Front tracking in two and three dimensions

Front tracking is a method for solving conservation laws in which the evolution of discontinuities is determined through the solution of Riemann problems. This method often does not require highly refined grids, and it has no numerical diffusion. We show the success of this method through a comparison of simulations of the Richtmyer-Meshkov instability, an unstable material interface, with experimental data. Good simulations of such instabilities are notoriously difficult, and we also demonstrate for the same physical problem that grid orientations have no effect on the numerical solution. We also present the first results of our three-dimensional front tracking code by simulating an important aspect of the computer chip manufacturing process: material deposition and etching. Our two- and three-dimensional front tracking code is parallelized for MIMD architectures and runs on our 128 node Intel Paragon.