Solving Two-Phase Incompressible Stokes Equations Using the Immersed Interface Method and LSMLIB

SIAM Computational Science & Engineering Conference, Costa Mesa, CA, February 21, 2007



Two-phase incompressible Stokes equations appear in many physical and biological applications. We use the second-order Immersed Interface Method (IIM) coupled with the Level Set Method (LSM) to solve multiphase Stokes flows with singular interface force and piecewise constant viscosity coefficient. The Stokes equations are decoupled into Poisson equations using the projection method. To use the IIM for the decoupled Poisson equations, we first derive the jump conditions for both the pressure and the velocity in the case where the two fluids may have unequal viscosity coefficients. Since the jump conditions for the kinematic variables can be decoupled by introducing augmented variables, we use the Generalized Minimal Residual (GMRES) method to solve for the augmented variables, and then solve the Stokes equations. The interface between two fluid phases is impleicitly represented using a level set function. We couple the LSM with IIM for moving interface problems such as mean curvature flows for both 2D and 3D. Numerical simulations show that our algorithm implemented using LSMLIB is both efficient and second-order accurate.