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Non-Oscillatory Boundary Treatment for Staggered Central Schemes

We are concerned with high-resolution, non-oscillatory central schemes for approximating solutions of nonlinear, multi-dimensional, hyperbolic conservation laws subject to prescribed initial values and to Dirichlet boundary conditions in inflow boundaries. We demonstrate that a naive continuation of these central schemes up to the boundary typically results in spurious oscillations at inflow boundaries. Consequently, we are led to present our new boundary scheme which is based on a different treatment in inflow and in outflow boundaries. We explicitly construct the boundary scheme in one and in two space dimensions and present numerical simulations that clearly demonstrate its desired non-oscillatory properties.