The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions (1995)
| Venue: | Comm. Pure Appl. Math |
| Citations: | 131 - 13 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...
