An upwind local radial basis functions-finite difference (RBF-FD) method for solving compressible Euler equation with application in finite-rate Chemistry

The main aim of the current paper is to propose an upwind local radial basis functions-finite difference (RBF-FD) method for solving compressible Euler equation. The mathematical formulation of chemically reacting, inviscid, unsteady flows with species conservation equations and finite-rate chemistry is studied. The presented technique is based on the developed idea in [58]. For checking the ability of the new procedure, the compressible Euler equation is solved. This equation has been classified in category of system of advection-diffusion equations. The solutions of advection equations have some shock, thus, special numerical methods should be applied for example discontinuous Galerkin and finite volume methods. Moreover, two problems are given that show the acceptable accuracy and efficiency of the proposed scheme.