A Hybrid Reproducing Kernel Particle Method for Three-Dimensional Advection-Diffusion Problems

Abstract

In this paper, a hybrid reproducing kernel particle method (HRKPM) for three-dimensional (3D) advection-diffusion problems is presented. The governing equation of the advection-diffusion problem includes the second derivative of the field function to space coordinates, the first derivative of the field function to space coordinates and time, so it is necessary to discretize the time domain after discretizing the space domain. By introducing the idea of dimension splitting, a 3D advection-diffusion problem can be transformed into a series of related two-dimensional (2D) ones in the dimension splitting direction. Then, the discrete equations of these 2D problems are established by using the RKPM, and these discrete equations are coupled by using the difference method. Finally, by using the difference method to discretize the time domain, the formula of the HRKPM for solving 3D advection-diffusion problem is obtained. Numerical results show that the HRKPM has higher computational efficiency than the RKPM when solving 3D advection-diffusion problems.