Numerical methods for hyperbolic conservation laws with stiff relaxation II. Higher-order Godunov methods

Journal Article · Thu Jul 01 00:00:00 EDT 1993 · SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States)

DOI:https://doi.org/10.1137/0914052· OSTI ID:7368802

Pember, R B ^[1]

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1. Lawrence Livermore National Lab., CA (United States)

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, the 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. The 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. The 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.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 7368802
• Journal Information: SIAM Journal on Scientific and Statistical Computing (Society for Industrial and Applied Mathematics); (United States), Vol. 14:4; ISSN 0196-5204
• Country of Publication: United States
• Language: English

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CONSERVATION LAWS
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GAS FLOW
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CALCULATION METHODS
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