A pressure correction-volume of fluid method for simulation of two-phase flows

A pressure correction method coupled with the volume of fluid (VOF) method is developed to simulate two-phase flows. A volume fraction function is introduced in the VOF method and is governed by an advection equation. A modified monotone upwind scheme for a conservation law (modified MUSCL) is used to solve the solution of the advection equation. To keep the initial sharpness of an interface, a slope modification scheme is introduced. The continuum surface tension (CST) model is used to calculate the surface tension force. Three schemes, central-upwind, Parker-Youngs, and mixed schemes, are introduced to compute the interface normal vector and the gradient of the volume fraction function. Moreover, a height function technique is applied to compute the local curvature of the interface. Several basic test problems are performed to check the order of accuracy of the present numerical schemes for computing the interface normal vector and the gradient of the volume fraction function. Three physical problems, two-dimensional broken dam problem, static drop, and spurious currents, and three-dimensional rising bubble, are performed to demonstrate the efficiency and accuracy of the pressure correction method.