A novel sharp interface capturing method for two- and three-phase incompressible flows

In this study, a novel sharp interface capturing method is developed for multiphase flows that are composed of two or three immiscible incompressible fluids with different densities and viscosities, and without phase change. The physical formulations are based on the Navier-Stokes (NS) equations and are solved by an implicit finite-volume Riemann solver method, which has the advantages of certainty and simplicity. An interface-sharpening technique (IST), which combines artificial compression and anti-diffusion, is applied to keep the interface sharp. The interface treatment is able to reduce the numerical diffusion error in the solution of the discretization scheme of the homogeneous equilibrium multiphase (HEM) model, and it constrains the thickness of the diffused interface constantly throughout the simulations. The numerical solver is developed in a generalized curvilinear coordinate system to enable simulations for complex geometries using general structured grids. The dual-time pseudo-compressibility method is applied to the NS equations to improve computational productivity. Different numerical results of the validation cases of two- and three-phase flows with presence of free surface or phasic interfaces are discussed.