An Implementation of MAC Grid-Based IIM-Stokes Solver for Incompressible Two-Phase Flows (Communications in Computational Physics, 2011)
In this paper, a novel implementation of immersed interface method combinedwith Stokes solver on a MAC staggered grid for solving the steady two-fluidStokes equations with interfaces. The velocity components along the interface are introducedas two augmented variables and the resulting augmented equation is thensolved by the GMRES method. The augmented variables and/or the forces are relatedto the jumps in pressure and the jumps in the derivatives of both pressure and velocity,and are interpolated using cubic splines and are then applied to the fluid throughthe jump conditions. The Stokes equations are discretized on a staggered Cartesiangrid via a second order finite difference method and solved by the conjugate gradientUzawa-type method. The numerical results show that the overall scheme is second orderaccuracy. The major advantages of the present IIM-Stokes solver are the efficiencyand flexibility in terms of types of fluid flow and different boundary conditions. Theproposed method avoids solution of the pressure Poisson equation, and comparisonsare made to show the advantages of time savings by the present method. The generalizedtwo-phase Stokes solver with correction terms has also been applied to incompressibletwo-phase Navier-Stokes flow.