Numerical simulation of incompressible interfacial flows by a level set re-distancing method with improved mass conservation

This paper presents a level set re-distancing (NLS) method to better preserve mass conservation and more accurately predict interface evolution in the simulation of incompressible interfacial flows. In this method, the level set function is first advected by an advection equation. The key to this method depends on the simulation of the re-distancing equation subject to a proper mass-correction term. The performance of the proposed NLS method is verified against benchmark cases such as vortex deforming and Zalesak's cases. The NLS method is then combined with an explicit Adams-Bashforth scheme on a staggered Eulerian grid to obtain Navier- Stokes solutions. Two-layer liquid sloshing, dam-break flow and Rayleigh-Taylor instability are simulated and compared with numerical or experimental results reported in literature. Two-phase flows that involve nonlinear phenomena such as bubble rising and bubble bursting at a free-surface are also chosen to demonstrate the ability of the proposed method in considering surface tension. The NLS method proposed in this paper is compared with the CLSVOF method of Li and Yu (2019) in terms of computational time in dam-break flow and Rayleigh-Taylor instability cases.