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Hele-Shaw flows with time-dependent gaps create fingering patterns, andmagnetic fluids in Hele-Shaw cells create intriguing patterns.We propose asimple numerical method for Hele-Shaw type problems by the method offundamental solutions.The method of fundamental solutions is one of themesh-free numerical solvers for potential problems, which provides a highlyaccurate approximate solution despite its simplicity.Moreover, combining withthe asymptotic uniform distribution method, the numerical method satisfies thevolume-preserving property.We use Amano's method to arrange the singular pointsin the method of fundamental solutions.We show several numerical results toexemplify the effectiveness of our numerical scheme.

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