Three-Dimensional Front Tracking

We describe a three dimensional front tracking algorithm, discuss its numerical implementation, and present studies to validate the correctness of this approach. Based on the results of the two dimensional computations, we expect three dimensional front tracking to improve signiicantly computational eeciencies for problems dominated by discontinu-ities. In some cases, for which the interface computations display considerable numerical sensitivity, we expect a greatly enhanced capability. 1. Introduction Front tracking is a numerical method in which surfaces of discontinuity are given explicit computational degrees of freedom; these degrees of freedom are supplemented by degrees of freedom representing continuous solution values at regular grid points. This method is ideal for solutions in which discontinuities are an important feature, and especially where their accurate computation is diicult by other methods. Computational continuum mechanics abounds in such problems, which include phase transition boundaries, ame fronts, material boundaries, slip surfaces, shear bands, and shock waves. The method was initiated by Richtmyer 55] and was used for high quality aerodynamic computations by Moretti 50, 51, 52]. A systematic development of front tracking in two dimensions has been carried out by the references in the survey 37] for other approaches to front tracking in two dimensions. Special purpose front tracking codes have been also developed, for example for simulation of the deposition and etching process for the manufacture of semiconductors 31]. CAD packages for solid geometry use similar concepts, under the terminology of non-manifold geometry. There are also a number of one dimensional front tracking codes 41, 33, 60, 9, 45, 56, 34]. The rst conclusion to emerge from this body of work is that it is possible to apply front tracking in a systematic fashion to complex shock or wave front interaction problems, including problems with bifurcations, with changes of wave front topology, as occurs after interaction, or crossing of one wave (tracked discontinuity) by another. In other words, the rst conclusion is that front tracking is a feasible method for problems with geometrically complex fronts. The second conclusion is that the front tracking solutions are often (a)