HIGH-RESOLUTION STAGGERED MESH APPROACH FOR NONLINEAR HYPERBOLIC SYSTEMS OF CONSERVATION-LAWS

A numerical technique is presented to approximate weak solutions of hyperbolic systems of conservation laws in one and two space dimensions. When strong shocks are present in the exact solution other techniques rely on approximate Riemann problem solvers to cope with this difficulty. The high-order approach here does not use approximate Riemann solvers as a building block and is therefore considerably easier to implement compared to the usual methods. Moreover, the approach here yields sharp nonoscillatory shocks, sharp corners at the base of rarefaction waves and has high order accuracy in regions where the solution is smooth. For the scalar one-dimensional problem the theoretical results confirm the reliability of this approach. © 1992.