A volume-of-fluid (VOF) interface-sharpening method for two-phase incompressible flows

Abstract A three-dimensional volume-of-fluid (VOF) interface-sharpening method is developed on the general curvilinear grid for two-phase incompressible flows. In this method, a VOF discretization scheme is formulated for the advection of a two-fluid interface. To maintain interface sharpness, a treatment is applied by solving an interface-sharpening equation after each advection time step, thereby reducing the numerical diffusion error in the solution of the discretization scheme. To demonstrate the accuracy and capability of the advection scheme, several numerical experiments involving three benchmark tests of pure advection were conducted. The results show that the method can realize a sharp interface reliably and efficiently, and reasonable mass conservation is obtained. For the flow field of viscous incompressible flows, the Navier–Stokes equations are solved by adopting the dual-time preconditioning method. A fully implicit method with a highly efficient lower-upper symmetrical Gauss–Seidel (LU-SGS) algorithm based on a dual-time stepping technique as a sub-iteration scheme is employed to advance the solution in time. To validate the proposed method for computing incompressible free surface flows, a dam-break flow over a dry horizontal bed and the water entry of a hemisphere with one degree of freedom are simulated. Comparisons of the predicted results with the available experimental data are presented herein.

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