Upwind difference schemes for hyperbolic systems of conservation laws

Osher, Stanley; Solomon, Fred

doi:10.1090/S0025-5718-1982-0645656-0

Upwind difference schemes for hyperbolic systems of conservation laws
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by Stanley Osher and Fred Solomon PDF

Math. Comp. 38 (1982), 339-374 Request permission

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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