Numerical Methods For A One-Dimensional Interface Separating Compressible And Incompressible Flows

We develop 1D numerical methods for treating an interface separating a liquid drop and a high speed gas ow. The droplet is an incompressible Navier-Stokes uid. The gas is a compressible, multi-species, chemically reactive Navier-Stokes uid (Fedkiw et al., 1996; Fedkiw, 1996). The interface is followed with a marker particle, although the level set method will be used for the eventual 2D extension (Sussman, 1995). Away from the interface, we solve the equations with TVD Runge Kutta schemes in time and conservative nite dierence ENO schemes in space (Shu and Osher, 1988). Near the interface, we cannot apply this discretization, since the equations dier in both number and type across the interface. Instead we use the interface location for domain decomposition, and apply a moving control volume formulation nearby. This is done in a conservative framework, compatible with the outer nite dierence scheme. Full details are given for a simple forward Euler time stepping scheme, and this has direct, although algorithmically complicated, extensions to 2nd and 3rd order Runge Kutta methods. Future work will focus on the extension to 2D, and simplications of the higher order time stepping algorithms. 0 Research supported in part by ARPA URI-ONR-N00014-92-J-1890, NSF #DMS 9404942, and ARO DAAH04-95-1-0155. 2 R. FEDKIW ET AL

A Lagrangian central scheme for multi-fluid flows

We develop a central scheme for multi-fluid flows in Lagrangian coordinates. The main contribution is the derivation of a special equation of state to be imposed at the interface in order to avoid non-physical oscillations. The proposed scheme is validated by solving several tests concerning one-dimensional hyperbolic interface problems

Fix for solution errors near interfaces in two-fluid flow computations

A finite-volume method is considered for the computation of flows of two compressible, immiscible fluids at very different densities. A level-set technique is employed to distinguish between the two fluids. A simple ghost-fluid method is presented as a fix for the solution errors ('pressure oscillations') that may occur near two-fluid interfaces when applying a capturing method. Computations with it for compressible two-fluid flows with arbitrarily large density ratios yield perfectly sharp, pressure-oscillation-free interfaces. The masses of the separate fluids appear to be conserved up to first-order accuracy