Numerical simulation of flows involving singularities

Abstract

Many interesting fluid interface problems involve singular events, as breaking-up or merging of the physical domain. In particular, wave propagation and breaking, droplet and bubble break-up, electro-jetting, rain drops, etc. are good examples of such processes. All these mentioned problems can be modeled using the potential flow assumptions, in which an interface needs to be advanced by a velocity determined by the solution of a surface partial differential equation posed on this moving boundary. The standard approach, the Lagrangian-Eulerian formulation together with some sort of front tracking method, is prone to fail when break-up or merging processes appear. The embedded formulation using level sets seamlessly allows topological breakup or merging of the fluid domain. In this work we present the numerical approximation of the embedded model and some computational results regarding electrohydrodynamic applications.