Upwind difference schemes for systems of conservation laws: Potential flow equations

We derive new upwind type finite difference approximations to systems of nonlinear hyperbolic conservation laws. The general technique is exemplified by the potential flow equations written as a first order system. The scheme has desirable properties for shock calculations. For the potential flow approximation, we show that the entropy condition is valid for limit solutions and that there exist discrete steady shocks which are unique and sharp. Numerical examples are given.