An Upwind Local Radial Basis Functions-finite Difference (RBF-FD) Method for Solving Compressible Euler Equation with Application in Finite-rate Chemistry

Document Type : Research Paper


1 Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran

2 Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, Iran


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.


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