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At least 1,261 records · Page 70
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

On the boundary treatment in spectral methods for hyperbolic systems

Spectral methods were successfully applied to the simulation of slow transients in gas transportation networks. Implicit time advancing techniques are naturally suggested by the nature of the problem. The correct treatment of the boundary conditions is clarified in order to avoid any stability restriction originated by the boundaries. The Beam and Warming and the Lerat schemes are unconditionally linearly stable when used with a Chebyshev pseudospectral method. Engineering accuracy for a gas transportation problem is achieved at Courant numbers up to 100.

Canuto, Claudio↗
NASA NTRS1989

The implementation of the graphics of program EAGLE: A numerical grid generation code on NASA Langley SNS computer system

Program EAGLE (Eglin Arbitrary Geometry Implicit Euler) Numerical Grid Generation System is a composite (multi-block) algebraic or elliptic grid generation system designed to discretize the domain in and/or around any arbitrarily shaped three dimensional regions. This system combines a boundary conforming surface generation scheme and includes plotting routines designed to take full advantage of the DISSPLA Graphics Package (Version 9.0). Program EAGLE is written to compile and execute efficiently on any Cray machine with or without solid state disk (SSD) devices. Also, the code uses namelist inputs which are supported by all Cray machines using the FORTRAN compiler CFT77. The namelist inputs makes it easier for the user to understand the inputs and operation of Program EAGLE. EAGLE's numerical grid generator is constructed in the following form: main program, EGG (executive routine); subroutine SURFAC (surface generation routine); subroutine GRID (grid generation routine); and subroutine GRDPLOT (grid plotting routines). The EAGLE code was modified to use on the NASA-LaRC SNS computer (Cray 2S) system. During the modification a conversion program was developed for the output data of EAGLE's subroutine GRID to permit the data to be graphically displayed by IRIS workstations, using Plot3D. The code of program EAGLE was modified to make operational subroutine GRDPLOT (using DI-3000 Graphics Software Packages) on the NASA-LaRC SNS Computer System. How to implement graphically, the output data of subroutine GRID was determined on any NASA-LaRC graphics terminal that has access to the SNS Computer System DI-300 Graphics Software Packages. A Quick Reference User Guide was developed for the use of program EAGLE on the NASA-LaRC SNS Computer System. One or more application program(s) was illustrated using program EAGLE on the NASA LaRC SNS Computer System, with emphasis on graphics illustrations.

Houston, Johnny L.↗
NASA NTRS1990

Efficient parallel solution of parabolic equations - Implicit methods on the Cedar multicluster

A class of implicit methods for the parallel solution of linear parabolic differential equations based on Pade and Chebyshev rational approximations to the matrix exponential are presented. It is pointed out that this approach incorporates both natural hierarchical parallelism, improved intrinsic efficiency, and fewer timesteps. These advantages lead to an extremely fast family of methods for the solution of certain time-dependent problems. These techniques are illustrated with numerical experiments on the University of Illinois Cedar multicluster architecture. The experiments indicate that implicit methods of very high degree offer great promise for the solution of certain parabolic problems when in computational environment with parallel resources. Hierarchically organized parallel computers, such as the Cedar multicluster, are found to be especially attractive for these schemes.

Gallopoulos, E.↗
NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - 2

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Yee, H. C.↗
NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - Part 2

The global asymptotic nonlinear behavior of 11 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDEs.

Yee, H. C.↗
DOE OSTI2012

An Analysis of Source Tilting and Sub-cell Opacity Sampling for IMC [Slides]

Implicit Monte Carlo (IMC) is a stochastic method for solving the radiative transfer equations for multiphysics application with the material in local thermodynamic equilibrium. The IMC method employs a fictitious scattering term that is computed from an implicit discretization of the material temperature equation. Unfortunately, the original histogram representation of the temperature and opacity with respect to the spatial domain leads to nonphysically fast propagation of radiation waves through optically thick material. In the past, heuristic source tilting schemes have been used to mitigate the numerical teleportation error of the radiation particles in IMC that cause this overly rapid radiation wave propagation. While improving the material temperature profile throughout the time duration, these tilting schemes alone do not generally alleviate the teleportation error to suitable levels. Another means of potentially reducing teleportation error in IMC is implementing continuous sub-cell opacities based on sub-cell temperature profiles. We present here an analysis of source tilting and continuous sub-cell opacity sampling applied to various discretizations of the temperature equation. Through this analysis, we demonstrate that applying both heuristics does not necessarily yield more accurate results if the discretization of the material equation is inconsistent with the Monte Carlo sub-cell transport.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1988

Numerical study of the vortex burst phenomenon for delta wings

A flux-difference splitting scheme is employed to compute low-speed flows over a delta wing for angles of attack from 0 to 40 deg as steady-state solutions to the three-dimensional, Reynolds-averaged Navier-Stokes equations in their thin-layer approximation. The finite-difference scheme is made spatially second-order accurate by applying a total variation diminishing-like discretization to the inviscid fluxes and central differencing to the viscous shear fluxes. Using first-order accurate Euler backward-time differencing, an efficient implicit algorithm is constructed, which combines approximate factorization in cross planes with a symmetric planar Gauss-Seidel relaxation in the remaining third spatial direction. The geometry of the thin (maximum thickness is 0.021), slender (aspect ratio is unity), sharp-edged delta wing is taken from Hummel's (1967, 1978) wind tunnel model. Over the entire angle-of-attack range, the computed values of lift and pitching moment are in good agreement with the experimental data. Also details of the flow-fieldlike spanwise surface pressure distributions compare well with the experiment. Computed flow-field results with a bubble-type vortex burst are analyzed in detail.

Hartwich, PETER-M.↗
NASA NTRS1988

Modeling of transitional flows

An effort directed at developing improved transitional models was initiated. The focus of this work was concentrated on the critical assessment of a popular existing transitional model developed by McDonald and Fish in 1972. The objective of this effort was to identify the shortcomings of the McDonald-Fish model and to use the insights gained to suggest modifications or alterations of the basic model. In order to evaluate the transitional model, a compressible boundary layer code was required. Accordingly, a two-dimensional compressible boundary layer code was developed. The program was based on a three-point fully implicit finite difference algorithm where the equations were solved in an uncoupled manner with second order extrapolation used to evaluate the non-linear coefficients. Iteration was offered as an option if the extrapolation error could not be tolerated. The differencing scheme was arranged to be second order in both spatial directions on an arbitrarily stretched mesh. A variety of boundary condition options were implemented including specification of an external pressure gradient, specification of a wall temperature distribution, and specification of an external temperature distribution. Overall the results of the initial phase of this work indicate that the McDonald-Fish model does a poor job at predicting the details of the turbulent flow structure during the transition region.

Lund, Thomas S.↗
NASA NTRS1989

An adaptive implicit/explicit finite element scheme for compressible viscous high speed flow

An adaptive implicit/explicit finite element procedure for the solution of three-dimensional problems of steady compressible viscous high-speed flows is presented. In the vicinity of solid walls, a grid-exhibiting structure in the normal direction is employed, while away from this region the grid is totally unstructured. The implicit form of the algorithm is used near solid walls, with the grid structure being utilized in an equation solution approach based upon line relaxation. The explicit form of the algorithm is used elsewhere. Grid adaptation is achieved by means of adaptive remeshing. To illustrate the performance of the proposed method, solutions are obtained for the problems of shock-boundary layer interaction and shock-shock interaction on a swept cylindrical leading edge. Comparisons are made with experimental observations.

Hassan, O.↗
DOE OSTI2022

Exponential integrators for non-linear diffusion

The goal of this project is to compare the performance of exponential time integrators with traditional methods such as diagonally implicit Runge-Kutta methods in the context of solving the system of reduced magnetohydrodynamics (RMHD). In this report, we present initial results of a proof of concept study that shows that exponential integrators can be an efficient alternative to traditional integration schemes.

42 ENGINEERING↗
NASA NTRS1985

High resolution TVD schemes using flux limiters

Roe (1981, 1985) has utilized flux limiters to obtain second order monotonicity preserving schemes. In the present paper, the foundation for flux limiters in the formulation of first order three-point schemes are discussed, and a systematic outline is provided of the method of using flux limiters to obtain second order accurate TVD schemes. Attention is given to Phi limiters, the Van Leer limiter, the Chakravarthy-Osher limiter, the linear advection equation and square wave data, the inviscid Burger's equation, and the extension of flux limiters to irregular grids, systems of equations, and implicit calculations.

Sweby, P. K.↗
NASA NTRS1990

Comparative study of computational efficiency of two LU schemes for non-equilibrium reacting flows

The systems of equations governing chemically nonequilibrium flows are solved numerically by two lower-upper(LU) algorithms, namely, LU-SSOR (Yoon and Jameson, 1987) and LU-SW (Steger and Warming, 1981). The methods of flux-Jacobian splitting differentiate the two LU algorithms. The LU-SSOR gives a simpler implicit operator with less temporal damping, while the LU-SW converges faster but requires more computation for each iteration. Relative efficiencies and mutual merits of these two LU algorithms are compared. The results show that LU-SW with upwind-differenced right-hand-side gives the best convergence.

Tsai, Y.-L. Peter↗
NASA NTRS1992

Finite-element solution scheme for compressible viscous flow

Adaptivity offers the possibility of using FEM for problems that are otherwise intractable. The solution algorithm is combined with an adaptive approach in which the unstructured portion of the grid is adaptively regenerated as the solution proceeds; the structured portion of the mesh is modified accordingly, to ensure both compatibility along the interface between the implicit and explicit element groups and increased resolution of the viscous layer. The approach offers significant computational savings in 3D simulations.

Hassan, O.↗
NASA NTRS1994

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

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.

Cohl, H.↗
DOE OSTI2020

A fully implicit, scalable, conservative nonlinear relativistic Fokker–Planck 0D-2P solver for runaway electrons

Upon application of a sufficiently strong electric field, electrons break away from thermal equilibrium and approach relativistic speeds. These highly energetic ‘runaway’ electrons (~ MeV) play a significant role in tokamak disruption physics, and therefore their accurate understanding is essential to develop reliable mitigation strategies. As such, we have developed a fully implicit solver for the 0D-2P (i.e., including two momenta coordinates) relativistic nonlinear Fokker–Planck equation (rFP). As in earlier implicit rFP studies (NORSE, CQL3D), electron–ion interactions are modeled using the Lorentz operator, and synchrotron damping using the Abraham–Lorentz–Dirac reaction term. However, our implementation improves on these earlier studies by (1) ensuring exact conservation properties for electron collisions, (2) strictly preserving positivity, and (3) being scalable algorithmically and in parallel. Key to our proposed approach is an efficient multigrid preconditioner for the linearized rFP equation, a multigrid elliptic solver for the Braams–Karney potentials, and a novel adaptive technique to determine the associated boundary values. We verify the accuracy and efficiency of the proposed scheme with numerical results ranging from small electric-field electrical conductivity measurements to the accurate reproduction of runaway tail dynamics when strong electric fields are applied.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS2015

Implicit LES of Turbulent, Separated Flow: Wall-Mounted Hump Configuration

Direct simulations (ILES) of turbulent, separated flow over the wall-mounted hump configuration is conducted to investigate the physics of separated flows. A chord-based Reynolds number of Re(sub c) = 47,500 is set up, with a turbulent in flow of Re(sub theta) = 1,400 (theta/c = 3%). FDL3DI, a code that solves the compressible Navier-Stokes equations using high- order compact-difference scheme and filter, with the standard recycling/rescaling method of turbulence generation, is used. Two different configurations of the upper-wall are analyzed, and results are compared with both a higher Re(sub c) (= 936,000, Re(sub theta) = 7,200, theta/c = 0.77%) experiment for major flow features, and RANS (k-omega SST) results. A lower Rec allows for DNS-like mesh resolution, and an adequately wide span. Both ILES and RANS show delayed reattachment compared to experiment, and significantly higher skin friction in the forebody of the hump, as expected. The upper-wall shape influences the C(sub p) distribution only. Results from this study are being used to setup higher Rec (lower theta/c) ILES.

Implicit LES↗
NASA NTRS1988

Navier-Stokes calculation of solid-propellant rocket motor internal flowfields

A comprehensive numerical analysis has been carried out to study the detailed physical and chemical processes involved in the combustion of homogeneous propellant in a rocket motor. The formulation is based on the time-dependent full Navier-Stokes equations, with special attention devoted to the chemical reactions in both gas and condensed phases. The turbulence closure is achieved using both the Baldwin-Lomax algebraic model and a modified k-epsilon two-equation scheme with a low Reynolds number and near-wall treatment. The effects of variable thermodynamic and transport properties are also included. The system of governing equations are solved using a multi-stage Runge-Kutta shceme with the source terms treated implicitly. Preliminary results clearly demonstrate the presence of various combustion regimes in the vicinity of propellant surface. The effects of propellant combustion on the motor internal flowfields are investigated in detail.

Hsieh, Kwang-Chung↗
NASA NTRS1992

A pressure correction method for the calculation of compressible chemical reacting flows

A recently developed noniterative method for the solution of the transient fluid flow equations at all speed is extended to handle chemical reacting flows. The species conservation equations are loosely coupled into the predictor/multicorrector sequence of the solution procedure. A split-operator method separates the chemical kinetics terms from the fluid-dynamical terms, as well as an implicit differencing method enhance the numerical stability. The method was applied for turbulent diffusion flame calculations and for the analyses of high pressure, axisymmetric turbulent hypersonic nozzle flows. The diffusion flame results were compared with a similar pressure method for fast chemistry integration scheme without operator-splitting. Simulations of the nozzle flow indicated that the nonideal intermolecular effects must be included in the analysis and design of high pressure hypersonic nozzle.

Chen, Z. J.↗