A hybrid method for moving interface problems with application to the Hele-Shaw flow

In this paper, a hybrid approach which combines the immersed interface method with the level set approach is presented. The fast version of the immersed interface method is used to solve the differential equations whose solutions and their derivatives may be discontinuous across the interfaces due to the discontinuity of the coefficients or/and singular sources along the interfaces. The moving interfaces then are updated using the newly developed fast level set formulation which involves computation only inside some small tubes containing the interfaces. This method combines the advantage of the two approaches and gives a second-order Eulerian discretization for interface problems. Several key steps in the implementation are addressed in detail. This new approach is then applied to Hele-Shaw flow, an unstable flow involving two fluids with very different viscosity. (C) 1997 Academic Press.