A consistent and balanced-force model for incompressible multiphase flows on polyhedral unstructured grids

Abstract

This paper presents a consistent and balanced-force model with level-set and volume-of-fluid function (CBLSVOF) to simulate incompressible multiphase flows. The model is constructed by combining FVMS3 (Finite Volume method based on Merged Stencil with 3rd-order reconstruction) and THINC/QQ (THINC method with quadratic surface representation and Gaussian quadrature) scheme which are newly developed on polyhedral unstructured grids. The key principles of this model are characterized by the consistent treatment of mass and momentum transport equation and balanced-force formulation based on LS and VOF methods. The former is realized by approximating the convective fluxes of volume fraction and momentum with identical discrete schemes while the latter is achieved by discretizing the surface tension and gravity forces in the same formulation as the pressure gradient. In addition, a novel algebraic re-initialization scheme is proposed to construct the smooth-varying LS function for curvature estimation which significantly improves the surface tension. The resulting model integrates the advantages of rigorous mass conservation of VOF scheme and of accurate curvature estimation of LS method without loss of simplicity. As verified by numerous benchmark tests, the present model demonstrates remarkable capability to handle large topological changes of interface and high density ratios in complex geometries which is of great importance for practical applications.