Construction of the High Order Accurate Generalized Finite Difference Schemes for Inviscid Compressible Flows (Communications in Computational Physics, 2018)
The construction of high order accurate generalized finite difference methodfor inviscid compressible flows still remains an open problem in the literature. In thispaper, the high order accurate generalized finite difference schemes have been developedbased on the high order reconstruction and the high order numerical flux evaluationon a local cloud of points. The WBAP limiter based on the secondary reconstructionis used to suppress oscillations near discontinuities. The implementation ofhigh order accurate boundary conditions is of critical importance in the construction ofhigh order schemes. A new method is proposed for the high order accurate boundarytreatment. Several standard test cases are solved to validate the accuracy, efficiencyand shock capturing capability of the proposed high order schemes.
Keywords: Cloud of points; high order accurate boundary treatment; high order schemes; generalized finite difference; shock capturing.