = 4.

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

NASA Technical Reports Server (NTRS)

Sankar, Lakshmi N.; Hixon, Duane

1991-01-01

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

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.

Advances in numerical and applied mathematics

NASA Technical Reports Server (NTRS)

South, J. C., Jr. (Editor); Hussaini, M. Y. (Editor)

1986-01-01

This collection of papers covers some recent developments in numerical analysis and computational fluid dynamics. Some of these studies are of a fundamental nature. They address basic issues such as intermediate boundary conditions for approximate factorization schemes, existence and uniqueness of steady states for time dependent problems, and pitfalls of implicit time stepping. The other studies deal with modern numerical methods such as total variation diminishing schemes, higher order variants of vortex and particle methods, spectral multidomain techniques, and front tracking techniques. There is also a paper on adaptive grids. The fluid dynamics papers treat the classical problems of imcompressible flows in helically coiled pipes, vortex breakdown, and transonic flows.

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries.

PubMed

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-15

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 - 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

A Newton–Krylov method with an approximate analytical Jacobian for implicit solution of Navier–Stokes equations on staggered overset-curvilinear grids with immersed boundaries

PubMed Central

Asgharzadeh, Hafez; Borazjani, Iman

2016-01-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for nonlinear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42 – 74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal Jacobian when the stretching factor was increased, respectively. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80–90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future. PMID:28042172

A Newton-Krylov method with an approximate analytical Jacobian for implicit solution of Navier-Stokes equations on staggered overset-curvilinear grids with immersed boundaries

NASA Astrophysics Data System (ADS)

Asgharzadeh, Hafez; Borazjani, Iman

2017-02-01

The explicit and semi-implicit schemes in flow simulations involving complex geometries and moving boundaries suffer from time-step size restriction and low convergence rates. Implicit schemes can be used to overcome these restrictions, but implementing them to solve the Navier-Stokes equations is not straightforward due to their non-linearity. Among the implicit schemes for non-linear equations, Newton-based techniques are preferred over fixed-point techniques because of their high convergence rate but each Newton iteration is more expensive than a fixed-point iteration. Krylov subspace methods are one of the most advanced iterative methods that can be combined with Newton methods, i.e., Newton-Krylov Methods (NKMs) to solve non-linear systems of equations. The success of NKMs vastly depends on the scheme for forming the Jacobian, e.g., automatic differentiation is very expensive, and matrix-free methods without a preconditioner slow down as the mesh is refined. A novel, computationally inexpensive analytical Jacobian for NKM is developed to solve unsteady incompressible Navier-Stokes momentum equations on staggered overset-curvilinear grids with immersed boundaries. Moreover, the analytical Jacobian is used to form a preconditioner for matrix-free method in order to improve its performance. The NKM with the analytical Jacobian was validated and verified against Taylor-Green vortex, inline oscillations of a cylinder in a fluid initially at rest, and pulsatile flow in a 90 degree bend. The capability of the method in handling complex geometries with multiple overset grids and immersed boundaries is shown by simulating an intracranial aneurysm. It was shown that the NKM with an analytical Jacobian is 1.17 to 14.77 times faster than the fixed-point Runge-Kutta method, and 1.74 to 152.3 times (excluding an intensively stretched grid) faster than automatic differentiation depending on the grid (size) and the flow problem. In addition, it was shown that using only the diagonal of the Jacobian further improves the performance by 42-74% compared to the full Jacobian. The NKM with an analytical Jacobian showed better performance than the fixed point Runge-Kutta because it converged with higher time steps and in approximately 30% less iterations even when the grid was stretched and the Reynold number was increased. In fact, stretching the grid decreased the performance of all methods, but the fixed-point Runge-Kutta performance decreased 4.57 and 2.26 times more than NKM with a diagonal and full Jacobian, respectivley, when the stretching factor was increased. The NKM with a diagonal analytical Jacobian and matrix-free method with an analytical preconditioner are the fastest methods and the superiority of one to another depends on the flow problem. Furthermore, the implemented methods are fully parallelized with parallel efficiency of 80-90% on the problems tested. The NKM with the analytical Jacobian can guide building preconditioners for other techniques to improve their performance in the future.

How implicit motives and everyday self-regulatory abilities shape cardiovascular risk in youth.

PubMed

Ewart, Craig K; Elder, Gavin J; Smyth, Joshua M

2012-06-01

Tested hypotheses from social action theory that (a) implicit and explicit measures of agonistic (social control) motives and transcendence (self-control) motives differentially predict cardiovascular risk; and (b) implicit motives interact with everyday self-regulation behaviors to magnify risk. Implicit/explicit agonistic/transcendence motives were assessed in a multi-ethnic sample of 64 high school students with the Social Competence Interview (SCI). Everyday self-regulation was assessed with teacher ratings of internalizing, externalizing, and self-control behaviors. Ambulatory blood pressure and daily activities were measured over 48 h. Study hypotheses were supported: implicit goals predicted blood pressure levels but explicit self-reported coping goals did not; self-regulation indices did not predict blood pressure directly but interacted with implicit agonistic/transcendence motives to identify individuals at greatest risk (all p ≤ 0.05). Assessment of implicit motives by SCI, and everyday self-regulation by teachers may improve identification of youth at risk for cardiovascular disease.

Stability of and Changes in Implicit Motives. A Narrative Review of Empirical Studies

PubMed Central

Denzinger, Ferdinand; Brandstätter, Veronika

2018-01-01

Although growing research indicates that certain personality traits change over the lifespan, implicit motives are often deemed to be rather stable personality characteristics. Researchers have been interested in implicit motives for several decades, but our understanding of how these dispositions change still lacks clarity. This article gives an overview and a discussion of the current evidence for the stability of and the changes in implicit motives. After elaborating on the theoretical background of the motive construct and its measurement, we present an overview of studies that have investigated the trainability of implicit motives and their dispositional stability and changes using cross-sectional and longitudinal methods. Although the results are inconclusive concerning the direction of change, the reviewed studies suggest that implicit motives adapt to life circumstances much like other personality traits. This review sets out to contribute to a better understanding of the functioning of implicit motives and to present a roadmap for further research. PMID:29887818

Using Implicit Instructional Cues to Influence False Memory Induction.

PubMed

Cirelli, Laura K; Dickinson, Joël; Poirier, Marie

2015-10-01

Previous research has shown that explicit cues specific to the encoding process (endogenous) or characteristic of the stimuli themselves (exogenous) can be used to direct a reader's attentional resources towards either relational or item-specific information. By directing attention to relational information (and therefore away from item-specific information) the rate of false memory induction can be increased. The purpose of the current study was to investigate if a similar effect would be found by manipulating implicitly endogenous cues. An instructional manipulation was used to influence the perceptual action participants performed on word stimuli during the encoding of DRM list words. Results demonstrated that the instructional conditions that encouraged faster processing also led to an increased rate of false memory induction for semantically related words, supporting the hypothesis that attention was directed towards relational information. This finding supports the impoverished relational processing account of false memory induction. This supports the idea that implicitly endogenous cues, exogenous cues (like font) or explicitly endogenous cues (like training) can direct attentional resources during encoding.

First-Order Hyperbolic System Method for Time-Dependent Advection-Diffusion Problems

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza; Nishikawa, Hiroaki

2014-01-01

A time-dependent extension of the first-order hyperbolic system method for advection-diffusion problems is introduced. Diffusive/viscous terms are written and discretized as a hyperbolic system, which recovers the original equation in the steady state. The resulting scheme offers advantages over traditional schemes: a dramatic simplification in the discretization, high-order accuracy in the solution gradients, and orders-of-magnitude convergence acceleration. The hyperbolic advection-diffusion system is discretized by the second-order upwind residual-distribution scheme in a unified manner, and the system of implicit-residual-equations is solved by Newton's method over every physical time step. The numerical results are presented for linear and nonlinear advection-diffusion problems, demonstrating solutions and gradients produced to the same order of accuracy, with rapid convergence over each physical time step, typically less than five Newton iterations.

Implicit Incompressible SPH.

PubMed

Ihmsen, Markus; Cornelis, Jens; Solenthaler, Barbara; Horvath, Christopher; Teschner, Matthias

2013-07-25

We propose a novel formulation of the projection method for Smoothed Particle Hydrodynamics (SPH). We combine a symmetric SPH pressure force and an SPH discretization of the continuity equation to obtain a discretized form of the pressure Poisson equation (PPE). In contrast to previous projection schemes, our system does consider the actual computation of the pressure force. This incorporation improves the convergence rate of the solver. Furthermore, we propose to compute the density deviation based on velocities instead of positions as this formulation improves the robustness of the time-integration scheme. We show that our novel formulation outperforms previous projection schemes and state-of-the-art SPH methods. Large time steps and small density deviations of down to 0.01% can be handled in typical scenarios. The practical relevance of the approach is illustrated by scenarios with up to 40 million SPH particles.

Implicit incompressible SPH.

PubMed

Ihmsen, Markus; Cornelis, Jens; Solenthaler, Barbara; Horvath, Christopher; Teschner, Matthias

2014-03-01

We propose a novel formulation of the projection method for Smoothed Particle Hydrodynamics (SPH). We combine a symmetric SPH pressure force and an SPH discretization of the continuity equation to obtain a discretized form of the pressure Poisson equation (PPE). In contrast to previous projection schemes, our system does consider the actual computation of the pressure force. This incorporation improves the convergence rate of the solver. Furthermore, we propose to compute the density deviation based on velocities instead of positions as this formulation improves the robustness of the time-integration scheme. We show that our novel formulation outperforms previous projection schemes and state-of-the-art SPH methods. Large time steps and small density deviations of down to 0.01 percent can be handled in typical scenarios. The practical relevance of the approach is illustrated by scenarios with up to 40 million SPH particles.

Assessing implicit odor localization in humans using a cross-modal spatial cueing paradigm.

PubMed

Moessnang, Carolin; Finkelmeyer, Andreas; Vossen, Alexandra; Schneider, Frank; Habel, Ute

2011-01-01

Navigation based on chemosensory information is one of the most important skills in the animal kingdom. Studies on odor localization suggest that humans have lost this ability. However, the experimental approaches used so far were limited to explicit judgements, which might ignore a residual ability for directional smelling on an implicit level without conscious appraisal. A novel cueing paradigm was developed in order to determine whether an implicit ability for directional smelling exists. Participants performed a visual two-alternative forced choice task in which the target was preceded either by a side-congruent or a side-incongruent olfactory spatial cue. An explicit odor localization task was implemented in a second experiment. No effect of cue congruency on mean reaction times could be found. However, a time by condition interaction emerged, with significantly slower responses to congruently compared to incongruently cued targets at the beginning of the experiment. This cueing effect gradually disappeared throughout the course of the experiment. In addition, participants performed at chance level in the explicit odor localization task, thus confirming the results of previous research. The implicit cueing task suggests the existence of spatial information processing in the olfactory system. Response slowing after a side-congruent olfactory cue is interpreted as a cross-modal attentional interference effect. In addition, habituation might have led to a gradual disappearance of the cueing effect. It is concluded that under immobile conditions with passive monorhinal stimulation, humans are unable to explicitly determine the location of a pure odorant. Implicitly, however, odor localization seems to exert an influence on human behaviour. To our knowledge, these data are the first to show implicit effects of odor localization on overt human behaviour and thus support the hypothesis of residual directional smelling in humans. © 2011 Moessnang et al.

Flow simulations about steady-complex and unsteady moving configurations using structured-overlapped and unstructured grids

NASA Technical Reports Server (NTRS)

Newman, James C., III

1995-01-01

The limiting factor in simulating flows past realistic configurations of interest has been the discretization of the physical domain on which the governing equations of fluid flow may be solved. In an attempt to circumvent this problem, many Computational Fluid Dynamic (CFD) methodologies that are based on different grid generation and domain decomposition techniques have been developed. However, due to the costs involved and expertise required, very few comparative studies between these methods have been performed. In the present work, the two CFD methodologies which show the most promise for treating complex three-dimensional configurations as well as unsteady moving boundary problems are evaluated. These are namely the structured-overlapped and the unstructured grid schemes. Both methods use a cell centered, finite volume, upwind approach. The structured-overlapped algorithm uses an approximately factored, alternating direction implicit scheme to perform the time integration, whereas, the unstructured algorithm uses an explicit Runge-Kutta method. To examine the accuracy, efficiency, and limitations of each scheme, they are applied to the same steady complex multicomponent configurations and unsteady moving boundary problems. The steady complex cases consist of computing the subsonic flow about a two-dimensional high-lift multielement airfoil and the transonic flow about a three-dimensional wing/pylon/finned store assembly. The unsteady moving boundary problems are a forced pitching oscillation of an airfoil in a transonic freestream and a two-dimensional, subsonic airfoil/store separation sequence. Accuracy was accessed through the comparison of computed and experimentally measured pressure coefficient data on several of the wing/pylon/finned store assembly's components and at numerous angles-of-attack for the pitching airfoil. From this study, it was found that both the structured-overlapped and the unstructured grid schemes yielded flow solutions of comparable accuracy for these simulations. This study also indicated that, overall, the structured-overlapped scheme was slightly more CPU efficient than the unstructured approach.

Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 2: Algorithmic developments and implementation

NASA Technical Reports Server (NTRS)

Li, Wei; Saleeb, Atef F.

1995-01-01

This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present second part of the report, we focus on the specific details of the numerical schemes, and associated computer algorithms, for the finite-element implementation of GVIPS and NAV models.

Robust integration schemes for generalized viscoplasticity with internal-state variables. Part 1: Theoretical developments and applications

NASA Technical Reports Server (NTRS)

Saleeb, Atef F.; Li, Wei

1995-01-01

This two-part report is concerned with the development of a general framework for the implicit time-stepping integrators for the flow and evolution equations in generalized viscoplastic models. The primary goal is to present a complete theoretical formulation, and to address in detail the algorithmic and numerical analysis aspects involved in its finite element implementation, as well as to critically assess the numerical performance of the developed schemes in a comprehensive set of test cases. On the theoretical side, the general framework is developed on the basis of the unconditionally-stable, backward-Euler difference scheme as a starting point. Its mathematical structure is of sufficient generality to allow a unified treatment of different classes of viscoplastic models with internal variables. In particular, two specific models of this type, which are representative of the present start-of-art in metal viscoplasticity, are considered in applications reported here; i.e., fully associative (GVIPS) and non-associative (NAV) models. The matrix forms developed for both these models are directly applicable for both initially isotropic and anisotropic materials, in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/strain, axisymmetric, generalized plane stress in shells). On the computational side, issues related to efficiency and robustness are emphasized in developing the (local) interative algorithm. In particular, closed-form expressions for residual vectors and (consistent) material tangent stiffness arrays are given explicitly for both GVIPS and NAV models, with their maximum sizes 'optimized' to depend only on the number of independent stress components (but independent of the number of viscoplastic internal state parameters). Significant robustness of the local iterative solution is provided by complementing the basic Newton-Raphson scheme with a line-search strategy for convergence. In the present first part of the report, we focus on the theoretical developments, and discussions of the results of numerical-performance studies using the integration schemes for GVIPS and NAV models.

Theoretical and experimental study on multimode optical fiber grating

NASA Astrophysics Data System (ADS)

Yunming, Wang; Jingcao, Dai; Mingde, Zhang; Xiaohan, Sun

2005-06-01

The characteristics of multimode optical fiber Bragg grating (MMFBG) are studied theoretically and experimentally. For the first time the analysis of MMFBG based on a novel quasi-three-dimensional (Q-3D) finite-difference time-domain beam propagation method (Q-FDTD-BPM) is described through separating the angle component of vector field solution from the cylindrical coordinate so that several discrete two-dimensional (2D) equations are obtained, which simplify the 3D equations. And then these equations are developed using an alternating-direction implicit method and generalized Douglas scheme, which achieves higher accuracy than the regular FD scheme. All of the 2D solutions for the field intensities are also added with different power coefficients for different angle mode order numbers to obtain 3D field distributions in MMFBG. The presented method has been demonstrated as suitable simulation tool for analyzing MMFBG. In addition, based on the hydrogen-loaded and phase mask techniques, a series of Bragg grating have been written into the silicon multimode optical fiber loaded hydrogen for a month, and the spectrums for that have been measured, which obtain good results approximate to the results in the experiment. Group delay/differentiate group delay spectrums are obtained using Agilent 81910A Photonic All-Parameter Analyzer.

A single session of prefrontal cortex transcranial direct current stimulation does not modulate implicit task sequence learning and consolidation.

PubMed

Savic, Branislav; Müri, René; Meier, Beat

Transcranial direct current stimulation (tDCS) is assumed to affect cortical excitability and dependent on the specific stimulation conditions either to increase or decrease learning. The purpose of this study was to modulate implicit task sequence learning with tDCS. As cortico-striatal loops are critically involved in implicit task sequence learning, tDCS was applied above the dorsolateral prefrontal cortex (DLPFC). In Experiment 1, anodal, cathodal, or sham tDCS was applied before the start of the sequence learning task. In Experiment 2, stimulation was applied during the sequence learning task. Consolidation of learning was assessed after 24 h. The results of both experiments showed that implicit task sequence learning occurred consistently but it was not modulated by different tDCS conditions. Similarly, consolidation measured after a 24 h-interval including sleep was also not affected by stimulation. These results indicate that a single session of DLPFC tDCS is not sufficient to modulate implicit task sequence learning. This study adds to the accumulating evidence that tDCS may not be as effective as originally thought. Copyright © 2017 Elsevier Inc. All rights reserved.

Multigrid time-accurate integration of Navier-Stokes equations

NASA Technical Reports Server (NTRS)

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

1993-01-01

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

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.

2-dimensional implicit hydrodynamics on adaptive grids

NASA Astrophysics Data System (ADS)

Stökl, A.; Dorfi, E. A.

2007-12-01

We present a numerical scheme for two-dimensional hydrodynamics computations using a 2D adaptive grid together with an implicit discretization. The combination of these techniques has offered favorable numerical properties applicable to a variety of one-dimensional astrophysical problems which motivated us to generalize this approach for two-dimensional applications. Due to the different topological nature of 2D grids compared to 1D problems, grid adaptivity has to avoid severe grid distortions which necessitates additional smoothing parameters to be included into the formulation of a 2D adaptive grid. The concept of adaptivity is described in detail and several test computations demonstrate the effectivity of smoothing. The coupled solution of this grid equation together with the equations of hydrodynamics is illustrated by computation of a 2D shock tube problem.

Diagonally Implicit Runge-Kutta Methods for Ordinary Differential Equations. A Review

NASA Technical Reports Server (NTRS)

Kennedy, Christopher A.; Carpenter, Mark H.

2016-01-01

A review of diagonally implicit Runge-Kutta (DIRK) methods applied to rst-order ordinary di erential equations (ODEs) is undertaken. The goal of this review is to summarize the characteristics, assess the potential, and then design several nearly optimal, general purpose, DIRK-type methods. Over 20 important aspects of DIRKtype methods are reviewed. A design study is then conducted on DIRK-type methods having from two to seven implicit stages. From this, 15 schemes are selected for general purpose application. Testing of the 15 chosen methods is done on three singular perturbation problems. Based on the review of method characteristics, these methods focus on having a stage order of two, sti accuracy, L-stability, high quality embedded and dense-output methods, small magnitudes of the algebraic stability matrix eigenvalues, small values of aii, and small or vanishing values of the internal stability function for large eigenvalues of the Jacobian. Among the 15 new methods, ESDIRK4(3)6L[2]SA is recommended as a good default method for solving sti problems at moderate error tolerances.

Operator splitting method for simulation of dynamic flows in natural gas pipeline networks

DOE PAGES

Dyachenko, Sergey A.; Zlotnik, Anatoly; Korotkevich, Alexander O.; ...

2017-09-19

Here, we develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for mass flow and pressure on a metric graph, where turbulent losses of momentum are modeled by phenomenological Darcy-Weisbach friction. Mass flow balance is maintained through the boundary conditions at the network nodes, where natural gas is injected or withdrawn from the system. Gas flow through the network is controlled by compressors boosting pressure at the inlet of the adjoint pipe. Our operator splitting numerical scheme ismore » unconditionally stable and it is second order accurate in space and time. The scheme is explicit, and it is formulated to work with general networks with loops. We test the scheme over range of regimes and network configurations, also comparing its performance with performance of two other state of the art implicit schemes.« less

Parameter estimation in IMEX-trigonometrically fitted methods for the numerical solution of reaction-diffusion problems

NASA Astrophysics Data System (ADS)

D'Ambrosio, Raffaele; Moccaldi, Martina; Paternoster, Beatrice

2018-05-01

In this paper, an adapted numerical scheme for reaction-diffusion problems generating periodic wavefronts is introduced. Adapted numerical methods for such evolutionary problems are specially tuned to follow prescribed qualitative behaviors of the solutions, making the numerical scheme more accurate and efficient as compared with traditional schemes already known in the literature. Adaptation through the so-called exponential fitting technique leads to methods whose coefficients depend on unknown parameters related to the dynamics and aimed to be numerically computed. Here we propose a strategy for a cheap and accurate estimation of such parameters, which consists essentially in minimizing the leading term of the local truncation error whose expression is provided in a rigorous accuracy analysis. In particular, the presented estimation technique has been applied to a numerical scheme based on combining an adapted finite difference discretization in space with an implicit-explicit time discretization. Numerical experiments confirming the effectiveness of the approach are also provided.

A cut-cell immersed boundary technique for fire dynamics simulation

NASA Astrophysics Data System (ADS)

Vanella, Marcos; McDermott, Randall; Forney, Glenn

2015-11-01

Fire simulation around complex geometry is gaining increasing attention in performance based design of fire protection systems, fire-structure interaction and pollutant transport in complex terrains, among others. This presentation will focus on our present effort in improving the capability of FDS (Fire Dynamics Simulator, developed at the Fire Research Division, NIST. https://github.com/firemodels/fds-smv) to represent fire scenarios around complex bodies. Velocities in the vicinity of the bodies are reconstructed using a classical immersed boundary scheme (Fadlun and co-workers, J. Comput. Phys., 161:35-60, 2000). Also, a conservative treatment of scalar transport equations (i.e. for chemical species) will be presented. In our method, discrete conservation and no penetration of species across solid boundaries are enforced using a cut-cell finite volume scheme. The small cell problem inherent to the method is tackled using explicit-implicit domain decomposition for scalar, within the FDS time integration scheme. Some details on the derivation, implementation and numerical tests of this numerical scheme will be discussed.

A well-balanced finite volume scheme for the Euler equations with gravitation. The exact preservation of hydrostatic equilibrium with arbitrary entropy stratification

NASA Astrophysics Data System (ADS)

Käppeli, R.; Mishra, S.

2016-03-01

Context. Many problems in astrophysics feature flows which are close to hydrostatic equilibrium. However, standard numerical schemes for compressible hydrodynamics may be deficient in approximating this stationary state, where the pressure gradient is nearly balanced by gravitational forces. Aims: We aim to develop a second-order well-balanced scheme for the Euler equations. The scheme is designed to mimic a discrete version of the hydrostatic balance. It therefore can resolve a discrete hydrostatic equilibrium exactly (up to machine precision) and propagate perturbations, on top of this equilibrium, very accurately. Methods: A local second-order hydrostatic equilibrium preserving pressure reconstruction is developed. Combined with a standard central gravitational source term discretization and numerical fluxes that resolve stationary contact discontinuities exactly, the well-balanced property is achieved. Results: The resulting well-balanced scheme is robust and simple enough to be very easily implemented within any existing computer code that solves time explicitly or implicitly the compressible hydrodynamics equations. We demonstrate the performance of the well-balanced scheme for several astrophysically relevant applications: wave propagation in stellar atmospheres, a toy model for core-collapse supernovae, convection in carbon shell burning, and a realistic proto-neutron star.

Coordination Logic for Repulsive Resolution Maneuvers

NASA Technical Reports Server (NTRS)

Narkawicz, Anthony J.; Munoz, Cesar A.; Dutle, Aaron M.

2016-01-01

This paper presents an algorithm for determining the direction an aircraft should maneuver in the event of a potential conflict with another aircraft. The algorithm is implicitly coordinated, meaning that with perfectly reliable computations and information, it will in- dependently provide directional information that is guaranteed to be coordinated without any additional information exchange or direct communication. The logic is inspired by the logic of TCAS II, the airborne system designed to reduce the risk of mid-air collisions between aircraft. TCAS II provides pilots with only vertical resolution advice, while the proposed algorithm, using a similar logic, provides implicitly coordinated vertical and horizontal directional advice.

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.

Flexible explicit but rigid implicit learning in a visuomotor adaptation task

PubMed Central

Bond, Krista M.

2015-01-01

There is mounting evidence for the idea that performance in a visuomotor rotation task can be supported by both implicit and explicit forms of learning. The implicit component of learning has been well characterized in previous experiments and is thought to arise from the adaptation of an internal model driven by sensorimotor prediction errors. However, the role of explicit learning is less clear, and previous investigations aimed at characterizing the explicit component have relied on indirect measures such as dual-task manipulations, posttests, and descriptive computational models. To address this problem, we developed a new method for directly assaying explicit learning by having participants verbally report their intended aiming direction on each trial. While our previous research employing this method has demonstrated the possibility of measuring explicit learning over the course of training, it was only tested over a limited scope of manipulations common to visuomotor rotation tasks. In the present study, we sought to better characterize explicit and implicit learning over a wider range of task conditions. We tested how explicit and implicit learning change as a function of the specific visual landmarks used to probe explicit learning, the number of training targets, and the size of the rotation. We found that explicit learning was remarkably flexible, responding appropriately to task demands. In contrast, implicit learning was strikingly rigid, with each task condition producing a similar degree of implicit learning. These results suggest that explicit learning is a fundamental component of motor learning and has been overlooked or conflated in previous visuomotor tasks. PMID:25855690

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.

A Unified Theoretical Framework for Cognitive Sequencing.

PubMed

Savalia, Tejas; Shukla, Anuj; Bapi, Raju S

2016-01-01

The capacity to sequence information is central to human performance. Sequencing ability forms the foundation stone for higher order cognition related to language and goal-directed planning. Information related to the order of items, their timing, chunking and hierarchical organization are important aspects in sequencing. Past research on sequencing has emphasized two distinct and independent dichotomies: implicit vs. explicit and goal-directed vs. habits. We propose a theoretical framework unifying these two streams. Our proposal relies on brain's ability to implicitly extract statistical regularities from the stream of stimuli and with attentional engagement organizing sequences explicitly and hierarchically. Similarly, sequences that need to be assembled purposively to accomplish a goal require engagement of attentional processes. With repetition, these goal-directed plans become habits with concomitant disengagement of attention. Thus, attention and awareness play a crucial role in the implicit-to-explicit transition as well as in how goal-directed plans become automatic habits. Cortico-subcortical loops basal ganglia-frontal cortex and hippocampus-frontal cortex loops mediate the transition process. We show how the computational principles of model-free and model-based learning paradigms, along with a pivotal role for attention and awareness, offer a unifying framework for these two dichotomies. Based on this framework, we make testable predictions related to the potential influence of response-to-stimulus interval (RSI) on developing awareness in implicit learning tasks.

A Unified Theoretical Framework for Cognitive Sequencing

PubMed Central

Savalia, Tejas; Shukla, Anuj; Bapi, Raju S.

2016-01-01

The capacity to sequence information is central to human performance. Sequencing ability forms the foundation stone for higher order cognition related to language and goal-directed planning. Information related to the order of items, their timing, chunking and hierarchical organization are important aspects in sequencing. Past research on sequencing has emphasized two distinct and independent dichotomies: implicit vs. explicit and goal-directed vs. habits. We propose a theoretical framework unifying these two streams. Our proposal relies on brain's ability to implicitly extract statistical regularities from the stream of stimuli and with attentional engagement organizing sequences explicitly and hierarchically. Similarly, sequences that need to be assembled purposively to accomplish a goal require engagement of attentional processes. With repetition, these goal-directed plans become habits with concomitant disengagement of attention. Thus, attention and awareness play a crucial role in the implicit-to-explicit transition as well as in how goal-directed plans become automatic habits. Cortico-subcortical loops basal ganglia-frontal cortex and hippocampus-frontal cortex loops mediate the transition process. We show how the computational principles of model-free and model-based learning paradigms, along with a pivotal role for attention and awareness, offer a unifying framework for these two dichotomies. Based on this framework, we make testable predictions related to the potential influence of response-to-stimulus interval (RSI) on developing awareness in implicit learning tasks. PMID:27917146

Controlled and implicit processes in evaluative conditioning on implicit and explicit attitudes toward alcohol and intentions to drink.

PubMed

Zerhouni, Oulmann; Bègue, Laurent; Comiran, Francisco; Wiers, Reinout W

2018-01-01

Since implicit attitudes (i.e. evaluations occurring outside of complete awareness) are highly predictive of alcohol consumption, we tested an evaluative learning procedure based on repeated pairing to a critical stimulus (i.e. alcohol, the CS) with a valenced stimulus (the US) in order to modify implicit attitudes (i.e. evaluative conditioning; EC). We hypothesized that manipulating the learning context to bolster implicit affect misattribution should strengthen EC effects on implicit attitudes toward alcohol, while encouraging deliberate processing of CS-US pairs, should strengthen EC effects on explicit attitudes. In our study (n=114 students) we manipulated whether CS-US pairs were presented simultaneously or sequentially. Recollective memory was estimated with a Process Dissociation Procedure. Both implicit and explicit attitudes were assessed immediately after the procedure. Behavioral intentions were measured directly after and one week after the EC-procedure. We found that EC with sequential presentation had a stronger impact on implicit and explicit measures and on purchase intentions immediately after the procedure and one week after. The present findings provide new evidence that (i) EC is an effective way to change implicit attitudes toward alcohol and (ii) evidence that EC may be better described by propositional rather than dual process accounts. Copyright © 2017 Elsevier Ltd. All rights reserved.

Implicit negotiation beliefs and performance: experimental and longitudinal evidence.

PubMed

Kray, Laura J; Haselhuhn, Michael P

2007-07-01

The authors argue that implicit negotiation beliefs, which speak to the expected malleability of negotiating ability, affect performance in dyadic negotiations. They expected negotiators who believe negotiating attributes are malleable (incremental theorists) to outperform negotiators who believe negotiating attributes are fixed (entity theorists). In Study 1, they gathered evidence of convergent and discriminant validity for the implicit negotiation belief construct. In Study 2, they examined the impact of implicit beliefs on the achievement goals that negotiators pursue. In Study 3, they explored the causal role of implicit beliefs on negotiation performance by manipulating negotiators' implicit beliefs within dyads. They also identified perceived ability as a moderator of the link between implicit negotiation beliefs and performance. In Study 4, they measured negotiators' beliefs in a classroom setting and examined how these beliefs affected negotiation performance and overall performance in the course 15 weeks later. Across all performance measures, incremental theorists outperformed entity theorists. Consistent with the authors' hypotheses, incremental theorists captured more of the bargaining surplus and were more integrative than their entity theorist counterparts, suggesting implicit theories are important determinants of how negotiators perform. Implications and future directions are discussed. Copyright 2007 APA, all rights reserved.

Preconditioned conjugate gradient methods for the compressible Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Venkatakrishnan, V.

1990-01-01

The compressible Navier-Stokes equations are solved for a variety of two-dimensional inviscid and viscous problems by preconditioned conjugate gradient-like algorithms. Roe's flux difference splitting technique is used to discretize the inviscid fluxes. The viscous terms are discretized by using central differences. An algebraic turbulence model is also incorporated. The system of linear equations which arises out of the linearization of a fully implicit scheme is solved iteratively by the well known methods of GMRES (Generalized Minimum Residual technique) and Chebyschev iteration. Incomplete LU factorization and block diagonal factorization are used as preconditioners. The resulting algorithm is competitive with the best current schemes, but has wide applications in parallel computing and unstructured mesh computations.

Multigrid calculation of three-dimensional viscous cascade flows

NASA Technical Reports Server (NTRS)

Arnone, A.; Liou, M.-S.; Povinelli, L. A.

1991-01-01

A 3-D code for viscous cascade flow prediction was developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full multigrid method. The Baldwin-Lomax eddy viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

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.

Numerical simulation of three dimensional transonic flows

NASA Technical Reports Server (NTRS)

Sahu, Jubaraj; Steger, Joseph L.

1987-01-01

The three-dimensional flow over a projectile has been computed using an implicit, approximately factored, partially flux-split algorithm. A simple composite grid scheme has been developed in which a single grid is partitioned into a series of smaller grids for applications which require an external large memory device such as the SSD of the CRAY X-MP/48, or multitasking. The accuracy and stability of the composite grid scheme has been tested by numerically simulating the flow over an ellipsoid at angle of attack and comparing the solution with a single grid solution. The flowfield over a projectile at M = 0.96 and 4 deg angle-of-attack has been computed using a fine grid, and compared with experiment.

Multigrid calculation of three-dimensional viscous cascade flows

NASA Technical Reports Server (NTRS)

Arnone, A.; Liou, M.-S.; Povinelli, L. A.

1991-01-01

A three-dimensional code for viscous cascade flow prediction has been developed. The space discretization uses a cell-centered scheme with eigenvalue scaling to weigh the artificial dissipation terms. Computational efficiency of a four-stage Runge-Kutta scheme is enhanced by using variable coefficients, implicit residual smoothing, and a full-multigrid method. The Baldwin-Lomax eddy-viscosity model is used for turbulence closure. A zonal, nonperiodic grid is used to minimize mesh distortion in and downstream of the throat region. Applications are presented for an annular vane with and without end wall contouring, and for a large-scale linear cascade. The calculation is validated by comparing with experiments and by studying grid dependency.

Task-Driven Tube Current Modulation and Regularization Design in Computed Tomography with Penalized-Likelihood Reconstruction.

PubMed

Gang, G J; Siewerdsen, J H; Stayman, J W

2016-02-01

This work applies task-driven optimization to design CT tube current modulation and directional regularization in penalized-likelihood (PL) reconstruction. The relative performance of modulation schemes commonly adopted for filtered-backprojection (FBP) reconstruction were also evaluated for PL in comparison. We adopt a task-driven imaging framework that utilizes a patient-specific anatomical model and information of the imaging task to optimize imaging performance in terms of detectability index ( d' ). This framework leverages a theoretical model based on implicit function theorem and Fourier approximations to predict local spatial resolution and noise characteristics of PL reconstruction as a function of the imaging parameters to be optimized. Tube current modulation was parameterized as a linear combination of Gaussian basis functions, and regularization was based on the design of (directional) pairwise penalty weights for the 8 in-plane neighboring voxels. Detectability was optimized using a covariance matrix adaptation evolutionary strategy algorithm. Task-driven designs were compared to conventional tube current modulation strategies for a Gaussian detection task in an abdomen phantom. The task-driven design yielded the best performance, improving d' by ~20% over an unmodulated acquisition. Contrary to FBP, PL reconstruction using automatic exposure control and modulation based on minimum variance (in FBP) performed worse than the unmodulated case, decreasing d' by 16% and 9%, respectively. This work shows that conventional tube current modulation schemes suitable for FBP can be suboptimal for PL reconstruction. Thus, the proposed task-driven optimization provides additional opportunities for improved imaging performance and dose reduction beyond that achievable with conventional acquisition and reconstruction.

COMPARISON OF IMPLICIT SCHEMES TO SOLVE EQUATIONS OF RADIATION HYDRODYNAMICS WITH A FLUX-LIMITED DIFFUSION APPROXIMATION: NEWTON–RAPHSON, OPERATOR SPLITTING, AND LINEARIZATION

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

Tetsu, Hiroyuki; Nakamoto, Taishi, E-mail: h.tetsu@geo.titech.ac.jp

Radiation is an important process of energy transport, a force, and a basis for synthetic observations, so radiation hydrodynamics (RHD) calculations have occupied an important place in astrophysics. However, although the progress in computational technology is remarkable, their high numerical cost is still a persistent problem. In this work, we compare the following schemes used to solve the nonlinear simultaneous equations of an RHD algorithm with the flux-limited diffusion approximation: the Newton–Raphson (NR) method, operator splitting, and linearization (LIN), from the perspective of the computational cost involved. For operator splitting, in addition to the traditional simple operator splitting (SOS) scheme,more » we examined the scheme developed by Douglas and Rachford (DROS). We solve three test problems (the thermal relaxation mode, the relaxation and the propagation of linear waves, and radiating shock) using these schemes and then compare their dependence on the time step size. As a result, we find the conditions of the time step size necessary for adopting each scheme. The LIN scheme is superior to other schemes if the ratio of radiation pressure to gas pressure is sufficiently low. On the other hand, DROS can be the most efficient scheme if the ratio is high. Although the NR scheme can be adopted independently of the regime, especially in a problem that involves optically thin regions, the convergence tends to be worse. In all cases, SOS is not practical.« less

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

The Demand for Child Care Quality. An Hedonic Price Theory Approach.

ERIC Educational Resources Information Center

Hagy, Alison P.

1998-01-01

An implicit price for child care staff-to-child ratio was used to study demand for child care quality. Direct purchase-of-service contracts or vouchers, which subsidize only providers meeting state regulations, effectively lower implicit price and have little influence on the demand for quality. (Author/SK)

Influence of Boussinesq coefficient on depth-averaged modelling of rapid flows

NASA Astrophysics Data System (ADS)

Yang, Fan; Liang, Dongfang; Xiao, Yang

2018-04-01

The traditional Alternating Direction Implicit (ADI) scheme has been proven to be incapable of modelling trans-critical flows. Its inherent lack of shock-capturing capability often results in spurious oscillations and computational instabilities. However, the ADI scheme is still widely adopted in flood modelling software, and various special treatments have been designed to stabilise the computation. Modification of the Boussinesq coefficient to adjust the amount of fluid inertia is a numerical treatment that allows the ADI scheme to be applicable to rapid flows. This study comprehensively examines the impact of this numerical treatment over a range of flow conditions. A shock-capturing TVD-MacCormack model is used to provide reference results. For unsteady flows over a frictionless bed, such as idealised dam-break floods, the results suggest that an increase in the value of the Boussinesq coefficient reduces the amplitude of the spurious oscillations. The opposite is observed for steady rapid flows over a frictional bed. Finally, a two-dimensional urban flooding phenomenon is presented, involving unsteady flow over a frictional bed. The results show that increasing the value of the Boussinesq coefficient can significantly reduce the numerical oscillations and reduce the predicted area of inundation. In order to stabilise the ADI computations, the Boussinesq coefficient could be judiciously raised or lowered depending on whether the rapid flow is steady or unsteady and whether the bed is frictional or frictionless. An increase in the Boussinesq coefficient generally leads to overprediction of the propagating speed of the flood wave over a frictionless bed, but the opposite is true when bed friction is significant.

First saccadic eye movement reveals persistent attentional guidance by implicit learning

PubMed Central

Jiang, Yuhong V.; Won, Bo-Yeong; Swallow, Khena M.

2014-01-01

Implicit learning about where a visual search target is likely to appear often speeds up search. However, whether implicit learning guides spatial attention or affects post-search decisional processes remains controversial. Using eye tracking, this study provides compelling evidence that implicit learning guides attention. In a training phase, participants often found the target in a high-frequency, “rich” quadrant of the display. When subsequently tested in a phase during which the target was randomly located, participants were twice as likely to direct the first saccadic eye movement to the previously rich quadrant than to any of the sparse quadrants. The attentional bias persisted for nearly 200 trials after training and was unabated by explicit instructions to distribute attention evenly. We propose that implicit learning guides spatial attention but in a qualitatively different manner than goal-driven attention. PMID:24512610

Equivalence between the Energy Stable Flux Reconstruction and Filtered Discontinuous Galerkin Schemes

NASA Astrophysics Data System (ADS)

Zwanenburg, Philip; Nadarajah, Siva

2016-02-01

The aim of this paper is to demonstrate the equivalence between filtered Discontinuous Galerkin (DG) schemes and the Energy Stable Flux Reconstruction (ESFR) schemes, expanding on previous demonstrations in 1D [1] and for straight-sided elements in 3D [2]. We first derive the DG and ESFR schemes in strong form and compare the respective flux penalization terms while highlighting the implications of the fundamental assumptions for stability in the ESFR formulations, notably that all ESFR scheme correction fields can be interpreted as modally filtered DG correction fields. We present the result in the general context of all higher dimensional curvilinear element formulations. Through a demonstration that there exists a weak form of the ESFR schemes which is both discretely and analytically equivalent to the strong form, we then extend the results obtained for the strong formulations to demonstrate that ESFR schemes can be interpreted as a DG scheme in weak form where discontinuous edge flux is substituted for numerical edge flux correction. Theoretical derivations are then verified with numerical results obtained from a 2D Euler testcase with curved boundaries. Given the current choice of high-order DG-type schemes and the question as to which might be best to use for a specific application, the main significance of this work is the bridge that it provides between them. Clearly outlining the similarities between the schemes results in the important conclusion that it is always less efficient to use ESFR schemes, as opposed to the weak DG scheme, when solving problems implicitly.

Numerical solution of transport equation for applications in environmental hydraulics and hydrology

NASA Astrophysics Data System (ADS)

Rashidul Islam, M.; Hanif Chaudhry, M.

1997-04-01

The advective term in the one-dimensional transport equation, when numerically discretized, produces artificial diffusion. To minimize such artificial diffusion, which vanishes only for Courant number equal to unity, transport owing to advection has been modeled separately. The numerical solution of the advection equation for a Gaussian initial distribution is well established; however, large oscillations are observed when applied to an initial distribution with sleep gradients, such as trapezoidal distribution of a constituent or propagation of mass from a continuous input. In this study, the application of seven finite-difference schemes and one polynomial interpolation scheme is investigated to solve the transport equation for both Gaussian and non-Gaussian (trapezoidal) initial distributions. The results obtained from the numerical schemes are compared with the exact solutions. A constant advective velocity is assumed throughout the transport process. For a Gaussian distribution initial condition, all eight schemes give excellent results, except the Lax scheme which is diffusive. In application to the trapezoidal initial distribution, explicit finite-difference schemes prove to be superior to implicit finite-difference schemes because the latter produce large numerical oscillations near the steep gradients. The Warming-Kutler-Lomax (WKL) explicit scheme is found to be better among this group. The Hermite polynomial interpolation scheme yields the best result for a trapezoidal distribution among all eight schemes investigated. The second-order accurate schemes are sufficiently accurate for most practical problems, but the solution of unusual problems (concentration with steep gradient) requires the application of higher-order (e.g. third- and fourth-order) accurate schemes.

Investigation of flow turning phenomenon - Effect of upstream and downstream propagation

NASA Astrophysics Data System (ADS)

Baum, Joseph D.

1988-01-01

Upstream acoustic-wave propagation in flow injected laterally through the boundary layer of a tube (simulating the flow in a solid-rocket motor) is investigated analytically. A noniterative linearized-block implicit scheme is used to solve the time-dependent compressible Navier-Stokes equations, and the results are presented in extensive graphs and characterized. Acoustic streaming interaction is shown to be significantly greater for upstream than for downstream propagation.

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.

Oscillations and stability of numerical solutions of the heat conduction equation

NASA Technical Reports Server (NTRS)

Kozdoba, L. A.; Levi, E. V.

1976-01-01

The mathematical model and results of numerical solutions are given for the one dimensional problem when the linear equations are written in a rectangular coordinate system. All the computations are easily realizable for two and three dimensional problems when the equations are written in any coordinate system. Explicit and implicit schemes are shown in tabular form for stability and oscillations criteria; the initial temperature distribution is considered uniform.

Watermarking scheme for authentication of compressed image

NASA Astrophysics Data System (ADS)

Hsieh, Tsung-Han; Li, Chang-Tsun; Wang, Shuo

2003-11-01

As images are commonly transmitted or stored in compressed form such as JPEG, to extend the applicability of our previous work, a new scheme for embedding watermark in compressed domain without resorting to cryptography is proposed. In this work, a target image is first DCT transformed and quantised. Then, all the coefficients are implicitly watermarked in order to minimize the risk of being attacked on the unwatermarked coefficients. The watermarking is done through registering/blending the zero-valued coefficients with a binary sequence to create the watermark and involving the unembedded coefficients during the process of embedding the selected coefficients. The second-order neighbors and the block itself are considered in the process of the watermark embedding in order to thwart different attacks such as cover-up, vector quantisation, and transplantation. The experiments demonstrate the capability of the proposed scheme in thwarting local tampering, geometric transformation such as cropping, and common signal operations such as lowpass filtering.

A generic efficient adaptive grid scheme for rocket propulsion modeling

NASA Technical Reports Server (NTRS)

Mo, J. D.; Chow, Alan S.

1993-01-01

The objective of this research is to develop an efficient, time-accurate numerical algorithm to discretize the Navier-Stokes equations for the predictions of internal one-, two-dimensional and axisymmetric flows. A generic, efficient, elliptic adaptive grid generator is implicitly coupled with the Lower-Upper factorization scheme in the development of ALUNS computer code. The calculations of one-dimensional shock tube wave propagation and two-dimensional shock wave capture, wave-wave interactions, shock wave-boundary interactions show that the developed scheme is stable, accurate and extremely robust. The adaptive grid generator produced a very favorable grid network by a grid speed technique. This generic adaptive grid generator is also applied in the PARC and FDNS codes and the computational results for solid rocket nozzle flowfield and crystal growth modeling by those codes will be presented in the conference, too. This research work is being supported by NASA/MSFC.

Supersonic nonlinear potential analysis

NASA Technical Reports Server (NTRS)

Siclari, M. J.

1984-01-01

The NCOREL computer code was established to compute supersonic flow fields of wings and bodies. The method encompasses an implicit finite difference transonic relaxation method to solve the full potential equation in a spherical coordinate system. Two basic topic to broaden the applicability and usefulness of the present method which is encompassed within the computer code NCOREL for the treatment of supersonic flow problems were studied. The first topic is that of computing efficiency. Accelerated schemes are in use for transonic flow problems. One such scheme is the approximate factorization (AF) method and an AF scheme to the supersonic flow problem is developed. The second topic is the computation of wake flows. The proper modeling of wake flows is important for multicomponent configurations such as wing-body and multiple lifting surfaces where the wake of one lifting surface has a pronounced effect on a downstream body or other lifting surfaces.

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.

New solution decomposition and minimization schemes for Poisson-Boltzmann equation in calculation of biomolecular electrostatics

NASA Astrophysics Data System (ADS)

Xie, Dexuan

2014-10-01

The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model in the calculation of electrostatic potential energy for biomolecules in ionic solvent, but its numerical solution remains a challenge due to its strong singularity and nonlinearity caused by its singular distribution source terms and exponential nonlinear terms. To effectively deal with such a challenge, in this paper, new solution decomposition and minimization schemes are proposed, together with a new PBE analysis on solution existence and uniqueness. Moreover, a PBE finite element program package is developed in Python based on the FEniCS program library and GAMer, a molecular surface and volumetric mesh generation program package. Numerical tests on proteins and a nonlinear Born ball model with an analytical solution validate the new solution decomposition and minimization schemes, and demonstrate the effectiveness and efficiency of the new PBE finite element program package.

The mimetic finite difference method for the Landau–Lifshitz equation

DOE PAGES

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

2017-01-01

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

Incompressible spectral-element method: Derivation of equations

NASA Technical Reports Server (NTRS)

Deanna, Russell G.

1993-01-01

A fractional-step splitting scheme breaks the full Navier-Stokes equations into explicit and implicit portions amenable to the calculus of variations. Beginning with the functional forms of the Poisson and Helmholtz equations, we substitute finite expansion series for the dependent variables and derive the matrix equations for the unknown expansion coefficients. This method employs a new splitting scheme which differs from conventional three-step (nonlinear, pressure, viscous) schemes. The nonlinear step appears in the conventional, explicit manner, the difference occurs in the pressure step. Instead of solving for the pressure gradient using the nonlinear velocity, we add the viscous portion of the Navier-Stokes equation from the previous time step to the velocity before solving for the pressure gradient. By combining this 'predicted' pressure gradient with the nonlinear velocity in an explicit term, and the Crank-Nicholson method for the viscous terms, we develop a Helmholtz equation for the final velocity.

The mimetic finite difference method for the Landau–Lifshitz equation

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

Kim, Eugenia Hail; Lipnikov, Konstantin Nikolayevich

The Landau–Lifshitz equation describes the dynamics of the magnetization inside ferromagnetic materials. This equation is highly nonlinear and has a non-convex constraint (the magnitude of the magnetization is constant) which poses interesting challenges in developing numerical methods. We develop and analyze explicit and implicit mimetic finite difference schemes for this equation. These schemes work on general polytopal meshes which provide enormous flexibility to model magnetic devices with various shapes. A projection on the unit sphere is used to preserve the magnitude of the magnetization. We also provide a proof that shows the exchange energy is decreasing in certain conditions. Themore » developed schemes are tested on general meshes that include distorted and randomized meshes. As a result, the numerical experiments include a test proposed by the National Institute of Standard and Technology and a test showing formation of domain wall structures in a thin film.« less

Semi-local machine-learned kinetic energy density functional with third-order gradients of electron density

NASA Astrophysics Data System (ADS)

Seino, Junji; Kageyama, Ryo; Fujinami, Mikito; Ikabata, Yasuhiro; Nakai, Hiromi

2018-06-01

A semi-local kinetic energy density functional (KEDF) was constructed based on machine learning (ML). The present scheme adopts electron densities and their gradients up to third-order as the explanatory variables for ML and the Kohn-Sham (KS) kinetic energy density as the response variable in atoms and molecules. Numerical assessments of the present scheme were performed in atomic and molecular systems, including first- and second-period elements. The results of 37 conventional KEDFs with explicit formulae were also compared with those of the ML KEDF with an implicit formula. The inclusion of the higher order gradients reduces the deviation of the total kinetic energies from the KS calculations in a stepwise manner. Furthermore, our scheme with the third-order gradient resulted in the closest kinetic energies to the KS calculations out of the presented functionals.

Application of Jacobian-free Newton–Krylov method in implicitly solving two-fluid six-equation two-phase flow problems: Implementation, validation and benchmark

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-03-09

This work represents a first-of-its-kind successful application to employ advanced numerical methods in solving realistic two-phase flow problems with two-fluid six-equation two-phase flow model. These advanced numerical methods include high-resolution spatial discretization scheme with staggered grids (high-order) fully implicit time integration schemes, and Jacobian-free Newton–Krylov (JFNK) method as the nonlinear solver. The computer code developed in this work has been extensively validated with existing experimental flow boiling data in vertical pipes and rod bundles, which cover wide ranges of experimental conditions, such as pressure, inlet mass flux, wall heat flux and exit void fraction. Additional code-to-code benchmark with the RELAP5-3Dmore » code further verifies the correct code implementation. The combined methods employed in this work exhibit strong robustness in solving two-phase flow problems even when phase appearance (boiling) and realistic discrete flow regimes are considered. Transitional flow regimes used in existing system analysis codes, normally introduced to overcome numerical difficulty, were completely removed in this work. As a result, this in turn provides the possibility to utilize more sophisticated flow regime maps in the future to further improve simulation accuracy.« less

A New Cell-Centered Implicit Numerical Scheme for Ions in the 2-D Axisymmetric Code Hall2de

NASA Technical Reports Server (NTRS)

Lopez Ortega, Alejandro; Mikellides, Ioannis G.

2014-01-01

We present a new algorithm in the Hall2De code to simulate the ion hydrodynamics in the acceleration channel and near plume regions of Hall-effect thrusters. This implementation constitutes an upgrade of the capabilities built in the Hall2De code. The equations of mass conservation and momentum for unmagnetized ions are solved using a conservative, finite-volume, cell-centered scheme on a magnetic-field-aligned grid. Major computational savings are achieved by making use of an implicit predictor/multi-corrector algorithm for time evolution. Inaccuracies in the prediction of the motion of low-energy ions in the near plume in hydrodynamics approaches are addressed by implementing a multi-fluid algorithm that tracks ions of different energies separately. A wide range of comparisons with measurements are performed to validate the new ion algorithms. Several numerical experiments with the location and value of the anomalous collision frequency are also presented. Differences in the plasma properties in the near-plume between the single fluid and multi-fluid approaches are discussed. We complete our validation by comparing predicted erosion rates at the channel walls of the thruster with measurements. Erosion rates predicted by the plasma properties obtained from simulations replicate accurately measured rates of erosion within the uncertainty range of the sputtering models employed.

Further along the Road Less Traveled: AMBER ff15ipq, an Original Protein Force Field Built on a Self-Consistent Physical Model

PubMed Central

2016-01-01

We present the AMBER ff15ipq force field for proteins, the second-generation force field developed using the Implicitly Polarized Q (IPolQ) scheme for deriving implicitly polarized atomic charges in the presence of explicit solvent. The ff15ipq force field is a complete rederivation including more than 300 unique atomic charges, 900 unique torsion terms, 60 new angle parameters, and new atomic radii for polar hydrogens. The atomic charges were derived in the context of the SPC/Eb water model, which yields more-accurate rotational diffusion of proteins and enables direct calculation of nuclear magnetic resonance (NMR) relaxation parameters from molecular dynamics simulations. The atomic radii improve the accuracy of modeling salt bridge interactions relative to contemporary fixed-charge force fields, rectifying a limitation of ff14ipq that resulted from its use of pair-specific Lennard-Jones radii. In addition, ff15ipq reproduces penta-alanine J-coupling constants exceptionally well, gives reasonable agreement with NMR relaxation rates, and maintains the expected conformational propensities of structured proteins/peptides, as well as disordered peptides—all on the microsecond (μs) time scale, which is a critical regime for drug design applications. These encouraging results demonstrate the power and robustness of our automated methods for deriving new force fields. All parameters described here and the mdgx program used to fit them are included in the AmberTools16 distribution. PMID:27399642

A Unified Approach to Adaptive Neural Control for Nonlinear Discrete-Time Systems With Nonlinear Dead-Zone Input.

PubMed

Liu, Yan-Jun; Gao, Ying; Tong, Shaocheng; Chen, C L Philip

2016-01-01

In this paper, an effective adaptive control approach is constructed to stabilize a class of nonlinear discrete-time systems, which contain unknown functions, unknown dead-zone input, and unknown control direction. Different from linear dead zone, the dead zone, in this paper, is a kind of nonlinear dead zone. To overcome the noncausal problem, which leads to the control scheme infeasible, the systems can be transformed into a m -step-ahead predictor. Due to nonlinear dead-zone appearance, the transformed predictor still contains the nonaffine function. In addition, it is assumed that the gain function of dead-zone input and the control direction are unknown. These conditions bring about the difficulties and the complicacy in the controller design. Thus, the implicit function theorem is applied to deal with nonaffine dead-zone appearance, the problem caused by the unknown control direction can be resolved through applying the discrete Nussbaum gain, and the neural networks are used to approximate the unknown function. Based on the Lyapunov theory, all the signals of the resulting closed-loop system are proved to be semiglobal uniformly ultimately bounded. Moreover, the tracking error is proved to be regulated to a small neighborhood around zero. The feasibility of the proposed approach is demonstrated by a simulation example.

Cathodal Transcranial Direct Current Stimulation Over Left Dorsolateral Prefrontal Cortex Area Promotes Implicit Motor Learning in a Golf Putting Task.

PubMed

Zhu, Frank F; Yeung, Andrew Y; Poolton, Jamie M; Lee, Tatia M C; Leung, Gilberto K K; Masters, Rich S W

2015-01-01

Implicit motor learning is characterized by low dependence on working memory and stable performance despite stress, fatigue, or multi-tasking. However, current paradigms for implicit motor learning are based on behavioral interventions that are often task-specific and limited when applied in practice. To investigate whether cathodal transcranial direct current stimulation (tDCS) over the left dorsolateral prefrontal cortex (DLPFC) area during motor learning suppressed working memory activity and reduced explicit verbal-analytical involvement in movement control, thereby promoting implicit motor learning. Twenty-seven healthy individuals practiced a golf putting task during a Training Phase while receiving either real cathodal tDCS stimulation over the left DLPFC area or sham stimulation. Their performance was assessed during a Test phase on another day. Verbal working memory capacity was assessed before and after the Training Phase, and before the Test Phase. Compared to sham stimulation, real stimulation suppressed verbal working memory activity after the Training Phase, but enhanced golf putting performance during the Training Phase and the Test Phase, especially when participants were required to multi-task. Cathodal tDCS over the left DLPFC may foster implicit motor learning and performance in complex real-life motor tasks that occur during sports, surgery or motor rehabilitation. Copyright © 2015 Elsevier Inc. All rights reserved.

Convergence issues in domain decomposition parallel computation of hovering rotor

NASA Astrophysics Data System (ADS)

Xiao, Zhongyun; Liu, Gang; Mou, Bin; Jiang, Xiong

2018-05-01

Implicit LU-SGS time integration algorithm has been widely used in parallel computation in spite of its lack of information from adjacent domains. When applied to parallel computation of hovering rotor flows in a rotating frame, it brings about convergence issues. To remedy the problem, three LU factorization-based implicit schemes (consisting of LU-SGS, DP-LUR and HLU-SGS) are investigated comparatively. A test case of pure grid rotation is designed to verify these algorithms, which show that LU-SGS algorithm introduces errors on boundary cells. When partition boundaries are circumferential, errors arise in proportion to grid speed, accumulating along with the rotation, and leading to computational failure in the end. Meanwhile, DP-LUR and HLU-SGS methods show good convergence owing to boundary treatment which are desirable in domain decomposition parallel computations.

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.

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.

A stable and accurate partitioned algorithm for conjugate heat transfer

NASA Astrophysics Data System (ADS)

Meng, F.; Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.

2017-09-01

We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in an implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems together with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode theory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized-Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and diffusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. The CHAMP scheme is also developed for general curvilinear grids and CHT examples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.

Minimal gain marching schemes: searching for unstable steady-states with unsteady solvers

NASA Astrophysics Data System (ADS)

de S. Teixeira, Renan; S. de B. Alves, Leonardo

2017-12-01

Reference solutions are important in several applications. They are used as base states in linear stability analyses as well as initial conditions and reference states for sponge zones in numerical simulations, just to name a few examples. Their accuracy is also paramount in both fields, leading to more reliable analyses and efficient simulations, respectively. Hence, steady-states usually make the best reference solutions. Unfortunately, standard marching schemes utilized for accurate unsteady simulations almost never reach steady-states of unstable flows. Steady governing equations could be solved instead, by employing Newton-type methods often coupled with continuation techniques. However, such iterative approaches do require large computational resources and very good initial guesses to converge. These difficulties motivated the development of a technique known as selective frequency damping (SFD) (Åkervik et al. in Phys Fluids 18(6):068102, 2006). It adds a source term to the unsteady governing equations that filters out the unstable frequencies, allowing a steady-state to be reached. This approach does not require a good initial condition and works well for self-excited flows, where a single nonzero excitation frequency is selected by either absolute or global instability mechanisms. On the other hand, it seems unable to damp stationary disturbances. Furthermore, flows with a broad unstable frequency spectrum might require the use of multiple filters, which delays convergence significantly. Both scenarios appear in convectively, absolutely or globally unstable flows. An alternative approach is proposed in the present paper. It modifies the coefficients of a marching scheme in such a way that makes the absolute value of its linear gain smaller than one within the required unstable frequency spectra, allowing the respective disturbance amplitudes to decay given enough time. These ideas are applied here to implicit multi-step schemes. A few chosen test cases shows that they enable convergence toward solutions that are unstable to stationary and oscillatory disturbances, with either a single or multiple frequency content. Finally, comparisons with SFD are also performed, showing significant reduction in computer cost for complex flows by using the implicit multi-step MGM schemes.

A stable and accurate partitioned algorithm for conjugate heat transfer

DOE PAGES

Meng, F.; Banks, J. W.; Henshaw, W. D.; ...

2017-04-25

We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in a implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems togethermore » with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode the- ory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized- Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and dif- fusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. Lastly, the CHAMP scheme is also developed for general curvilinear grids and CHT ex- amples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.« less

A Class of High-Resolution Explicit and Implicit Shock-Capturing Methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1994-01-01

The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art developments and applications to fluid dynamics problems can only be found in meeting proceedings, scientific journals and internal reports. This paper attempts to give a unified and generalized formulation of a class of high-resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock waves, perfect gases, equilibrium real gases and nonequilibrium flow computations. These numerical methods are formulated for the purpose of ease and efficient implementation into a practical computer code. The various constructions of high-resolution shock-capturing methods fall nicely into the present framework and a computer code can be implemented with the various methods as separate modules. Included is a systematic overview of the basic design principle of the various related numerical methods. Special emphasis will be on the construction of the basic nonlinear, spatially second and third-order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and flux-vector splitting approaches. Generalization of these methods to efficiently include real gases and large systems of nonequilibrium flows will be discussed. Some perbolic conservation laws to problems containing stiff source terms and terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for one-, two- and three-dimensional gas-dynamics problems. The use of the Lax-Friedrichs numerical flux to obtain high-resolution shock-capturing schemes is generalized. This method can be extended to nonlinear systems of equations without the use of Riemann solvers or flux-vector splitting approaches and thus provides a large savings for multidimensional, equilibrium real gases and nonequilibrium flow computations.

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.

Implicit and explicit self-esteem as concurrent predictors of suicidal ideation, depressive symptoms, and loneliness.

PubMed

Creemers, Daan H M; Scholte, Ron H J; Engels, Rutger C M E; Prinstein, Mitchell J; Wiers, Reinout W

2012-03-01

The aim of the present study was to examine whether explicit and implicit self-esteem, the interaction between these two constructs, and their discrepancy are associated with depressive symptoms, suicidal ideation, and loneliness. Participants were 95 young female adults (M = 21.2 years, SD = 1.88) enrolled in higher education. We administered the Name Letter Task to measure implicit self-esteem, and the Rosenberg self-esteem scale to assess explicit self-esteem. The results indicated that explicit but not implicit self-esteem was negatively associated with depressive symptoms, suicidal ideation, and loneliness. The interaction of implicit and explicit self-esteem was associated with suicidal ideation, indicating that participants with high implicit self-esteem combined with a low explicit self-esteem showed more suicidal ideation. Furthermore, the size of the discrepancy between implicit and explicit self-esteem was positively associated with depressive symptoms, suicidal ideation, and loneliness. In addition, results showed that the direction of the discrepancy is an important: damaged self-esteem (high implicit self-esteem combined with low explicit self-esteem) was consistently associated with increased levels of depressive symptoms, suicidal ideation, and loneliness, while defensive or fragile self-esteem (high explicit and low implicit self-esteem) was not. Together, these findings provide new insights into the relationship of implicit and explicit self-esteem with depressive symptoms, suicidal ideation, and loneliness. Copyright © 2011 Elsevier Ltd. All rights reserved.

Discrepancies between explicit and implicit self-esteem and their relationship to symptoms of depression and mania.

PubMed

Pavlickova, Hana; Turnbull, Oliver H; Bentall, Richard P

2014-09-01

Self-esteem is a key feature of bipolar symptomatology. However, so far no study has examined the interaction between explicit and implicit self-esteem in individuals vulnerable to bipolar disorder. Cross-sectional design was employed. Thirty children of parents with bipolar disorder and 30 offspring of control parents completed Hamilton Rating Scale for Depression, the Bech-Rafaelson Mania Scale, the Self-esteem Rating Scale and the Implicit Association Test. No differences between groups were revealed in levels of explicit or implicit self-esteem. However, bipolar offspring showed increased levels of symptoms of depression and mania. Furthermore, depressive symptoms were associated with low explicit self-esteem, whilst symptoms of mania were associated with low implicit self-esteem. When self-esteem discrepancies were examined, damaged self-esteem (i.e., low explicit but high implicit self-esteem) was associated with depression, whilst no associations between mania and self-esteem discrepancies were found. Not only explicit, but also implicit self-esteem, and the interactions between the two are of relevance in bipolar symptoms. Clinical implications and future research directions are discussed. Explicit as well as implicit SE, and particularly their relationship, are relevant for mental health. Fluctuations in implicit SE may serve as an early indicator for risk of bipolarity. Psychotherapeutic approaches may be more suitable for one kind of SE challenge than the other. © 2013 The British Psychological Society.

Primary motor and premotor cortex in implicit sequence learning--evidence for competition between implicit and explicit human motor memory systems.

PubMed

Kantak, Shailesh S; Mummidisetty, Chaithanya K; Stinear, James W

2012-09-01

Implicit and explicit memory systems for motor skills compete with each other during and after motor practice. Primary motor cortex (M1) is known to be engaged during implicit motor learning, while dorsal premotor cortex (PMd) is critical for explicit learning. To elucidate the neural substrates underlying the interaction between implicit and explicit memory systems, adults underwent a randomized crossover experiment of anodal transcranial direct current stimulation (AtDCS) applied over M1, PMd or sham stimulation during implicit motor sequence (serial reaction time task, SRTT) practice. We hypothesized that M1-AtDCS during practice will enhance online performance and offline learning of the implicit motor sequence. In contrast, we also hypothesized that PMd-AtDCS will attenuate performance and retention of the implicit motor sequence. Implicit sequence performance was assessed at baseline, at the end of acquisition (EoA), and 24 h after practice (retention test, RET). M1-AtDCS during practice significantly improved practice performance and supported offline stabilization compared with Sham tDCS. Performance change from EoA to RET revealed that PMd-AtDCS during practice attenuated offline stabilization compared with M1-AtDCS and sham stimulation. The results support the role of M1 in implementing online performance gains and offline stabilization for implicit motor sequence learning. In contrast, enhancing the activity within explicit motor memory network nodes such as the PMd during practice may be detrimental to offline stabilization of the learned implicit motor sequence. These results support the notion of competition between implicit and explicit motor memory systems and identify underlying neural substrates that are engaged in this competition. © 2012 The Authors. European Journal of Neuroscience © 2012 Federation of European Neuroscience Societies and Blackwell Publishing Ltd.

Awareness of Implicit Attitudes

PubMed Central

Hahn, Adam; Judd, Charles M.; Hirsh, Holen K.; Blair, Irene V.

2013-01-01

Research on implicit attitudes has raised questions about how well people know their own attitudes. Most research on this question has focused on the correspondence between measures of implicit attitudes and measures of explicit attitudes, with low correspondence interpreted as showing that people have little awareness of their implicit attitudes. We took a different approach and directly asked participants to predict their results on upcoming IAT measures of implicit attitudes toward five different social groups. We found that participants were surprisingly accurate in their predictions. Across four studies, predictions were accurate regardless of whether implicit attitudes were described as true attitudes or culturally learned associations (Studies 1 and 2), regardless of whether predictions were made as specific response patterns (Study 1) or as conceptual responses (Studies 2–4), and regardless of how much experience or explanation participants received before making their predictions (Study 4). Study 3 further suggested that participants’ predictions reflected unique insight into their own implicit responses, beyond intuitions about how people in general might respond. Prediction accuracy occurred despite generally low correspondence between implicit and explicit measures of attitudes, as found in prior research. All together, the research findings cast doubt on the belief that attitudes or evaluations measured by the IAT necessarily reflect unconscious attitudes. PMID:24294868

When truth is personally inconvenient, attitudes change: the impact of extreme weather on implicit support for green politicians and explicit climate-change beliefs.

PubMed

Rudman, Laurie A; McLean, Meghan C; Bunzl, Martin

2013-11-01

A naturalistic investigation of New Jersey residents, both before and after they experienced Hurricanes Irene and Sandy, examined support for politicians committed or opposed to policies designed to combat climate change. At Time 1, before both hurricanes, participants showed negative implicit attitudes toward a green politician, but at Time 2, after the hurricanes, participants drawn from the same cohort showed a reversed automatic preference. Moreover, those who were significantly affected by Hurricane Sandy were especially likely to implicitly prefer the green politician, and implicit attitudes were the best predictor of voting after the storms, whereas explicit climate-change beliefs was the best predictor before the storms. In concert, the results suggest that direct experience with extreme weather can increase pro-environmentalism, and further support conceptualizing affective experiences as a source of implicit attitudes.

Human Infant Faces Provoke Implicit Positive Affective Responses in Parents and Non-Parents Alike

PubMed Central

Senese, Vincenzo Paolo; De Falco, Simona; Bornstein, Marc H.; Caria, Andrea; Buffolino, Simona; Venuti, Paola

2013-01-01

Human infants' complete dependence on adult caregiving suggests that mechanisms associated with adult responsiveness to infant cues might be deeply embedded in the brain. Behavioural and neuroimaging research has produced converging evidence for adults' positive disposition to infant cues, but these studies have not investigated directly the valence of adults' reactions, how they are moderated by biological and social factors, and if they relate to child caregiving. This study examines implicit affective responses of 90 adults toward faces of human and non-human (cats and dogs) infants and adults. Implicit reactions were assessed with Single Category Implicit Association Tests, and reports of childrearing behaviours were assessed by the Parental Style Questionnaire. The results showed that human infant faces represent highly biologically relevant stimuli that capture attention and are implicitly associated with positive emotions. This reaction holds independent of gender and parenthood status and is associated with ideal parenting behaviors. PMID:24282537

Human infant faces provoke implicit positive affective responses in parents and non-parents alike.

PubMed

Senese, Vincenzo Paolo; De Falco, Simona; Bornstein, Marc H; Caria, Andrea; Buffolino, Simona; Venuti, Paola

2013-01-01

Human infants' complete dependence on adult caregiving suggests that mechanisms associated with adult responsiveness to infant cues might be deeply embedded in the brain. Behavioural and neuroimaging research has produced converging evidence for adults' positive disposition to infant cues, but these studies have not investigated directly the valence of adults' reactions, how they are moderated by biological and social factors, and if they relate to child caregiving. This study examines implicit affective responses of 90 adults toward faces of human and non-human (cats and dogs) infants and adults. Implicit reactions were assessed with Single Category Implicit Association Tests, and reports of childrearing behaviours were assessed by the Parental Style Questionnaire. The results showed that human infant faces represent highly biologically relevant stimuli that capture attention and are implicitly associated with positive emotions. This reaction holds independent of gender and parenthood status and is associated with ideal parenting behaviors.

Application of a derivative-free global optimization algorithm to the derivation of a new time integration scheme for the simulation of incompressible turbulence

NASA Astrophysics Data System (ADS)

Alimohammadi, Shahrouz; Cavaglieri, Daniele; Beyhaghi, Pooriya; Bewley, Thomas R.

2016-11-01

This work applies a recently developed Derivative-free optimization algorithm to derive a new mixed implicit-explicit (IMEX) time integration scheme for Computational Fluid Dynamics (CFD) simulations. This algorithm allows imposing a specified order of accuracy for the time integration and other important stability properties in the form of nonlinear constraints within the optimization problem. In this procedure, the coefficients of the IMEX scheme should satisfy a set of constraints simultaneously. Therefore, the optimization process, at each iteration, estimates the location of the optimal coefficients using a set of global surrogates, for both the objective and constraint functions, as well as a model of the uncertainty function of these surrogates based on the concept of Delaunay triangulation. This procedure has been proven to converge to the global minimum of the constrained optimization problem provided the constraints and objective functions are twice differentiable. As a result, a new third-order, low-storage IMEX Runge-Kutta time integration scheme is obtained with remarkably fast convergence. Numerical tests are then performed leveraging the turbulent channel flow simulations to validate the theoretical order of accuracy and stability properties of the new scheme.

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

NASA Technical Reports Server (NTRS)

Hixon, Duane; Sankar, L. N.

1993-01-01

During the past two decades, there has been significant progress in the field of numerical simulation of unsteady compressible viscous flows. At present, a variety of solution techniques exist such as the transonic small disturbance analyses (TSD), transonic full potential equation-based methods, unsteady Euler solvers, and unsteady Navier-Stokes solvers. These advances have been made possible by developments in three areas: (1) improved numerical algorithms; (2) automation of body-fitted grid generation schemes; and (3) advanced computer architectures with vector processing and massively parallel processing features. In this work, the GMRES scheme has been considered as a candidate for acceleration of a Newton iteration time marching scheme for unsteady 2-D and 3-D compressible viscous flow calculation; from preliminary calculations, this will provide up to a 65 percent reduction in the computer time requirements over the existing class of explicit and implicit time marching schemes. The proposed method has ben tested on structured grids, but is flexible enough for extension to unstructured grids. The described scheme has been tested only on the current generation of vector processor architecture of the Cray Y/MP class, but should be suitable for adaptation to massively parallel machines.

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.

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

NASA Astrophysics Data System (ADS)

Chen, G.; Chacón, L.; Barnes, D. C.

2011-08-01

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

Forced in-plane vibration of a thick ring on a unilateral elastic foundation

NASA Astrophysics Data System (ADS)

Wang, Chunjian; Ayalew, Beshah; Rhyne, Timothy; Cron, Steve; Dailliez, Benoit

2016-10-01

Most existing studies of a deformable ring on elastic foundation rely on the assumption of a linear foundation. These assumptions are insufficient in cases where the foundation may have a unilateral stiffness that vanishes in compression or tension such as in non-pneumatic tires and bushing bearings. This paper analyzes the in-plane dynamics of such a thick ring on a unilateral elastic foundation, specifically, on a two-parameter unilateral elastic foundation, where the stiffness of the foundation is treated as linear in the circumferential direction but unilateral (i.e. collapsible or tensionless) in the radial direction. The thick ring is modeled as an orthotropic and extensible circular Timoshenko beam. An arbitrarily distributed time-varying in-plane force is considered as the excitation. The Equations of Motion are explicitly derived and a solution method is proposed that uses an implicit Newmark scheme for the time domain solution and an iterative compensation approach to determine the unilateral zone of the foundation at each time step. The dynamic axle force transmission is also analyzed. Illustrative forced vibration responses obtained from the proposed model and solution method are compared with those obtained from a finite element model.

One-step methods for the prediction of orbital motion, taking its periodic components into account

NASA Astrophysics Data System (ADS)

Lavrov, K. N.

1988-03-01

The paper examines the design and analysis of the properties of implicit one-step integration methods which use the trigonometric approximation of ordinary differential equations containing periodic components. With reference to an orbital-motion prediction example, it is shown that the proposed schemes are more efficient in terms of computer memory than Everhart's (1974) approach. The results obtained make it possible to improve Everhart's method.

High Fidelity and Multiscale Algorithms for Collisional-radiative and Nonequilibrium Plasmas (Briefing Charts)

DTIC Science & Technology

2014-07-01

of models for variable conditions: – Use implicit models to eliminate constraint of sequence of fast time scales: c, ve, – Price to pay: lack...collisions: – Elastic – Bragiinski terms – Inelastic – warning! Rates depend on both T and relative velocity – Multi-fluid CR model from...merge/split for particle management, efficient sampling, inelastic collisions … – Level grouping schemes of electronic states, for dynamical coarse

On the Solution of the Three-Dimensional Flowfield About a Flow-Through Nacelle. Ph.D. Thesis

NASA Technical Reports Server (NTRS)

Compton, William Bernard

1985-01-01

The solution of the three dimensional flow field for a flow through nacelle was studied. Both inviscid and viscous inviscid interacting solutions were examined. Inviscid solutions were obtained with two different computational procedures for solving the three dimensional Euler equations. The first procedure employs an alternating direction implicit numerical algorithm, and required the development of a complete computational model for the nacelle problem. The second computational technique employs a fourth order Runge-Kutta numerical algorithm which was modified to fit the nacelle problem. Viscous effects on the flow field were evaluated with a viscous inviscid interacting computational model. This model was constructed by coupling the explicit Euler solution procedure with a flag entrainment boundary layer solution procedure in a global iteration scheme. The computational techniques were used to compute the flow field for a long duct turbofan engine nacelle at free stream Mach numbers of 0.80 and 0.94 and angles of attack of 0 and 4 deg.

Improved Boundary Layer Module (BLM) for the Solid Performance Program (SPP)

NASA Astrophysics Data System (ADS)

Coats, D. E.; Cebeci, T.

1982-03-01

The requirements for a replacement to the Bartz boundary layer code, the standard method of computing the performance loss due to viscous effects by the solid performance program, were discussed by the propulsion community along with four nationally recognized boundary layer experts. A consensus was reached regarding the preferred features for the analysis of the replacement code. The major points that were agreed upon are: (1) finite difference methods are preferred over integral methods; (2) a single equation eddy viscosity model was considered to be adequate for the purpose of computing performance loss; (3) a variable grid capability in both coordinate directions would be required; (4) a proven finite difference algorithm which is not stability restricted should be used, that is, an implicit numerical scheme would be required; and (5) the replacement code should be able to compute both turbulent and laminar flows. The program should treat mass addition at the wall as well as being able to calculate a stagnation point starting line.

Advanced Imaging Methods for Long-Baseline Optical Interferometry

NASA Astrophysics Data System (ADS)

Le Besnerais, G.; Lacour, S.; Mugnier, L. M.; Thiebaut, E.; Perrin, G.; Meimon, S.

2008-11-01

We address the data processing methods needed for imaging with a long baseline optical interferometer. We first describe parametric reconstruction approaches and adopt a general formulation of nonparametric image reconstruction as the solution of a constrained optimization problem. Within this framework, we present two recent reconstruction methods, Mira and Wisard, representative of the two generic approaches for dealing with the missing phase information. Mira is based on an implicit approach and a direct optimization of a Bayesian criterion while Wisard adopts a self-calibration approach and an alternate minimization scheme inspired from radio-astronomy. Both methods can handle various regularization criteria. We review commonly used regularization terms and introduce an original quadratic regularization called ldquosoft support constraintrdquo that favors the object compactness. It yields images of quality comparable to nonquadratic regularizations on the synthetic data we have processed. We then perform image reconstructions, both parametric and nonparametric, on astronomical data from the IOTA interferometer, and discuss the respective roles of parametric and nonparametric approaches for optical interferometric imaging.

A solid reactor core thermal model for nuclear thermal rockets

NASA Astrophysics Data System (ADS)

Rider, William J.; Cappiello, Michael W.; Liles, Dennis R.

1991-01-01

A Helium/Hydrogen Cooled Reactor Analysis (HERA) computer code has been developed. HERA has the ability to model arbitrary geometries in three dimensions, which allows the user to easily analyze reactor cores constructed of prismatic graphite elements. The code accounts for heat generation in the fuel, control rods, and other structures; conduction and radiation across gaps; convection to the coolant; and a variety of boundary conditions. The numerical solution scheme has been optimized for vector computers, making long transient analyses economical. Time integration is either explicit or implicit, which allows the use of the model to accurately calculate both short- or long-term transients with an efficient use of computer time. Both the basic spatial and temporal integration schemes have been benchmarked against analytical solutions.

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.

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.

Efficiency and Accuracy of Time-Accurate Turbulent Navier-Stokes Computations

NASA Technical Reports Server (NTRS)

Rumsey, Christopher L.; Sanetrik, Mark D.; Biedron, Robert T.; Melson, N. Duane; Parlette, Edward B.

1995-01-01

The accuracy and efficiency of two types of subiterations in both explicit and implicit Navier-Stokes codes are explored for unsteady laminar circular-cylinder flow and unsteady turbulent flow over an 18-percent-thick circular-arc (biconvex) airfoil. Grid and time-step studies are used to assess the numerical accuracy of the methods. Nonsubiterative time-stepping schemes and schemes with physical time subiterations are subject to time-step limitations in practice that are removed by pseudo time sub-iterations. Computations for the circular-arc airfoil indicate that a one-equation turbulence model predicts the unsteady separated flow better than an algebraic turbulence model; also, the hysteresis with Mach number of the self-excited unsteadiness due to shock and boundary-layer separation is well predicted.

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

NASA Astrophysics Data System (ADS)

Li, Gaohua; Fu, Xiang; Wang, Fuxin

2017-10-01

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

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.

Explicit pre-training instruction does not improve implicit perceptual-motor sequence learning

PubMed Central

Sanchez, Daniel J.; Reber, Paul J.

2012-01-01

Memory systems theory argues for separate neural systems supporting implicit and explicit memory in the human brain. Neuropsychological studies support this dissociation, but empirical studies of cognitively healthy participants generally observe that both kinds of memory are acquired to at least some extent, even in implicit learning tasks. A key question is whether this observation reflects parallel intact memory systems or an integrated representation of memory in healthy participants. Learning of complex tasks in which both explicit instruction and practice is used depends on both kinds of memory, and how these systems interact will be an important component of the learning process. Theories that posit an integrated, or single, memory system for both types of memory predict that explicit instruction should contribute directly to strengthening task knowledge. In contrast, if the two types of memory are independent and acquired in parallel, explicit knowledge should have no direct impact and may serve in a “scaffolding” role in complex learning. Using an implicit perceptual-motor sequence learning task, the effect of explicit pre-training instruction on skill learning and performance was assessed. Explicit pre-training instruction led to robust explicit knowledge, but sequence learning did not benefit from the contribution of pre-training sequence memorization. The lack of an instruction benefit suggests that during skill learning, implicit and explicit memory operate independently. While healthy participants will generally accrue parallel implicit and explicit knowledge in complex tasks, these types of information appear to be separately represented in the human brain consistent with multiple memory systems theory. PMID:23280147

Retrieval of Concrete Words Involves More Contextual Information than Abstract Words: Multiple Components for the Concreteness Effect

ERIC Educational Resources Information Center

Xiao, Xin; Zhao, Di; Zhang, Qin; Guo, Chun-yan

2012-01-01

The current study used the directed forgetting paradigm in implicit and explicit memory to investigate the concreteness effect. Event-related potentials (ERPs) were recorded to explore the neural basis of this phenomenon. The behavioral results showed a clear concreteness effect in both implicit and explicit memory tests; participants responded…

Phrase Length Matters: The Interplay between Implicit Prosody and Syntax in Korean "Garden Path" Sentences

ERIC Educational Resources Information Center

Hwang, Hyekyung; Steinhauer, Karsten

2011-01-01

In spoken language comprehension, syntactic parsing decisions interact with prosodic phrasing, which is directly affected by phrase length. Here we used ERPs to examine whether a similar effect holds for the on-line processing of written sentences during silent reading, as suggested by theories of "implicit prosody." Ambiguous Korean sentence…

Subjective Evaluations of Intelligence and Academic Self-Concept Predict Academic Achievement: Evidence from a Selective Student Population

ERIC Educational Resources Information Center

Kornilova, Tatiana V.; Kornilov, Sergey A.; Chumakova, Maria A.

2009-01-01

The study examined the relationship between implicit theories, goal orientations, subjective and test estimates of intelligence, academic self-concept, and achievement in a selective student population (N=300). There was no direct impact of implicit theories of intelligence and goal orientations on achievement. However, subjective evaluations of…

Nutrition warnings as front-of-pack labels: influence of design features on healthfulness perception and attentional capture.

PubMed

Cabrera, Manuel; Machín, Leandro; Arrúa, Alejandra; Antúnez, Lucía; Curutchet, María Rosa; Giménez, Ana; Ares, Gastón

2017-12-01

Warnings are a new directive front-of-pack (FOP) nutrition labelling scheme that highlights products with high content of key nutrients. The design of warnings influences their ability to catch consumers' attention and to clearly communicate their intended meaning, which are key determinants of their effectiveness. The aim of the present work was to evaluate the influence of design features of warnings as a FOP nutrition labelling scheme on perceived healthfulness and attentional capture. Five studies with a total of 496 people were carried out. In the first study, the association of colour and perceived healthfulness was evaluated in an online survey in which participants had to rate their perceived healthfulness of eight colours. In the second study, the influence of colour, shape and textual information on perceived healthfulness was evaluated using choice-conjoint analysis. The third study focused on implicit associations between two design features (shape and colour) on perceived healthfulness. The fourth and fifth studies used visual search to evaluate the influence of colour, size and position of the warnings on attentional capture. Perceived healthfulness was significantly influenced by shape, colour and textual information. Colour was the variable with the largest contribution to perceived healthfulness. Colour, size and position of the warnings on the labels affected attentional capture. Results from the experiments provide recommendations for the design of warnings to identify products with unfavourable nutrient profile.

The Effects of Oncologist Implicit Racial Bias in Racially Discordant Oncology Interactions

PubMed Central

Dovidio, John F.; Gonzalez, Richard; Albrecht, Terrance L.; Chapman, Robert; Foster, Tanina; Harper, Felicity W.K.; Hagiwara, Nao; Hamel, Lauren M.; Shields, Anthony F.; Gadgeel, Shirish; Simon, Michael S.; Griggs, Jennifer J.; Eggly, Susan

2016-01-01

Purpose Health providers’ implicit racial bias negatively affects communication and patient reactions to many medical interactions. However, its effects on racially discordant oncology interactions are largely unknown. Thus, we examined whether oncologist implicit racial bias has similar effects in oncology interactions. We further investigated whether oncologist implicit bias negatively affects patients’ perceptions of recommended treatments (i.e., degree of confidence, expected difficulty). We predicted oncologist implicit bias would negatively affect communication, patient reactions to interactions, and, indirectly, patient perceptions of recommended treatments. Methods Participants were 18 non-black medical oncologists and 112 black patients. Oncologists completed an implicit racial bias measure several weeks before video-recorded treatment discussions with new patients. Observers rated oncologist communication and recorded interaction length of time and amount of time oncologists and patients spoke. Following interactions, patients answered questions about oncologists’ patient-centeredness and difficulty remembering contents of the interaction, distress, trust, and treatment perceptions. Results As predicted, oncologists higher in implicit racial bias had shorter interactions, and patients and observers rated these oncologists’ communication as less patient-centered and supportive. Higher implicit bias also was associated with more patient difficulty remembering contents of the interaction. In addition, oncologist implicit bias indirectly predicted less patient confidence in recommended treatments, and greater perceived difficulty completing them, through its impact on oncologists’ communication (as rated by both patients and observers). Conclusion Oncologist implicit racial bias is negatively associated with oncologist communication, patients’ reactions to racially discordant oncology interactions, and patient perceptions of recommended treatments. These perceptions could subsequently directly affect patient-treatment decisions. Thus, implicit racial bias is a likely source of racial treatment disparities and must be addressed in oncology training and practice. PMID:27325865

The Effects of Oncologist Implicit Racial Bias in Racially Discordant Oncology Interactions.

PubMed

Penner, Louis A; Dovidio, John F; Gonzalez, Richard; Albrecht, Terrance L; Chapman, Robert; Foster, Tanina; Harper, Felicity W K; Hagiwara, Nao; Hamel, Lauren M; Shields, Anthony F; Gadgeel, Shirish; Simon, Michael S; Griggs, Jennifer J; Eggly, Susan

2016-08-20

Health providers' implicit racial bias negatively affects communication and patient reactions to many medical interactions. However, its effects on racially discordant oncology interactions are largely unknown. Thus, we examined whether oncologist implicit racial bias has similar effects in oncology interactions. We further investigated whether oncologist implicit bias negatively affects patients' perceptions of recommended treatments (i.e., degree of confidence, expected difficulty). We predicted oncologist implicit bias would negatively affect communication, patient reactions to interactions, and, indirectly, patient perceptions of recommended treatments. Participants were 18 non-black medical oncologists and 112 black patients. Oncologists completed an implicit racial bias measure several weeks before video-recorded treatment discussions with new patients. Observers rated oncologist communication and recorded interaction length of time and amount of time oncologists and patients spoke. Following interactions, patients answered questions about oncologists' patient-centeredness and difficulty remembering contents of the interaction, distress, trust, and treatment perceptions. As predicted, oncologists higher in implicit racial bias had shorter interactions, and patients and observers rated these oncologists' communication as less patient-centered and supportive. Higher implicit bias also was associated with more patient difficulty remembering contents of the interaction. In addition, oncologist implicit bias indirectly predicted less patient confidence in recommended treatments, and greater perceived difficulty completing them, through its impact on oncologists' communication (as rated by both patients and observers). Oncologist implicit racial bias is negatively associated with oncologist communication, patients' reactions to racially discordant oncology interactions, and patient perceptions of recommended treatments. These perceptions could subsequently directly affect patient-treatment decisions. Thus, implicit racial bias is a likely source of racial treatment disparities and must be addressed in oncology training and practice. © 2016 by American Society of Clinical Oncology.

Face puzzle—two new video-based tasks for measuring explicit and implicit aspects of facial emotion recognition

PubMed Central

Kliemann, Dorit; Rosenblau, Gabriela; Bölte, Sven; Heekeren, Hauke R.; Dziobek, Isabel

2013-01-01

Recognizing others' emotional states is crucial for effective social interaction. While most facial emotion recognition tasks use explicit prompts that trigger consciously controlled processing, emotional faces are almost exclusively processed implicitly in real life. Recent attempts in social cognition suggest a dual process perspective, whereby explicit and implicit processes largely operate independently. However, due to differences in methodology the direct comparison of implicit and explicit social cognition has remained a challenge. Here, we introduce a new tool to comparably measure implicit and explicit processing aspects comprising basic and complex emotions in facial expressions. We developed two video-based tasks with similar answer formats to assess performance in respective facial emotion recognition processes: Face Puzzle, implicit and explicit. To assess the tasks' sensitivity to atypical social cognition and to infer interrelationship patterns between explicit and implicit processes in typical and atypical development, we included healthy adults (NT, n = 24) and adults with autism spectrum disorder (ASD, n = 24). Item analyses yielded good reliability of the new tasks. Group-specific results indicated sensitivity to subtle social impairments in high-functioning ASD. Correlation analyses with established implicit and explicit socio-cognitive measures were further in favor of the tasks' external validity. Between group comparisons provide first hints of differential relations between implicit and explicit aspects of facial emotion recognition processes in healthy compared to ASD participants. In addition, an increased magnitude of between group differences in the implicit task was found for a speed-accuracy composite measure. The new Face Puzzle tool thus provides two new tasks to separately assess explicit and implicit social functioning, for instance, to measure subtle impairments as well as potential improvements due to social cognitive interventions. PMID:23805122

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.

Multilayer shallow water models with locally variable number of layers and semi-implicit time discretization

NASA Astrophysics Data System (ADS)

Bonaventura, Luca; Fernández-Nieto, Enrique D.; Garres-Díaz, José; Narbona-Reina, Gladys

2018-07-01

We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in which the number of vertical layers and their distribution are allowed to change in different regions of the computational domain. Furthermore, semi-implicit schemes are employed for the time discretization, leading to a significant efficiency improvement for subcritical regimes. We show that, in the typical regimes in which the application of multilayer shallow water models is justified, the resulting discretization does not introduce any major spurious feature and allows again to reduce substantially the computational cost in areas with complex bathymetry. As an example of the potential of the proposed technique, an application to a sediment transport problem is presented, showing a remarkable improvement with respect to standard discretization approaches.

On coupling fluid plasma and kinetic neutral physics models

DOE PAGES

Joseph, I.; Rensink, M. E.; Stotler, D. P.; ...

2017-03-01

The coupled fluid plasma and kinetic neutral physics equations are analyzed through theory and simulation of benchmark cases. It is shown that coupling methods that do not treat the coupling rates implicitly are restricted to short time steps for stability. Fast charge exchange, ionization and recombination coupling rates exist, even after constraining the solution by requiring that the neutrals are at equilibrium. For explicit coupling, the present implementation of Monte Carlo correlated sampling techniques does not allow for complete convergence in slab geometry. For the benchmark case, residuals decay with particle number and increase with grid size, indicating that theymore » scale in a manner that is similar to the theoretical prediction for nonlinear bias error. Progress is reported on implementation of a fully implicit Jacobian-free Newton–Krylov coupling scheme. The present block Jacobi preconditioning method is still sensitive to time step and methods that better precondition the coupled system are under investigation.« 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

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.

An Explicit Upwind Algorithm for Solving the Parabolized Navier-Stokes Equations

NASA Technical Reports Server (NTRS)

Korte, John J.

1991-01-01

An explicit, upwind algorithm was developed for the direct (noniterative) integration of the 3-D Parabolized Navier-Stokes (PNS) equations in a generalized coordinate system. The new algorithm uses upwind approximations of the numerical fluxes for the pressure and convection terms obtained by combining flux difference splittings (FDS) formed from the solution of an approximate Riemann (RP). The approximate RP is solved using an extension of the method developed by Roe for steady supersonic flow of an ideal gas. Roe's method is extended for use with the 3-D PNS equations expressed in generalized coordinates and to include Vigneron's technique of splitting the streamwise pressure gradient. The difficulty associated with applying Roe's scheme in the subsonic region is overcome. The second-order upwind differencing of the flux derivatives are obtained by adding FDS to either an original forward or backward differencing of the flux derivative. This approach is used to modify an explicit MacCormack differencing scheme into an upwind differencing scheme. The second order upwind flux approximations, applied with flux limiters, provide a method for numerically capturing shocks without the need for additional artificial damping terms which require adjustment by the user. In addition, a cubic equation is derived for determining Vegneron's pressure splitting coefficient using the updated streamwise flux vector. Decoding the streamwise flux vector with the updated value of Vigneron's pressure splitting improves the stability of the scheme. The new algorithm is applied to 2-D and 3-D supersonic and hypersonic laminar flow test cases. Results are presented for the experimental studies of Holden and of Tracy. In addition, a flow field solution is presented for a generic hypersonic aircraft at a Mach number of 24.5 and angle of attack of 1 degree. The computed results compare well to both experimental data and numerical results from other algorithms. Computational times required for the upwind PNS code are approximately equal to an explicit PNS MacCormack's code and existing implicit PNS solvers.

Development and Application of a Numerical Framework for Improving Building Foundation Heat Transfer Calculations

NASA Astrophysics Data System (ADS)

Kruis, Nathanael J. F.

Heat transfer from building foundations varies significantly in all three spatial dimensions and has important dynamic effects at all timescales, from one hour to several years. With the additional consideration of moisture transport, ground freezing, evapotranspiration, and other physical phenomena, the estimation of foundation heat transfer becomes increasingly sophisticated and computationally intensive to the point where accuracy must be compromised for reasonable computation time. The tools currently available to calculate foundation heat transfer are often either too limited in their capabilities to draw meaningful conclusions or too sophisticated to use in common practices. This work presents Kiva, a new foundation heat transfer computational framework. Kiva provides a flexible environment for testing different numerical schemes, initialization methods, spatial and temporal discretizations, and geometric approximations. Comparisons within this framework provide insight into the balance of computation speed and accuracy relative to highly detailed reference solutions. The accuracy and computational performance of six finite difference numerical schemes are verified against established IEA BESTEST test cases for slab-on-grade heat conduction. Of the schemes tested, the Alternating Direction Implicit (ADI) scheme demonstrates the best balance between accuracy, performance, and numerical stability. Kiva features four approaches of initializing soil temperatures for an annual simulation. A new accelerated initialization approach is shown to significantly reduce the required years of presimulation. Methods of approximating three-dimensional heat transfer within a representative two-dimensional context further improve computational performance. A new approximation called the boundary layer adjustment method is shown to improve accuracy over other established methods with a negligible increase in computation time. This method accounts for the reduced heat transfer from concave foundation shapes, which has not been adequately addressed to date. Within the Kiva framework, three-dimensional heat transfer that can require several days to simulate is approximated in two-dimensions in a matter of seconds while maintaining a mean absolute deviation within 3%.

Implicit race attitudes predict trustworthiness judgments and economic trust decisions

PubMed Central

Stanley, Damian A.; Sokol-Hessner, Peter; Banaji, Mahzarin R.; Phelps, Elizabeth A.

2011-01-01

Trust lies at the heart of every social interaction. Each day we face decisions in which we must accurately assess another individual's trustworthiness or risk suffering very real consequences. In a global marketplace of increasing heterogeneity with respect to nationality, race, and multiple other social categories, it is of great value to understand how implicitly held attitudes about group membership may support or undermine social trust and thereby implicitly shape the decisions we make. Recent behavioral and neuroimaging work suggests that a common mechanism may underlie the expression of implicit race bias and evaluations of trustworthiness, although no direct evidence of a connection exists. In two behavioral studies, we investigated the relationship between implicit race attitude (as measured by the Implicit Association Test) and social trust. We demonstrate that race disparity in both an individual's explicit evaluations of trustworthiness and, more crucially, his or her economic decisions to trust is predicted by that person's bias in implicit race attitude. Importantly, this relationship is robust and is independent of the individual's bias in explicit race attitude. These data demonstrate that the extent to which an individual invests in and trusts others with different racial backgrounds is related to the magnitude of that individual's implicit race bias. The core dimension of social trust can be shaped, to some degree, by attitudes that reside outside conscious awareness and intention. PMID:21518877

Implicit race attitudes predict trustworthiness judgments and economic trust decisions.

PubMed

Stanley, Damian A; Sokol-Hessner, Peter; Banaji, Mahzarin R; Phelps, Elizabeth A

2011-05-10

Trust lies at the heart of every social interaction. Each day we face decisions in which we must accurately assess another individual's trustworthiness or risk suffering very real consequences. In a global marketplace of increasing heterogeneity with respect to nationality, race, and multiple other social categories, it is of great value to understand how implicitly held attitudes about group membership may support or undermine social trust and thereby implicitly shape the decisions we make. Recent behavioral and neuroimaging work suggests that a common mechanism may underlie the expression of implicit race bias and evaluations of trustworthiness, although no direct evidence of a connection exists. In two behavioral studies, we investigated the relationship between implicit race attitude (as measured by the Implicit Association Test) and social trust. We demonstrate that race disparity in both an individual's explicit evaluations of trustworthiness and, more crucially, his or her economic decisions to trust is predicted by that person's bias in implicit race attitude. Importantly, this relationship is robust and is independent of the individual's bias in explicit race attitude. These data demonstrate that the extent to which an individual invests in and trusts others with different racial backgrounds is related to the magnitude of that individual's implicit race bias. The core dimension of social trust can be shaped, to some degree, by attitudes that reside outside conscious awareness and intention.

High-Order Residual-Distribution Hyperbolic Advection-Diffusion Schemes: 3rd-, 4th-, and 6th-Order

NASA Technical Reports Server (NTRS)

Mazaheri, Alireza R.; Nishikawa, Hiroaki

2014-01-01

In this paper, spatially high-order Residual-Distribution (RD) schemes using the first-order hyperbolic system method are proposed for general time-dependent advection-diffusion problems. The corresponding second-order time-dependent hyperbolic advection- diffusion scheme was first introduced in [NASA/TM-2014-218175, 2014], where rapid convergences over each physical time step, with typically less than five Newton iterations, were shown. In that method, the time-dependent hyperbolic advection-diffusion system (linear and nonlinear) was discretized by the second-order upwind RD scheme in a unified manner, and the system of implicit-residual-equations was solved efficiently by Newton's method over every physical time step. In this paper, two techniques for the source term discretization are proposed; 1) reformulation of the source terms with their divergence forms, and 2) correction to the trapezoidal rule for the source term discretization. Third-, fourth, and sixth-order RD schemes are then proposed with the above techniques that, relative to the second-order RD scheme, only cost the evaluation of either the first derivative or both the first and the second derivatives of the source terms. A special fourth-order RD scheme is also proposed that is even less computationally expensive than the third-order RD schemes. The second-order Jacobian formulation was used for all the proposed high-order schemes. The numerical results are then presented for both steady and time-dependent linear and nonlinear advection-diffusion problems. It is shown that these newly developed high-order RD schemes are remarkably efficient and capable of producing the solutions and the gradients to the same order of accuracy of the proposed RD schemes with rapid convergence over each physical time step, typically less than ten Newton iterations.

On Feeling Torn About One’s Sexuality

PubMed Central

Windsor-Shellard, Ben

2014-01-01

Three studies offer novel evidence addressing the consequences of explicit–implicit sexual orientation (SO) ambivalence. In Study 1, self-identified straight females completed explicit and implicit measures of SO. The results revealed that participants with greater SO ambivalence took longer responding to explicit questions about their sexual preferences, an effect moderated by the direction of ambivalence. Study 2 replicated this effect using a different paradigm. Study 3 included self-identified straight and gay female and male participants; participants completed explicit and implicit measures of SO, plus measures of self-esteem and affect regarding their SO. Among straight participants, the response time results replicated the findings of Studies 1 and 2. Among gay participants, trends suggested that SO ambivalence influenced time spent deliberating on explicit questions relevant to sexuality, but in a different way. Furthermore, the amount and direction of SO ambivalence was related to self-esteem. PMID:24972940

Cocaine, Appetitive Memory and Neural Connectivity

PubMed Central

Ray, Suchismita

2013-01-01

This review examines existing cognitive experimental and brain imaging research related to cocaine addiction. In section 1, previous studies that have examined cognitive processes, such as implicit and explicit memory processes in cocaine users are reported. Next, in section 2, brain imaging studies are reported that have used chronic users of cocaine as study participants. In section 3, several conclusions are drawn. They are: (a) in cognitive experimental literature, no study has examined both implicit and explicit memory processes involving cocaine related visual information in the same cocaine user, (b) neural mechanisms underlying implicit and explicit memory processes for cocaine-related visual cues have not been directly investigated in cocaine users in the imaging literature, and (c) none of the previous imaging studies has examined connectivity between the memory system and craving system in the brain of chronic users of cocaine. Finally, future directions in the field of cocaine addiction are suggested. PMID:25009766

Control of parallel manipulators using force feedback

NASA Technical Reports Server (NTRS)

Nanua, Prabjot

1994-01-01

Two control schemes are compared for parallel robotic mechanisms actuated by hydraulic cylinders. One scheme, the 'rate based scheme', uses the position and rate information only for feedback. The second scheme, the 'force based scheme' feeds back the force information also. The force control scheme is shown to improve the response over the rate control one. It is a simple constant gain control scheme better suited to parallel mechanisms. The force control scheme can be easily modified for the dynamic forces on the end effector. This paper presents the results of a computer simulation of both the rate and force control schemes. The gains in the force based scheme can be individually adjusted in all three directions, whereas the adjustment in just one direction of the rate based scheme directly affects the other two directions.

Representational momentum for the human body: awkwardness matters, experience does not.

PubMed

Wilson, Margaret; Lancaster, Jessy; Emmorey, Karen

2010-08-01

Perception of the human body appears to involve predictive simulations that project forward to track unfolding body-motion events. Here we use representational momentum (RM) to investigate whether implicit knowledge of a learned arbitrary system of body movement such as sign language influences this prediction process, and how this compares to implicit knowledge of biomechanics. Experiment 1 showed greater RM for sign language stimuli in the correct direction of the sign than in the reverse direction, but unexpectedly this held true for non-signers as well as signers. Experiment 2 supported two biomechanical explanations for this result (an effect of downward movement, and an effect of the direction that the movement had actually been performed by the model), and Experiments 3 and 4 found no residual enhancement of RM in signers when these factors were controlled. In fact, surprisingly, the opposite was found: signers showed reduced RM for signs. Experiment 5 verified the effect of biomechanical knowledge by testing arm movements that are easy to perform in one direction but awkward in the reverse direction, and found greater RM for the easy direction. We conclude that while perceptual prediction is shaped by implicit knowledge of biomechanics (the awkwardness effect), it is surprisingly insensitive to expectations derived from learned movement patterns. Results are discussed in terms of recent findings on the mirror system. Copyright (c) 2010 Elsevier B.V. All rights reserved.

An improved 2D MoF method by using high order derivatives

NASA Astrophysics Data System (ADS)

Chen, Xiang; Zhang, Xiong

2017-11-01

The MoF (Moment of Fluid) method is one of the most accurate approaches among various interface reconstruction algorithms. Alike other second order methods, the MoF method needs to solve an implicit optimization problem to obtain the optimal approximate interface, so an iteration process is inevitable under most circumstances. In order to solve the optimization efficiently, the properties of the objective function are worthy of studying. In 2D problems, the first order derivative has been deduced and applied in the previous researches. In this paper, the high order derivatives of the objective function are deduced on the convex polygon. We show that the nth (n ≥ 2) order derivatives are discontinuous, and the number of the discontinuous points is two times the number of the polygon edge. A rotation algorithm is proposed to successively calculate these discontinuous points, thus the target interval where the optimal solution is located can be determined. Since the high order derivatives of the objective function are continuous in the target interval, the iteration schemes based on high order derivatives can be used to improve the convergence rate. Moreover, when iterating in the target interval, the value of objective function and its derivatives can be directly updated without explicitly solving the volume conservation equation. The direct update makes a further improvement of the efficiency especially when the number of edges of the polygon is increasing. The Halley's method, which is based on the first three order derivatives, is applied as the iteration scheme in this paper and the numerical results indicate that the CPU time is about half of the previous method on the quadrilateral cell and is about one sixth on the decagon cell.

Deductive Evaluation: Implicit Code Verification With Low User Burden

NASA Technical Reports Server (NTRS)

Di Vito, Ben L.

2016-01-01

We describe a framework for symbolically evaluating C code using a deductive approach that discovers and proves program properties. The framework applies Floyd-Hoare verification principles in its treatment of loops, with a library of iteration schemes serving to derive loop invariants. During evaluation, theorem proving is performed on-the-fly, obviating the generation of verification conditions normally needed to establish loop properties. A PVS-based prototype is presented along with results for sample C functions.

Gradient of the temperature function at the voxel (i, j, k) for heterogeneous bio-thermal model

NASA Astrophysics Data System (ADS)

Cen, Wei; Hoppe, Ralph; Sun, Aiwu; Gu, Ning; Lu, Rongbo

2018-06-01

Determination of the relationship between electromagnetic power absorption and temperature distributions inside highly heterogeneous biological samples based on numerical methods is essential in biomedical engineering (e.g. microwave thermal ablation in clinic). In this paper, the gradient expression is examined and analyzed in detail, as how the gradient operators can be discretized is the only real difficulty to the solution of bio-heat equation for highly inhomogeneous model utilizing implicit scheme.

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.

Isochronal Ice Sheet Model: a New Approach to Tracer Transport by Explicitly Tracing Accumulation Layers

NASA Astrophysics Data System (ADS)

Born, A.; Stocker, T. F.

2014-12-01

The long, high-resolution and largely undisturbed depositional record of polar ice sheets is one of the greatest resources in paleoclimate research. The vertical profile of isotopic and other geochemical tracers provides a full history of depositional and dynamical variations. Numerical simulations of this archive could afford great advances both in the interpretation of these tracers as well as to help improve ice sheet models themselves, as show successful implementations in oceanography and atmospheric dynamics. However, due to the slow advection velocities, tracer modeling in ice sheets is particularly prone to numerical diffusion, thwarting efforts that employ straightforward solutions. Previous attemps to circumvent this issue follow conceptually and computationally extensive approaches that augment traditional Eulerian models of ice flow with a semi-Lagrangian tracer scheme (e.g. Clarke et al., QSR, 2005). Here, we propose a new vertical discretization for ice sheet models that eliminates numerical diffusion entirely. Vertical motion through the model mesh is avoided by mimicking the real-world ice flow as a thinning of underlying layers (see figure). A new layer is added to the surface at equidistant time intervals (isochronally). Therefore, each layer is uniquely identified with an age. Horizontal motion follows the shallow ice approximation using an implicit numerical scheme. Vertical diffusion of heat which is physically desirable is also solved implicitly. A simulation of a two-dimensional section through the Greenland ice sheet will be discussed.

Implicitly solving phase appearance and disappearance problems using two-fluid six-equation model

DOE PAGES

Zou, Ling; Zhao, Haihua; Zhang, Hongbin

2016-01-25

Phase appearance and disappearance issue presents serious numerical challenges in two-phase flow simulations using the two-fluid six-equation model. Numerical challenges arise from the singular equation system when one phase is absent, as well as from the discontinuity in the solution space when one phase appears or disappears. In this work, a high-resolution spatial discretization scheme on staggered grids and fully implicit methods were applied for the simulation of two-phase flow problems using the two-fluid six-equation model. A Jacobian-free Newton-Krylov (JFNK) method was used to solve the discretized nonlinear problem. An improved numerical treatment was proposed and proved to be effectivemore » to handle the numerical challenges. The treatment scheme is conceptually simple, easy to implement, and does not require explicit truncations on solutions, which is essential to conserve mass and energy. Various types of phase appearance and disappearance problems relevant to thermal-hydraulics analysis have been investigated, including a sedimentation problem, an oscillating manometer problem, a non-condensable gas injection problem, a single-phase flow with heat addition problem and a subcooled flow boiling problem. Successful simulations of these problems demonstrate the capability and robustness of the proposed numerical methods and numerical treatments. As a result, volume fraction of the absent phase can be calculated effectively as zero.« less

AMITIS: A 3D GPU-Based Hybrid-PIC Model for Space and Plasma Physics

NASA Astrophysics Data System (ADS)

Fatemi, Shahab; Poppe, Andrew R.; Delory, Gregory T.; Farrell, William M.

2017-05-01

We have developed, for the first time, an advanced modeling infrastructure in space simulations (AMITIS) with an embedded three-dimensional self-consistent grid-based hybrid model of plasma (kinetic ions and fluid electrons) that runs entirely on graphics processing units (GPUs). The model uses NVIDIA GPUs and their associated parallel computing platform, CUDA, developed for general purpose processing on GPUs. The model uses a single CPU-GPU pair, where the CPU transfers data between the system and GPU memory, executes CUDA kernels, and writes simulation outputs on the disk. All computations, including moving particles, calculating macroscopic properties of particles on a grid, and solving hybrid model equations are processed on a single GPU. We explain various computing kernels within AMITIS and compare their performance with an already existing well-tested hybrid model of plasma that runs in parallel using multi-CPU platforms. We show that AMITIS runs ∼10 times faster than the parallel CPU-based hybrid model. We also introduce an implicit solver for computation of Faraday’s Equation, resulting in an explicit-implicit scheme for the hybrid model equation. We show that the proposed scheme is stable and accurate. We examine the AMITIS energy conservation and show that the energy is conserved with an error < 0.2% after 500,000 timesteps, even when a very low number of particles per cell is used.

The Achievement Flow Motive as an Element of the Autotelic Personality: Predicting Educational Attainment in Three Cultures

ERIC Educational Resources Information Center

Busch, Holger; Hofer, Jan; Chasiotis, Athanasios; Campos, Domingo

2013-01-01

Human behavior is directed by an implicit and an explicit motivational system. The intrinsic form of the implicit achievement motive has been demonstrated to predict the experience of flow. Thus, this achievement flow motive can be considered an integral component of the autotelic personality, posited in Flow Theory as dispositional difference in…

Application of implicit attitude measures to the blood donation context.

PubMed

Warfel, Regina M; France, Christopher R; France, Janis L

2012-02-01

Past blood donation research has relied on explicit (self-report) measures to understand blood donation motivations, but has not yet considered the inherent implicit or automatic processing involved in decision-making. This study addresses this limitation by introducing and validating two novel implicit measures of blood donation attitudes. Healthy young adults (n = 253) performed both image and word versions of a Single Target Implicit Association Test (ST-IAT) and then completed self-report measures of blood donation attitudes, blood and needle fears, social desirability, and donation intention. These results affirmed the validity of the blood donation ST-IATs in at least three ways. First, as expected, nondonors demonstrated more negative implicit donation attitudes than donors. Second, the implicit measures were significantly related in expected directions with explicit measures of donation attitudes as well as blood and needle fears. Finally, implicit donation attitudes were significantly related to donation intention, and the Image ST-IAT (but not the Word ST-IAT) significantly enhanced prediction of donation intention over and above needle fears and marginally enhanced prediction over and above blood fears. Image and word versions of the blood donation ST-IAT offer a valid method of assessing underlying automatic attitudes toward blood donation. © 2012 American Association of Blood Banks.

The explicit and implicit dance in psychoanalytic change.

PubMed

Fosshage, James L

2004-02-01

How the implicit/non-declarative and explicit/declarative cognitive domains interact is centrally important in the consideration of effecting change within the psychoanalytic arena. Stern et al. (1998) declare that long-lasting change occurs in the domain of implicit relational knowledge. In the view of this author, the implicit and explicit domains are intricately intertwined in an interactive dance within a psychoanalytic process. The author views that a spirit of inquiry (Lichtenberg, Lachmann & Fosshage 2002) serves as the foundation of the psychoanalytic process. Analyst and patient strive to explore, understand and communicate and, thereby, create a 'spirit' of interaction that contributes, through gradual incremental learning, to new implicit relational knowledge. This spirit, as part of the implicit relational interaction, is a cornerstone of the analytic relationship. The 'inquiry' more directly brings explicit/declarative processing to the foreground in the joint attempt to explore and understand. The spirit of inquiry in the psychoanalytic arena highlights both the autobiographical scenarios of the explicit memory system and the mental models of the implicit memory system as each contributes to a sense of self, other, and self with other. This process facilitates the extrication and suspension of the old models, so that new models based on current relational experience can be gradually integrated into both memory systems for lasting change.

Directional Agglomeration Multigrid Techniques for High Reynolds Number Viscous Flow Solvers

NASA Technical Reports Server (NTRS)

1998-01-01

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