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.
Keywords
Conservation lawMathematicsUpwind schemeEuler equationsNonlinear systemFinite differenceEntropy (arrow of time)Euler systemShock waveTotal variation diminishingLimit (mathematics)Applied mathematicsCompressible flowMathematical analysisHyperbolic partial differential equationCompressibilityShock (circulatory)Partial differential equationMechanicsPhysics
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Publication Info
- Year
- 1982
- Type
- article
- Volume
- 38
- Issue
- 158
- Pages
- 339-374
- Citations
- 771
- Access
- Closed
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Cite This
Stanley Osher,
Fred Solomon
(1982).
Upwind difference schemes for hyperbolic systems of conservation laws.
Mathematics of Computation
, 38
(158)
, 339-374.
https://doi.org/10.1090/s0025-5718-1982-0645656-0
Identifiers
- DOI
- 10.1090/s0025-5718-1982-0645656-0