## The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions (1995)

Venue: | Comm. Pure Appl. Math |

Citations: | 197 - 20 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}

}

### Years of Citing Articles

### OpenURL

### 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...

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