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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Chapter 1 briefly reviews several related topics associated with the symmetrization of systems of conservation laws and quasi-conservation laws: (1) Basic Entropy Symmetrization Theory; (2) Symmetrization and eigenvector scaling; (3) Symmetrization of the compressible Navier-Stokes equations; and (4) Symmetrization of the quasi-conservative form of the magnetohydrodynamic (MHD) equations. Chapter 2 describes one of the best known tools employed in the study of differential equations, the maximum principle: any function f(x) which satisfies the inequality f(double prime)>0 on the interval [a,b] attains its maximum value at one of the endpoints on the interval. Chapter three examines the upwind finite volume schemes for scalar and system conservation laws. The basic tasks in the upwind finite volume approach have already been presented: reconstruction, flux evaluation, and evolution. By far, the most difficult task in this process is the reconstruction step.

Bart, Timothy J.↗
NASA NTRS1995

Numerical Solution of Multi-Dimensional Hyperbolic Conservation Laws on Unstructured Meshes

The lecture material will discuss the application of one-dimensional approximate Riemann solutions and high order accurate data reconstruction as building blocks for solving multi-dimensional hyperbolic equations. This building block procedure is well-documented in the nationally available literature. The relevant stability and convergence theory using positive operator analysis will also be presented. All participants in the minisymposium will be asked to solve one or more generic test problems so that a critical comparison of accuracy can be made among differing approaches.

Barth, Timothy J.↗
NASA NTRS1997

Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured Meshes

Several stabilized discretization procedures for conservation law equations on triangulated domains will be considered. Specifically, numerical schemes based on upwind finite volume, fluctuation splitting, Galerkin least-squares, and space discontinuous Galerkin discretization will be considered in detail. A standard energy analysis for several of these methods will be given via entropy symmetrization. Next, we will present some relatively new theoretical results concerning congruence relationships for left or right symmetrized equations. These results suggest new variants of existing FV, DG, GLS and FS methods which are computationally more efficient while retaining the pleasant theoretical properties achieved by entropy symmetrization. In addition, the task of Jacobian linearization of these schemes for use in Newton's method is greatly simplified owing to exploitation of exact symmetries which exist in the system. These variants have been implemented in the "ELF" library for which example calculations will be shown. The FV, FS and DG schemes also permit discrete maximum principle analysis and enforcement which greatly adds to the robustness of the methods. Some prevalent limiting strategies will be reviewed. Next, we consider embedding these nonlinear space discretizations into exact and inexact Newton solvers which are preconditioned using a nonoverlapping (Schur complement) domain decomposition technique. Elements of nonoverlapping domain decomposition for elliptic problems will be reviewed followed by the present extension to hyperbolic and elliptic-hyperbolic problems. Other issues of practical relevance such the meshing of geometries, code implementation, turbulence modeling, global convergence, etc. will be addressed as needed.

Barth, Timothy↗
NASA NTRS2002

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

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.

Jothiprasad, Giridhar↗
NASA NTRS2006

Time-Accurate, Unstructured-Mesh Navier-Stokes Computations with the Space-Time CESE Method

Application of the newly emerged space-time conservation element solution element (CESE) method to compressible Navier-Stokes equations is studied. In contrast to Euler equations solvers, several issues such as boundary conditions, numerical dissipation, and grid stiffness warrant systematic investigations and validations. Non-reflecting boundary conditions applied at the truncated boundary are also investigated from the stand point of acoustic wave propagation. Validations of the numerical solutions are performed by comparing with exact solutions for steady-state as well as time-accurate viscous flow problems. The test cases cover a broad speed regime for problems ranging from acoustic wave propagation to 3D hypersonic configurations. Model problems pertinent to hypersonic configurations demonstrate the effectiveness of the CESE method in treating flows with shocks, unsteady waves, and separations. Good agreement with exact solutions suggests that the space-time CESE method provides a viable alternative for time-accurate Navier-Stokes calculations of a broad range of problems.

Chang, Chau-Lyan↗
NASA NTRSDate not supplied

Exploring Unstructured Mesh Adaptation for Hybrid Reynolds-Averaged Navier–Stokes/Large Eddy Simulation

Mesh adaptation methods for the Reynolds-averaged Navier–Stokes (RANS) equations are rapidly maturing and beginning to impact the design of aerospace vehicles. RANS turbulence modeling improvements have slowed and may stagnate. Wall-modeled large eddy simulation (LES) and hybrid RANS/LES (HRLES) may provide an improved modeling capability but require specialized expertise to construct appropriate meshes and are considered be too ex-pensive for routine practical use. The realization of the CFD Vision 2030 Study includes improving geometry linkage, mesh generation/adaptation, and turbulence modeling/resolving methods for automated management of errors and uncertainties of physics-based, predictive modeling that can set the stage for ensuring a vehicle is in compliance with a regulation or specification (i.e., certification or qualification by analysis). An exploration of mesh adaptation for HRLES is performed to document synergies and challenges between mesh adaptation and HRLES. Vortex breakdown over a delta wing is examined to show the improvement of HRLES over RANS turbulence modeling approaches. A high lift configuration is shown to demonstrate complex geometry capability. Research and development opportunities are identified to advocate for continuing investments that may allow HRLES to enter routine practical use as a tool for aerospace vehicle analysis and design.

Michael A Park↗
DOE OSTI2022

Transient MOC with frequency transform and DSA on unstructured mesh

We present an implementation of the transient method of characteristics (MOC) with isotropic time derivatives, accelerated by diffusion synthetic acceleration (DSA). The fully implicit frequency transform method is used to solve the transient problem with analytic precursor integration. The code works on meshes composed of almost any of the commonly used non-curvilinear finite element types, and can handle the deformation of geometry in time-dependent transport calculations. We present results of a continuous Fourier analysis for the transient multigroup DSA problem, and representative benchmarking results are presented for the C5G7-TD benchmark in 2D showing reasonable performance and agreement compared to other codes. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗