Evaluation of a Coupled Level Set and Volume of Fluid Method for Unstructured Meshes

A model for free surface flows has been developped for fully unstructured CFD solvers, coupling a Volume of Fluid (VOF) method (Hirt et al. 1981) with a Level Set (LS) method (Sussman et al. 1994) for the interface capturing, in the context of an unsteady formulation of the mass-momentum equations. The present study seeks to overcome some of the challenges brought by coupling both methods for an unstructured solver using basic test cases.
The goal of coupling both VOF and LS methods is to leverage the advantages. Ideally, an interface capturing method would be able to describe the interface as sharply as possible without leading to instability of the mass-momentum equations, while also achieving global conservation of quantities. Traditionally, either method can only achieve one of these two goals. The VOF method succeeds in conserving mass but has difficulty in controlling the interface thickness without complicated reconstruction; the LS method succeeds in defining an interface thickness, but fails at globally conserving mass (Wang et al. 2009). The blending method often employed uses a VOF method with Piecewise Linear Interface Calculation (PLIC) as a base for transport of the phases, from which the interface location is calculated. This is followed by a redistancing function based on the LS method around the VOF interface, which then allows to prescribe an interface thickness (Figure 1). This new interface is then used to update densities and viscosities of the fluids in the mixed cells (Zhao & Chen 2015).
One of the challenges lies in the redistancing algorithm. In structured solvers, the redistancing equation, which takes the form of an Eikonal equation (Sethian 1999), can be solved using higher-order Essentially Non-Oscillatory (ENO) orWeighted Essential Non-Oscillatory (WENO) discretization schemes for the spatial derivatives (Chen 2011). In unstructured solvers, however, the use of such higher order schemes is complicated by the access to only direct neighbouring cell information.
This study examines the implementation of a Coupled Level Set and Volume of Fluid (CLSVOF) method, using a Flux-Positive (FP) scheme for calculating the spatial derivative in the redistancing algorithm, with an extremum correction for the level set field. The algorithm has been implemented in ReFRESCO, and numerical tests were done using the slotted disk case geometry (Zalesak 1979) and the breaking dam case (Martin et al. 1952). ReFRESCO is a fully unstructured CFD code developped by MARIN and collaborating universities, with a VOF formulation for free surface capturing (Klaij et al. 2018). For the momentum-pressure coupling, the SIMPLE algorithm (Patankar 1983) is used.