Posteriori Error Estimation of Adaptive Finite Difference Schemes for Hyperbolic Systems

摘要

We describe several techniques that are based on Richardson's extrapolation for estimating discretization errors of finite difference solutions of one- and two-dimensional hyperbolic systems. These a posteriori error estimates are intended for use with adaptive mesh moving and local refinement procedures. Mesh moving algorithms produce nonuniform grids which necessitate special treatment of solution and error estimation techniques. The required adjustments are discussed using a two-step MacCormack method as a model finite difference scheme. We also discuss automatic time step selection procedures and the effects of artificial viscosity. Extrapolation schemes that produce separate estimates of the temporal and spatial discretization errors are presented and we show how these may be used to control local mesh refinement procedures. Several examples illustrating these procedures are presented. Keywords: Hyperbolic systems, Adaptive methods, Posteriori error estimation, Finite difference methods. (mjm)