A collocated unstructured finite volume Level Set / Front Tracking method for two-phase flows with large density-ratios

We propose the rhoLENT method, an extension of the unstructured Level Set / Front Tracking (LENT) method, based on the collocated Finite Volume equation discretization, that recovers exact numerical stability for the two-phase momentum convection with a range of density ratios, namely $rho^-/rho^+in [1, 10000]$. We provide the theoretical basis for the numerical inconsistency in the collocated finite volume equation discretization of the single-field two-phase momentum convection. The cause of the numerical inconsistency lies in the way the cell-centered density is computed in the new time step ($rho_c^{n+1}$). Specifically, if $rho_c^{n+1}$ is computed from the approximation of the fluid interface at $t^{n+1}$, and it is not computed by solving a mass conservation equation (or its equivalent), the two-phase momentum convection term will automatically be inconsistently discretized. We provide the theoretical justification behind using the auxiliary mass conservation equation to stabilize flows with strong density ratios. The evaluation of the face-centered (mass flux) density we base on the fundamental principle of mass conservation, used to model the single-field density, contrary to the use of different weighted averages of cell-centered single-field densities and alternative reconstructions of the mass flux density by other contemporary methods. Implicit discretization of the two-phase momentum convection term is achieved, removing the CFL stability criterion. Numerical stability is demonstrated in terms of the relative $L_infty$ velocity error norm with realistic viscosity and strong surface tension forces. The stabilization technique in the rhoLENT method is also applicable to other two-phase flow simulation methods that utilize the collocated unstructured Finite Volume Method to discretize single-field two-phase Navier-Stokes Equations.