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

05/31/2021

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by   Koya Sakakibara, et al.

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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.