A Family of High Order Meshless Methods for Solving 2D Inviscid Compr essible Flows

摘要

The construction of arbitrary high order meshless methods forrncompressible flows still remains an open question. This paper puts forwards arngenuine multi-dimensional framework for high order meshless methods. As thernsolving of Euler equations, these schemes mainly adopt weighted least squaresrnbased on the polynomial basis for the reconstruction of primitive variables and thernflux divergence. To suppress the oscillations near discontinuities, this paper adoptsrnthe WBAP limiter based on the secondary reconstruction procedure. Also anrnendeavor is made for the treatment of high order boundary conditions. Somernstandard cases are performed to validate the accuracy and robustness of thernproposed limiters for the meshless methods.