A decoupled augmented IIM strategy for incompressible two‐phase flows with interfaces on irregular domains

A decoupled augmented immersed interface method for solving incompressible two‐phase flows involving both irregular domains and interfaces is presented. In order to impose the prescribed velocity at the boundary of the irregular domain, singular force as one set of augmented variables is introduced. The velocity components at the two‐fluid interface as another set of augmented variables are introduced to satisfy the continuity condition of the velocity across the interface so that the jump conditions for the velocity and pressure are decoupled across the interface. The augmented variables and/or the forces along the interface/boundary are related to the jumps in both pressure and velocity and the jumps in their derivatives across the interface/boundary and applied to the fluid through jump conditions. The resulting augmented equation is a couple system of these two sets of augmented variables, and the direct application of the GMRES is impractical due to larger iterations. In this work, the novel decoupling of two sets of the augmented variables is proposed, and the decoupled augmented equation is then solved by the LU or the GMRES method. The Stokes equations are discretized via the finite difference method with the incorporation of jump contributions on a staggered Cartesian grid and solved by the conjugate gradient Uzawa‐type method. The numerical results show that second‐order accuracy for the velocity is confirmed. The present method has also been applied to solve for incompressible two‐phase Navier–Stokes flow with interfaces on irregular domains. Copyright © 2011 John Wiley & Sons, Ltd.