Traveling Wavelets for the Simulation of a Hele–Shaw Flow with Surface Tension

Abstract

Abstract-The singularity dynamics of two immiscible fluids in a Hele-Shaw cell is studied using the traveling wavelet method. The singularities of the conformal mapping of the flow are accurately approximated by the solutions of a system of ordinary differential equations for the position of couples of zeros and poles. This model also describes secondary tip-splitting instabilities and remains valid for values of the surface tension and time intervals where previous perturbative calculations do not apply.