Conservative Front Tracking in Higher Space Dimensions

We propose a fully conservative Front Tracking algorithm in two space dimension. The algorithm rst uses the point shifted algorithm 12] on two adjacent time levels and then constructs space time hexahedra as computational units. We develope and prove a successful geometric construction under certain interface requirement. This algorithm has a rst order local truncation error for cells near the tracked discontinuity, which is an improvement by one order of accuracy over most nite diierence schemes, which have O(1) local truncation errors near discontinuities.