THE RELAXATION SCHEMES FOR SYSTEMS OF CONSERVATION-LAWS IN ARBITRARY SPACE DIMENSIONS
THE RELAXATION SCHEMES FOR SYSTEMS OF CONSERVATION-LAWS IN ARBITRARY SPACE DIMENSIONS
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DOI：
10.1002/cpa.3160480303
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发表时间：
1995-03-01
影响因子：
3
通讯作者：
XIN, ZP
中科院分区：
文献类型：
--
作者：
JIN, S;XIN, ZP
我们为多个空间维度的守恒定律系统提出一类数值方案（称为松弛方案）。这个想法是使用局部松弛近似。我们构建了一个具有刚性低阶项的线性双曲系统，该系统通过小的耗散校正来近似原始系统。新系统可以通过欠解析的稳定数值离散来服务，而无需在空间上使用黎曼求解器或在时间上使用代数方程求解器的非线性系统。给出了一维和二维问题的数值结果。二阶方案在标量方程的零松弛极限中显示为全变分递减 (TVD)。 (C) 1995 约翰威利父子公司
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 served by underresolved stable numerical discretizations without using either Riemann solvers spatially or a nonlinear system of algebraic equations solvers 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. (C) 1995 John Wiley & Sons, Inc.