Difference potentials method based on LOD splitting technique for nonlinear convection–diffusion equations with interfaces

Abstract

In this paper, we construct a difference potentials method (DPM) based on the locally one-dimensional (LOD) technique to solve the two-dimensional nonlinear convection-diffusion interface problems. The advantage of using the LOD scheme is that the linear system resulting from the auxiliary problem has a simpler structure and can be solved efficiently and accurately with less central processor (CPU) time. Numerical results validate the robustness, accuracy, and efficiency of the proposed method.

Keywords

• difference potentials
• finite difference method
• spectral method
• interface problems