Element-free characteristic Galerkin method for Burgers’ equation

Abstract

A new meshfree method named element-free characteristic Galerkin method (EFCGM) is proposed for solving Burgers’ equation with various values of viscosity. Based on the characteristic method, the convection terms of Burgers’ equation disappear and this process makes Burgers’ equation self-adjoint, which ensures that the spatial discretization by the Galerkin method can be optimal. After the temporal discretization, element-free Galerkin method is then applied to solve the semi-discrete equation in space. Moreover, the process is fully explicit at each time step. In order to show the efficiency of the presented method, one-dimensional and two-dimensional Burgers’ equations are considered. The numerical solutions obtained with different values of viscosity are compared with the analytical solutions as well as the results by other numerical schemes. It can be easily seen that the proposed method is efficient, robust and reliable for solving Burgers’ equation, even involving high Reynolds number for which the analytical solution fails.