A simple augmented IIM for 3D incompressible two-phase Stokes flows with interfaces and singular forces

Abstract

In this paper, a Stokes solver on a MAC staggered grid for three-dimensional incompressible two-phase flows with interfaces and singular forces is presented. The main purpose is to develop the simplified IIM to ensure the accuracy near the interface represented by a level-set function. The idea of the simplified IIM is to apply Taylor expansion only along the normal direction and incorporate the jump conditions up to the second normal derivatives into the finite difference scheme. A Newton iteration method is applied to approximate the orthogonal projections for points near the interface. The augmented variables are introduced to decouple the coupled jump conditions of velocity and pressure. The determination of the augmented variables is finally reduced to a linear system, which is solved by the GMRES method. A CG-Uzawa type method is used to solve the discetized Stokes equation with some correction terms. Numerical results show that the proposed algorithm is efficient and can reach global second-order accuracy. The present algorithm can also preserve the area conservation and the discrete divergence free condition very well.