Novel Numerical Method Based on the Analog Equation Method for a Class of Anisotropic Convection-Diffusion Problems

Abstract

In this work, a CMFS method based on the analogy equation method, the radial basis function and the method of fundamental solutions for linear and nonlinear convection-diffusion equations in anisotropic materials is presented. The analog equation method is utilized to transform the linear and nonlinear convection-diffusion equation into an equivalent one. The expressions of the homogeneous solution and particular solution are derived by utilizing the radial basis function approximation and the method of fundamental solutions, respectively. By enforcing the desired solution to satisfy the original convection-diffusion equation with boundary conditions at boundary and internal collocation points yield a nonlinear system of equations, which can be solved by using the Newton-Raphson iteration or the Picard method of iteration. The error convergence curves of the proposed meshless method have been investigated by using different globally supported radial basis functions. Numerical experiments show that the proposed CMFS method is promising for anisotropic convection-diffusion problems with accurate and stable results.