A PDE-Based Velocity Extrapolation Method for the Transport of the Level Set Function in Two Phase Liquid-Gas Flows

Abstract

This work presents a numerical scheme to improve the velocity field used to transport the level set function in two phase liquid–gas flows. Since the material properties (density and viscosity) are discontinuous at the moving interface, the velocity field that results from the Navier-Stokes solver is inaccurate close to the interface, leading to non negligible errors in the transport of the level set function. The methodology is based on the resolution of an elasticity-like partial differential equation to compute an improved velocity field, being thus much easier to implement in standard finite element codes than other geometrical extrapolation methodologies. In the computation, only the physical velocity on the liquid side is considered, since it governs the dynamics. The improved velocity field is then exclusively used for the transport of the level set function. Though no incompressibility constraint is imposed to the extrapolated velocity, numerical evidence shows that the method improves the accuracy of computations and, in particular, the mass conservation.