NDLI: Numerical Methods for Hyperbolic Conservation Laws with Stiff Relaxation II. Higher-Order Godunov Methods

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Pember, Richard B.
Copyright Year	1993
Abstract	A higher-order Godunov method is presented for hyperbolic systems of conservation laws with stiff, relaxing source terms. The goal is to develop a Godunov method that produces higher-order accurate solutions using time and space increments governed solely by the nonstiff part of the system, i.e., without fully resolving the effect of the stiff source terms. It is assumed that the system satisfies a certain subcharacteristic condition. The method is a semi-implicit form of a method developed by Colella for hyperbolic conservation laws with nonstiff source terms. In addition to being semi-implicit, our method differs from the method for nonstiff systems in its treatment of the characteristic form of the equations. The method is applied to a model system of equations and to a system of equations for gas flow with heat transfer. Our analytical and numerical results show that the modifications to the nonstiff method are necessary for obtaining second-order accuracy as the relaxation time tends to zero. Our numerical results also suggest that certain modifications to the Riemann solver used by the Godunov method would help reduce numerical oscillations produced by the scheme near discontinuities. The development of a modified Riemann solver is a topic of future work.
Starting Page	824
Ending Page	859
Page Count	36
File Format	PDF
ISSN	10648275
DOI	10.1137/0914052
e-ISSN	10957197
Issue Number	4
Volume Number	14
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-13
Access Restriction	Subscribed
Subject Keyword	Method of characteristics Conservation laws stiff source terms hyperbolic conservation laws with relaxation finite difference methods Godunov-type methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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