An upwind finite difference scheme for meshless solvers

In this paper, we present a new upwind finite difference scheme for meshless solvers. This new scheme, capable of working on any type of grid (structure, unstructured or even a random distribution of points) produces superior results. A means to construct schemes of specified order of accuracy is discussed. Numerical computations for different types of flow over a wide range of Mach numbers are presented. Also, these results were compared with those obtained using a cell vertex finite volume code on the same grids and with theoretical values wherever possible. The present framework has the flexibility to choose between various upwind flux formulas.