Upwind Difference Schemes for Hyperbolic Systems of Conservation Laws

Stanley Osher, Fred Solomon
1982 Mathematics of Computation  
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.
doi:10.2307/2007275 fatcat:jn3xcwit7zelpmxibklbtt2mnu