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The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions (1995)
| Venue: | Comm. Pure Appl. Math |
| Citations: | 250 - 21 self |
BibTeX
@ARTICLE{Jin95therelaxation,
author = {S. Jin and Z. Xin and Shi Jin and Zhouping Xin},
title = {The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions},
journal = {Comm. Pure Appl. Math},
year = {1995},
volume = {48},
pages = {235--277}
}
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Abstract
We present a class of numerical schemes (called the relaxation schemes) for systems of conservation laws in several space dimensions. The idea is to use a local relaxation approximation. We construct a linear hyperbolic system with a stiff lower order term that approximates the original system with a small dissipative correction. The new system can be solved by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solver temporally. Numerical results for 1-D and 2-D problems are presented. The second order schemes are shown to be total variation diminishing (TVD) in the zero relaxation limit for scalar equations. 1. Introduction In this paper we present a class of nonoscillatory numerical schemes for systems of conservation laws in several space dimensions. The basic idea is to use a local relaxation approximation. For any given system of conservation laws, we will construct a corresponding linear hyp...
Keyphrases
conservation law relaxation scheme arbitrary space dimension local relaxation approximation several space dimension numerical result corresponding linear hyp order term nonoscillatory numerical scheme linear hyperbolic system algebraic equation relaxation limit small dissipative correction new system second order scheme 2-d problem scalar equation nonlinear system basic idea total variation diminishing numerical scheme riemann solver original system underresolved stable numerical discretizations
