Numerical methods for hyperbolic conservation laws with stiff relaxation--1: Spurious solutions

Journal Article · Fri Oct 01 04:00:00 EDT 1993 · SIAM Journal of Applied Mathematics (Society for Industrial and Applied Mathematics); (United States)

DOI:https://doi.org/10.1137/0153062· OSTI ID:5791627

Pember, R B ^[1]

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

The author considers the numerical solution of hyperbolic systems of conservation laws with relaxation using a shock-capturing finite difference scheme on a fixed, uniform spatial grid. It is conjectured that certain a priori criteria ensure that the numerical method does not produce spurious solutions as the relaxation time vanishes. One criterion is that the limits of vanishing relaxation time and vanishing viscosity commute for the viscous regularization of the hyperbolic system. A second criterion is that a certain subcharacteristic'' condition be satisfied by the hyperbolic system. This conjecture is supported with analytical and numerical results for a specific example, the solution of generalized Riemann problems of a model system of equations with a fractional step scheme in which Godunov's method is coupled with the backward Euler method. Similar ideas are applied to the numerical solution of stiff detonation problems.

• DOE Contract Number: W-7405-ENG-48
• OSTI ID: 5791627
• Journal Information: SIAM Journal of Applied Mathematics (Society for Industrial and Applied Mathematics); (United States), Journal Name: SIAM Journal of Applied Mathematics (Society for Industrial and Applied Mathematics); (United States) Vol. 53:5; ISSN SMJMAP; ISSN 0036-1399
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990200* -- Mathematics & Computers
ANALYTICAL SOLUTION
CALCULATION METHODS
CONSERVATION LAWS
DETONATIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FINITE DIFFERENCE METHOD
ITERATIVE METHODS
NUMERICAL SOLUTION
PARTIAL DIFFERENTIAL EQUATIONS
USES