Numerical simulation of two-phase flow with interface tracking by adaptive Eulerian grid subdivision

A numerical model for the simulation of three-dimensional liquid–gas flow with free surfaces is presented. The incompressible Navier–Stokes equations are assumed to hold in the liquid domain, while the surrounding gas is assumed to be compressible, with constant pressure in each bubble of gas. An implicit time splitting scheme couples a method of characteristics for the solution of advection problems, the continuum surface force model for the computation of surface tension effects, and an implicit scheme for the solution of a time dependent Stokes problem. A two-grid method that couples a structured grid of small cells and a finite element mesh of tetrahedrons is used. A novel interface tracking technique involving local adaptive mesh refinement around the interface is detailed to obtain a more accurate approximation of the free surfaces and the surface forces. Numerical experiments, including sloshing and oscillations problems, illustrate the accuracy improvement when using the adaptive Eulerian grid subdivision.