Construction of the High Order Accurate Generalized Finite Difference Schemes for Inviscid Compressible Flows

Abstract

The construction of high order accurate generalized finite difference method for inviscid compressible flows still remains an open problem in the literature. In this paper, the high order accurate generalized finite difference schemes have been developed based on the high order reconstruction and the high order numerical flux evaluation on a local cloud of points. The WBAP limiter based on the secondary reconstruction is used to suppress oscillations near discontinuities. The implementation of high order accurate boundary conditions is of critical importance in the construction of high order schemes. A new method is proposed for the high order accurate boundary treatment. Several standard test cases are solved to validate the accuracy, efficiency and shock capturing capability of the proposed high order schemes.