A conservative solver for surface-tension-driven multiphase flows on collocated unstructured grids

Abstract

We developed a novel conservative model for simulating incompressible multiphase flows on collocated unstructured grids. In conventional schemes, the divergence-free condition is enforced by the numerical approximations based on the least-square approach which inherently cannot guarantee its conservative property for volume integrated average (VIA) of velocity. In this study, point values (PVs) at cell vertices are defined in addition to its VIAs for the pressure variable and a novel discretized formulation is devised for the pressure Poisson equation so as to enforce the VIA of velocity to satisfy the divergence-free condition. Considering the large density ratios in the vicinity of fluid interface, we have also put forward a non-oscillatory and less dissipative reconstruction scheme to improve the resolvability of discontinuous solutions. For the surface-tension dominated flow problems, a novel reinitialization scheme is proposed to transform the abruptly-varying volume fractions into a smooth-varying level-set function which significantly improves the solution accuracy of curvature estimation so as to suppress the spurious currents in presence of the unphysical oscillation. The resulting multiphase model that combines above numerical methods and techniques, therefore adequately assures divergence-free condition to preserve mass conservation, effectively controls the numerical oscillations and dissipations in the vicinity of moving interface and accurately resolves surface tension force with substantially suppressed spurious currents. Various numerical examples have been presented which demonstrate the excellent performance of the newly developed model to predict both fluid dynamics and interfacial deformations with high-fidelity.