Mullins-Sekerka流动的快速数值方法及其在接触角问题中的应用
A rapid numerical method for the Mullins-Sekerka flow with application to contact angle problems
摘要：
在$\mathbb{R}^2$中借助于电荷模拟法数值求解了Mullins-Sekerka问题。这是Sakakibara和Yazaki计算Hele-Shaw流的数值方案的扩展。我们调查的配置点的数量，以确保生成的近似多边形曲线的长度逐渐减少的充分条件。我们提出了一个新的基准函数的Mullins-Sekerka流，以确认该计划工作良好。此外，通过改变电荷模拟法的基本解，我们成功地建立了一个数值格式，可以用来处理具有接触角条件的Mullins-Sekerka问题。
英文摘要：
The Mullins-Sekerka problem is numerically solved in $\mathbb{R}^2$ with the aid of the charge simulation method. This is an expansion of the numerical scheme by which Sakakibara and Yazaki computed the Hele-Shaw flow. We investigate a sufficient condition for the number of collocation points to ensure that the length of the generated approximate polygonal curves gradually decreases. We propose a new benchmark function for the Mullins-Sekerka flow to confirm that the scheme works well. Moreover, by changing the fundamental solutions of the charge simulation method, we are successful to establish a numerical scheme that can be used to treat the Mullins-Sekerka problem with the contact angle condition.
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