Numerical simulations of the Rayleigh-Taylor instability

Abstract

Two Lagrangian-Eulerian vortex methods to simulate the motion of an interface between inviscid fluids of different densities are presented. The representation of the interface as a vortex sheet eliminates numerical diffusion, and by coupling the tracked interface with a stationary grid (using the well-known vortex-in-cell method) the high cost associated with traditional vortex methods is reduced. These methods are applied to the Rayleigh-Taylor instability. For finite density ratios the appearance of rolled up vortices and a possible singularity formation has limited simulations in the past. By providing proper regularization our methods overcome some of these difficulties.