Numerical simulation of nonlinear coupled Burgers’ equation through meshless radial point interpolation method

Abstract

In present paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the solution of nonlinear coupled Burgers’ equation in two dimensions. Firstly, we obtain a time discrete scheme by approximating time derivative via a finite difference formula, then we use the SMRPI approach to approximate the spatial derivatives. This method is based on a combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which act as basis functions in the frame of SMRPI. In the current work, the thin plate splines (TPS) are used as the basis functions and in order to eliminate the nonlinearity, a simple predictor-corrector (P-C) scheme is performed. The aim of this paper is to show that the SMRPI method is suitable for the treatment of nonlinear coupled Burgers’ equation. With regard to test problems that have not exact solutions, we consider two strategies for checking the stability of time difference scheme and for survey the convergence of the fully discrete scheme. The results of numerical experiments confirm the accuracy and efficiency of the presented scheme.