一种求解运动曲面上对流扩散方程的三维水平集方法

A 3D level-set method for solving convection-diffusion along moving surfaces

给出了一种求解运动曲面上对流扩散方程的三维水平集算法.水平集函数被用来表示曲面.曲面上的微分方程及其解通过水平集方法被延拓到包含曲面的一个小邻域中.一种半隐式的Crank-Nicholson格式被用来做时间推进,中心差分和三阶加权实质无振荡(WENO)格式被分别用来离散方程中的扩散项和对流项.分析证明了它在标准的Courant-Friedrichs-Lewy(CFL)条件下的稳定性.数值算例显示了它能取得二阶精度.

In this note, we present a 3D level-set method for solving convection-diffusion equations on moving surfaces. A level-set function is used to implicitly capture the surface. The PDE is extended into a small neighborhood of the surface via the level-set techniques. It is solved in the neighborhood by using a semi-implicit Crank-Nicholson scheme. Von Neumann stability analysis shows that it is stable under standard CFL condition. Numerical results demonstrate that the second-order accuracy can be achieved.