An Upwind Local Radial Basis Functions-finite Difference (RBF-FD) Method for Solving Compressible Euler Equation with Application in Finite-rate Chemistry
نویسندگان
1 Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran
2 Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Science and Technology, South Mehrabad, Tehran, Iran
3 Department of Applied Mathematics, Faculty of Mathematics and Computer Sciences, Amirkabir University of Technology, No. 424, Hafez Ave.,15914, Tehran, Iran
doi
10.22052/ijmc.2017.106402.1325چکیده
The main aim of the current paper is to propose an upwind local radial basis functions-finitedifference (RBF-FD) method for solving compressible Euler equation. The mathematical formulation of chemically reacting, inviscid, unsteady flows with species conservation equationsand 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. Thesolutions of advection equations have some shock, thus, special numerical methods should beapplied for example discontinuous Galerkin and finite volume methods. Moreover, two problems are given that show the acceptable accuracy and efficiency of the proposed scheme.
