Explicit and implicity multidimensional compact high-resolution shock-capturing methods: formulation

摘要

Two families of explicit and implicit compact high-resolution shock-capturing methods for the multidimensional compressible euler equations for fluid dynamics are constructed. Some of the these schemes can be fourth- and sixth-order accurate away from disconti- nuities. For the semi-discrete case their shock-capturing properties are of the total variation diminishing (TVD), total variation bounded (TVB), total variation diminishing in the mean (TVDM), essentially nonoscillatory (ENO), or positive type of scheme for 1D scalar hyper- bolic conservation laws and are positive schemes in more than one dimension.