NASA Logo

NTRS

NTRS - NASA Technical Reports Server

Back to Results
Discretization and Preconditioning Algorithms for the Euler and Navier-Stokes Equations on Unstructured MeshesSeveral 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.
Document ID
20020048259
Acquisition Source
Ames Research Center
Document Type
Preprint (Draft being sent to journal)
Authors
Barth, Timothy
(NASA Ames Research Center Moffett Field, CA United States)
Chancellor, Marisa K.
Date Acquired
August 20, 2013
Publication Date
January 1, 1997
Subject Category
Fluid Mechanics And Thermodynamics
Funding Number(s)
PROJECT: RTOP 519-40-12
Distribution Limits
Public
Copyright
Work of the US Gov. Public Use Permitted.

Available Downloads

There are no available downloads for this record.
No Preview Available