A non-oscillatory Eulerian approach to interfaces in multimaterial flows (the ghost fluid method)

While Eulerian schemes work well for most gas flows, they have been shown t o admit nonphysical oscillations near some material interfaces. In contrast , Lagrangian schemes work well at multimaterial interfaces, but suffer from their own difficulties in problems with large deformations and vorticity c haracteristic of most gas flows. We believe that the most robust schemes wi ll combine the best properties of Eulerian and Lagrangian schemes. In this paper, we propose a new numerical method for treating interfaces in Euleria n schemes that maintains a Heaviside profile of the density with no numeric al smearing along the lines of earlier work and most Lagrangian schemes. We use a level set function to track the motion of a multimaterial interface in an Eulerian framework. In addition, the use of ghost cells (actually gho st nodes in our finite difference framework) and a new isobaric fix techniq ue allows us to keep the density profile from smearing out, while still kee ping the scheme robust and easy to program with simple extensions to multid imensions and multilevel time integration, e.g., Runge-Kutta methods. In co ntrast, previous methods used ill-advised dimensional splitting for multidi mensional problems and suffered from great complexity when used in conjunct ion with multilevel time integrators. (C) 1999 Academic Press.