Allen-Cahn型相场模型的移动网格方法

Moving mesh method for solving Allen-Cahn phase-field model

针对2种流体的Allen-Cahn型相场模型提出了一种自适应移动网格方法。移动网格方法包括网格重分布和偏微分方程求解2个相对独立的部分。通过求解一个类似于Poisson方程的偏微分方程组获得网格重分布,大量的网格点聚集在2种流体的界面附近从而提高了分辨率,而在其他的区域则仅有比较稀疏的网格点。Allen-Cahn模型用有限差分方法求解,其中的大型稀疏线性方程组使用代数多重网格快速算法求解。数值实验表明移动网格算法在提高分辨率和计算效率方面非常有效。

In this paper,an adaptive moving mesh method is proposed and applied for solving Allen-Cahn phase-field model.The mesh redistribution is obtained by solving a Poisson like partial differential equation system.A plenty of grid points are clustered within the region with large solution variations,while less grid points are located in the regions with smooth solutions.The Allen-Cahn model is discretized by a semi-implicit finite difference scheme,which will lead to a large sparse linear algebra system.The algebra multigrid method is used to solve the linear system.Numerical experiments show that the proposed adaptive approach is effective in improving resolution and computational efficiency.