A Rapid Numerical Method for the Mullins–Sekerka Flow with Application to Contact Angle Problems

Abstract

The Mullins–Sekerka problem is numerically solved in R2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathbb {R}}^2$$\\end{document} 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 relationship among a time step, the number of collocation points and the position of singular 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.