Upwind difference schemes for hyperbolic systems of conservation laws

Authors:
Stanley Osher and Fred Solomon

Journal:
Math. Comp. **38** (1982), 339-374

MSC:
Primary 65M05

DOI:
https://doi.org/10.1090/S0025-5718-1982-0645656-0

MathSciNet review:
645656

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Abstract: We derive a new upwind finite difference approximation to systems of nonlinear hyperbolic conservation laws. The scheme has desirable properties for shock calculations. Under fairly general hypotheses we prove that limit solutions satisfy the entropy condition and that discrete steady shocks exist which are unique and sharp. Numerical examples involving the Euler and Lagrange equations of compressible gas dynamics in one and two space dimensions are given.

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Keywords:
Finite difference approximation,
upwind schemes,
hyperbolic conservation laws

Article copyright:
© Copyright 1982
American Mathematical Society