自适应网格在水平集方法中的优化与应用

Optimization and Application of Cartesian Adaptive Grid in Level Set Method

在水平集方法对运动界面进行追踪的过程中,利用自适应笛卡尔网格可以在水平集演化的关键区域对网格进行自动细化。水平集方程每个时间步求解后,细化区域和粗化区域的选择是决定迭代求解效率的一个重要因素,由于不同细化级别边界处的节点部分缺少同级别的邻接点,加大了求解水平集演化方程中偏微分近似解的复杂度。提出一种优化后的笛卡尔自适应网格方法,引入了窄带法对细化区域进行自动选择,使用了red-green混合细化策略,在窄带的边界处对T节点进行消除。加入了优化笛卡尔自适应网格的水平集方法被应用于模拟血管内血栓生长的计算模型中,提高了血栓仿真实验的计算效率。

When using level set method to track a free interface,the adaptive Cartesian grid method could automatically refine the grid of key area in the evolution.In the process of solving level set equation,the refined region and coarse region should be redecided after each time step.Due to hierarchical refinement,the nodes between different refinement levels have an incomplete neighbor node set,it becomes complex to obtain the approximate solution of the partial differential equation in Level set equation.An optimized adaptive Cartesian grid method was proposed.Firstly,the narrow-band method was introduced to select the refinement area automatically.Then,the red-green hybrid refinement strategy was used to eliminate the T node at the boundary of the narrowband.The Level set method with optimized adaptive Cartesian grid was applied to the computational model of thrombus growth inside vessel to improve the computation efficiency of the thrombosis simulation.