Analyzing 3D advection-diffusion problems by using the dimension splitting element-free Galerkin method

Abstract

By combining the dimension splitting method with the improved element-free Galerkin (IEFG) method, the dimension splitting element-free Galerkin (DSEFG) method is proposed to solve 3D advection-diffusion problems. By using the dimension splitting method, a 3D advection-diffusion problem is transformed a series of 2D ones. The IEFG method is used for solving these related 2D advection-diffusion problems, and the finite difference method (FDM) is applied in the time space and dimension splitting direction. The discretized system equation is obtained depended on the Galerkin weak form of 2D problems, and the essential boundary conditions are imposed with penalty method, then the formulae of the DSEFG method for 3D advection-diffusion problem are obtained. Numerical examples are given to verify the efficiency of the DSEFG method. And the numerical results show that the DSEFG method can improve the computational efficiency and precision of the IEFG method greatly under the similar computational accuracy.