隱式最近點方法求解在變動曲面上的對流擴散方程

Abstract

本文提出一個數值計算方法去求解變動曲面上的對流擴散方程。利用水平集函數捕捉變動曲面。根據最近點方法，利用最近點將對流擴散方程延拓到曲面附近的小區域，並且在這小區域上用Crank-Nichoson方法求解嵌入方程。

We propose a numerical method to solving convection-diffusion equation on a moving surface. We use the level set function to capture the deforming surface. Based on the closest point method, we extend the convection-diffusion equation into a small neighborhood of the surface by closest point, and use Crank-Nicolson scheme to solving the embedding PDE on the neighborhood of the surface.