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The Mullins-Sekerka problem is numerically solved in $\mathbb{R}^2$ with theaid of the charge simulation method. This is an expansion of the numericalscheme by which Sakakibara and Yazaki computed the Hele-Shaw flow. Weinvestigate a sufficient condition for the number of collocation points toensure that the length of the generated approximate polygonal curves graduallydecreases. We propose a new benchmark function for the Mullins-Sekerka flow toconfirm that the scheme works well. Moreover, by changing the fundamentalsolutions of the charge simulation method, we are successful to establish anumerical scheme that can be used to treat the Mullins-Sekerka problem with thecontact angle condition.

A rapid numerical method for the Mullins-Sekerka flow with application to contact angle problems