A numerical method for two-phase flow consisting of separate compressible and incompressible regions

We propose a numerical method for modeling two-phase flow consisting of sep arate compressible and incompressible regions. This is of interest, for exa mple, when the combustion of fuel droplets or the shock-induced mixing of l iquids is numerically modeled. We use the level set method to track the int erface between the compressible and incompressible regions, as well as the Ghost Fluid Method (GFM) to create accurate discretizations across the inte rface. The GFM is particularly effective here since the equations differ in both number and type across the interface. The numerical method is present ed in two spatial dimensions with numerical examples in both one and two sp atial dimensions, while three-dimensional extensions are straightforward. ( C) 2001 Academic Press.