SEARCH · Search NASA

Results for “Implicit”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10

All sources NASA NTRS DOE OSTI

NASA NTRS1991

An intrinsically n-dimensional generalized flux vector splitting implicit finite element Euler algorithm

A generalized flux-vector splitting implicit Galerkin finite-element algorithm for the Euler equations in curvilinear coordinates for ideal and reacting gases is derived. For an arbitrary equation of state, the curvilinear-coordinate flux vector is split in kinematic and kinetic components, and the associated jacobian matrix eigenvalues explicitly depend on the metric data. After directional semidiscretization, the terminal ordinary differential-equation system is solved via a nonlinearly stable implicit Runge-Kutta scheme in concert with an accurate tensor matrix product factorization. The results for selected two-dimensional supersonic and axisymmetric hypersonic flows validate the algorithm and verify its robustness for curvilinear-coordinate computations. The evolution towards a steady state is achieved for large Courant numbers without indication of numerical instabilities.

Iannelli, G. S.↗

NASA NTRS1991

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

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

Tamma, Kumar K.↗

NASA NTRS1991

Acceleration of convergence by shifting the spectrum of implicit finite difference operators associated with the equations of gas dynamics

Eigensystem analysis techniques are applied to finite difference formulations of the Navier-Stokes equations in one dimension. Spectra of the resulting implicit difference operators are computed. The largest eigenvalues are calculated by using a combination of the Frechet derivative of the operators and Arnoldi's method. The accuracy of Arnoldi's method is tested by comparing the rate of convergence of the iterative method with the dominant eigenvalue of the original iteration matrix. On the basis of the pattern of eigenvalue distributions for various flow configurations, a shifting of the implicit operators in question is devised. This procedure has improved the rates of convergence of CFD codes by 20 - 50 percent.

Cheer, A.↗

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 NTRS1991

Diagonal implicit multigrid solution of compressible turbulent flows

The Caughey (1988) multigrid diagonal implicit algorithm for Euler equations is extended to solve the two-dimensional thin layer Navier-Stokes equations for turbulent transonic flows. To further accelerate convergence to a steady state, the implicit scheme is used within the multigrid method. Results are presented for transonic flows past airfoils, and the flow-field results are compared with other computational data and experiments demonstrating the accuracy of the method.

Varma, R. R.↗

NASA NTRS1990

Implicit methods for the Navier-Stokes equations

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.

Yoon, S.↗

NASA NTRS1992

A non-linearly stable implicit finite element algorithm for hypersonic aerodynamics

A generalized curvilinear coordinate Taylor weak statement implicit finite element algorithm is developed for the two-dimensional and axisymmetric compressible Navier-Stokes equations for ideal and reacting gases. For accurate hypersonic simulation, air is modeled as a mixture of five perfect gases, i.e., molecular and atomic oxygen and nitrogen as well as nitric oxide. The associated pressure is then determined via Newton solution of the classical chemical equilibrium equation system. The directional semidiscretization is achieved using an optimal metric data Galerkin finite element weak statement, on a developed 'companion conservation law system', permitting classical test and trial space definitions. Utilizing an implicit Runge-Kutta scheme, the terminal algorithm is then nonlinearly stable, and second-order accurate in space and time on arbitrary curvilinear coordinates. Subsequently, a matrix tensor product factorization procedure permits an efficient numerical linear algebra handling for large Courant numbers. For ideal- and real-gas hypersonic flows, the algorithm generates essentially nonoscillatory numerical solutions in the presence of strong detached shocks and boundary layer-inviscid flow interactions.

Iannelli, G. S.↗

NASA NTRS1992

An implicit multigrid scheme for hypersonic strong-interaction flowfields

An implicit multigrid method for the compressible Navier-Stokes equations is applied to a series of two-dimensional, steady, laminar hypersonic flows over a compression ramp, including both attached and separated flow conditions. The algorithm uses upwind-biased differencing for the convective and pressure terms and central differencing for the shear-stress and heat-transfer terms. An implicit spatially factored scheme is used to advance the solution in terms on a given mesh, and a V-cycle multigrid strategy is used to accelerate convergence. The multigrid algorithm provided an order of magnitude decrease in the computational time required to obtain a converged position of the separation location and enabled a substantially grid-independent result to be obtained for each of the flows considered.

Thomas, James L.↗

NASA NTRS1993

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

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

Shih, T. I.-P.↗

NASA NTRS1993

Multigrid convergence of an implicit symmetric relaxation scheme

Multigrid has been applied to an existing three-dimensional compressible Euler solver to accelerate the convergence of the implicit symmetric relaxation scheme. This lower-upper symmetric Gauss-Seidel implicit scheme is shown to be an effective multigrid driver in three-dimensions. A grid refinement study is performed including the effects of large cell aspect ratio meshes. Performance figures of the present multigrid code on Cray computers including the new C90 are presented. A reduction of three orders of of magnitude in the residual for a three-dimensional transonic inviscid flow using 920K grid points is obtained in less than 4 minutes on a Cray C90.

Yoon, Seokkwan↗

NASA NTRS1993

Time accuracy and the use of implicit methods

Some of the approximations used to make implicit methods more efficient and practical for the solution of the Euler and Navier-Stokes equations are addressed. In particular, approximate factorizations, diagonalizations, and linearization approximations are reviewed and categorized. A subiteration correction scheme commonly in use at present is introduced, improved, demonstrated, and analyzed. This scheme is used to produce a second-order accurate, more robust implicit method for unsteady flow computations. The subiteration approach can be employed to recover time accuracy without increasing computational time (in most cases producing substantial savings).

Pulliam, Thomas H.↗

NASA NTRS1993

An implicit method for two-dimensional hydrodynamics

An implicit method for compressible multidimensional flows is presented. The method, which is strongly oriented toward astrophysical applications, enables one to simulate very subsonic flows by removing the Courant condition upon time steps. It consists of an implicit purely Lagrangian step, followed by an explicit and second-order accurate (at least in one dimension) remapping step, which is optional. When the remapping step is performed the time step is limited by the 'particle crossing time' and otherwise it is limited only by accuracy considerations. The suggested method, which results from a compromise between accuracy and efficiency, is very efficient relative to other methods. It enables the computation of many multidimensional problems in stellar evolution, such as those governed by very subsonic flows, which were not calculable with existing explicit methods.

Livne, Eli↗

NASA NTRS1989

Upwind-biased, point-implicit relaxation strategies for hypersonic flowfield simulations on supercomputers

An upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for three-dimensional, viscous, hypersonic flows in chemical and thermal nonequilibrium is described. The algorithm is derived using a finite-volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. The relaxation strategy is well suited for computers employing either vector or parallel architectures, and the relation between computer architecture and algorithm is emphasized. It is also well suited to the numerical solution of the governing equations on unstructured grids. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large. block tri-diagonal systems. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over a blunt body. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium (velocity = 8917 m/s, altitude = 78 km.) over the Aeroassist Flight Experiment (AFE) configuration obtained on a multi-domain grid are discussed.

Gnoffo, Peter A.↗

NASA NTRS1994

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on an MIMD (multiple instruction/multiple data stream) parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed, one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the iPSC/860.

Venkatakrishnan, V.↗

NASA NTRS1994

A Fully Implicit Time Accurate Method for Hypersonic Combustion: Application to Shock-induced Combustion Instability

A new fully implicit, time accurate algorithm suitable for chemically reacting, viscous flows in the transonic-to-hypersonic regime is described. The method is based on a class of Total Variation Diminishing (TVD) schemes and uses successive Gauss-Siedel relaxation sweeps. The inversion of large matrices is avoided by partitioning the system into reacting and nonreacting parts, but still maintaining a fully coupled interaction. As a result, the matrices that have to be inverted are of the same size as those obtained with the commonly used point implicit methods. In this paper we illustrate the applicability of the new algorithm to hypervelocity unsteady combustion applications. We present a series of numerical simulations of the periodic combustion instabilities observed in ballistic-range experiments of blunt projectiles flying at subdetonative speeds through hydrogen-air mixtures. The computed frequencies of oscillation are in excellent agreement with experimental data.

Yungster, Shaye↗

NASA NTRS1995

Examples of grid generation with implicitly specified surfaces using GridPro (TM)/az3000. 1: Filleted multi-tube configurations

With examples, we illustrate how implicitly specified surfaces can be used for grid generation with GridPro/az3000. The particular examples address two questions: (1) How do you model intersecting tubes with fillets? and (2) How do you generate grids inside the intersected tubes? The implication is much more general. With the results in a forthcoming paper which develops an easy-to-follow procedure for implicit surface modeling, we provide a powerful means for rapid prototyping in grid generation.

Cheng, Zheming↗

NASA NTRS1994

Parallel implicit unstructured grid Euler solvers

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a multiple-instruction/multiple-data stream parallel computer. An explicit four-stage Runge-Kutta scheme is used to solve two-dimensional flow problems. A family of implicit schemes is also developed to solve these problems, where the linear system that arises at each time step is solved by a preconditioned GMRES algorithm. Two partitioning strategies are employed: one that partitions triangles and the other that partitions vertices. The choice of the preconditioner in a distributed memory setting is discussed. All of the methods are compared both in terms of elapsed times and convergence rates. It is shown that the implicit schemes offer adequate parallelism at the expense of minimal sequential overhead. The use of a global coarse grid to further minimize this overhead is also investigated. The schemes are implemented on a distributed memory parallel computer, the Intel iPSC/860.

TRT-THEORETICAL↗

NASA NTRS1994

Multigrid convergence of an implicit symmetric relaxation scheme

The multigrid method has been applied to an existing three-dimensional compressible Euler solver to accelerate the convergence of the implicit symmetric relaxation scheme. This lower-upper symmetric Gauss-Seidel implicit scheme is shown to be an effective multigrid driver in three dimensions. A grid refinement study is performed including the effects of large cell aspect ratio meshes. Performance figures of the present multigrid code on Cray computers including the new C90 are presented. A reduction of three orders of magnitude in the residual for a three-dimensional transonic inviscid flow using 920 k grid points is obtained in less than 4 min on a Cray C90.

Yoon, Seokkwan↗