Simulation of the two-dimensional Rayleigh-Taylor instability problem by using diffuse-interface model

The purpose of this paper is to simulate a two-dimensional Rayleigh-Taylor instability problem using the diffuse-interface formulation of the incompressible Navier-Stokes equations. The governing equations consist of a system of coupled nonlinear partial differential equations for conservation of mass, momentum and phase transport. The Boussinesq approximation is introduced in the momentum equation to relax the complexity of variable density formulation. Due to the simplicity, this approximation can be used for small density variations in simulating two-phase flows. The numerical scheme is based on an artificial compressibility formulation with a finite difference scheme for the space discretization. To validate the method, the penetration of a heavier fluid into the lighter one is computed and illustrated graphically.