A Boundary Condition Capturing Method for Multiphase Incompressible Flow

In [6], the Ghost Fluid Method (GFM) was developed to capture the boundary conditions at a contact discontinuity in the inviscid compressible Euler equations. In [11], related techniques were used to develop a boundary condition capturing approach for the variable coefficient Poisson equation on domains with an embedded interface. In this paper, these new numerical techniques are extended to treat multiphase incompressible flow including the effects of viscosity, surface tension and gravity. While the most notable finite difference techniques for multiphase incompressible flow involve numerical smearing of the equations near the interface, see e.g. [19, 17, 1], this new approach treats the interface in a sharp fashion. We would like to thank Dr. David Wasson of Arete Entertainment (www.areteis.com) for developing the fast level set rendering software that was used in the visualization of the three dimensional calculations. Department of Mathematics, University of California Los Angeles, Los Angeles, California 90095 Research supported in part by NSF and DARPA grant NSF-DMS961854, for Virtual Integrated Prototyping (VIP) Computer Science Department, Stanford University, Stanford, California 94305 Research supported in part by ONR N00014-97-1-0027 Department of Mathematics, University of California Santa Barbara, Santa Barbara, California, 93106 Research supported in part by NSF DMS-9805546 1