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arXiv · 2105.14811

A simple numerical method for Hele-Shaw type problems by the method of fundamental solutions

Koya Sakakibara·Yusaku Shimoji·Shigetoshi Yazaki
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Abstract

Hele-Shaw flows with time-dependent gaps create fingering patterns, and magnetic fluids in Hele-Shaw cells create intriguing patterns.We propose a simple numerical method for Hele-Shaw type problems by the method of fundamental solutions.The method of fundamental solutions is one of the mesh-free numerical solvers for potential problems, which provides a highly accurate approximate solution despite its simplicity.Moreover, combining with the asymptotic uniform distribution method, the numerical method satisfies the volume-preserving property.We use Amano's method to arrange the singular points in the method of fundamental solutions.We show several numerical results to exemplify the effectiveness of our numerical scheme.

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Koya Sakakibara, Yusaku Shimoji, Shigetoshi Yazaki. 2021-05-31. A simple numerical method for Hele-Shaw type problems by the method of fundamental solutions. https://arxiv.org/abs/2105.14811

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