Fast and accurate numerical approaches for Stefan problems and crystal growth
Fast and accurate numerical approaches for Stefan problems and crystal growth
复制标题
DOI：
10.1080/104077999275848
复制
发表时间：
1999-06-01
影响因子：
1
通讯作者：
Soni, B
中科院分区：
文献类型：
--
作者：
Li, ZL;Soni, B
本文针对Stefan问题和晶体生长模拟提出了新的移动边界/界面数值方法。重点是准确性和速度的问题。提出了一种二阶精度稳定的修正Crank-Nicolson方法。为了加快某类问题的模拟速度，还提出了交替方向隐式（ADI）方法。ADI方法被证明是渐近稳定的，至少一阶精度。然而，数值结果表明，ADI方法实际上提供了二阶精度，如果速度可以精确计算。采用水平集方法对运动界面进行更新，使拓扑结构的变化易于处理。数值实验进行了比较精确的解决方案和文献中的结果。
New numerical approaches for moving boundary/interface applications tailored for Stefan problems and crystal growth simulation are proposed in this article. The focus is on the issues of accuracy and speed-up. A modified Crank-Nicolson method that is second-order accurate and stable is developed. The alternating directional implicit (ADI) method is also developed to speed up the simulation for a certain class of problems. The ADI method is shown to be asymptotically stable and at least first-order accurate. Numerical results, however, show that the ADI method actually provides second-order accuracy if the velocity can be calculated accurately. The level set method is used to update the moving interface so that the topological changes can be handled easily. Numerical experiments are compared to exact solutions and results in the literature.