A hybrid improved complex variable element-free Galerkin method for three-dimensional advection-diffusion problems

In this paper, combining the dimension splitting method with the improved complex variable element-free Galerkin method, a hybrid improved complex variable element-free Galerkin (H-ICVEFG) method is presented for three-dimensional advection-diffusion problems. Using the dimension splitting method, a three-dimensional advection-diffusion problem is transformed into a series of two-dimensional ones which can be solved with the improved complex variable element-free Galerkin (ICVEFG) method. In the ICVEFG method, the improved complex variable moving least-squares (ICVMLS) approximation is used to obtain the shape functions, and the penalty method is used to apply the essential boundary conditions. Finite difference method is used in the one-dimensional direction. And Galerkin weak form of three-dimensional advection-diffusion problems is used to obtain the final discretized equations. Then the H-ICVEFG method for three-dimensional advection-diffusion problems is presented. Numerical examples are provided to discuss the influences of the weight functions, the effects of the scale parameter, the penalty factor, the number of nodes, the step number and the time step on the numerical solutions. And the advantages of the H-ICVEFG method with higher computational accuracy and efficiency are shown.