Finite volume schemes with equilibrium type discretization of source terms for scalar conservation laws

被引：32

作者：

Botchorishvili, R

Pironneau, O

机构：

[1] Tbilisi State Univ, VIAM, GE-380043 Tbilisi, Georgia

[2] Univ Paris 06, Anal Numer Lab, F-75252 Paris 05, France

来源：

JOURNAL OF COMPUTATIONAL PHYSICS | 2003年 / 187卷 / 02期

关键词：

hyperbolic conservation laws; finite volume schemes; stiff source terms; convergence;

D O I：

10.1016/S0021-9991(03)00086-X

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We develop here a new class of finite volume schemes on unstructured meshes for scalar conservation laws with stiff source terms. The schemes are of equilibrium type, hence with uniform bounds on approximate solutions, valid in cell entropy inequalities and exact for some equilibrium states. Convergence is investigated in the framework of kinetic schemes. Numerical tests show high computational efficiency and a significant advantage over standard cell centered discretization of source terms. Equilibrium type schemes produce accurate results even on test problems for which the standard approach fails. For some numerical tests they exhibit exponential type convergence rate. In two of our numerical tests an equilibrium type scheme with 441 nodes on a triangular mesh is more accurate than a standard scheme with 5000(2) grid points. (C) 2003 Elsevier Science B.V. All rights reserved.

引用

页码：391 / 427

页数：37

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