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

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