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.

翻译：本文借助电荷模拟法在$\mathbb{R}^2$中数值求解Mullins-Sekerka问题。这是对Sakakibara与Yazaki计算Hele-Shaw流所采用的数值格式的推广。我们研究了确保生成的多边形近似曲线长度逐渐减小的配置点数量的充分条件。提出了一个新的Mullins-Sekerka流动基准函数，以验证该格式的有效性。此外，通过改变电荷模拟法的基本解，我们成功建立了一个可用于处理带接触角条件的Mullins-Sekerka问题的数值格式。