Front-Tracking Methods

Front tracking is the use of surfaces or lower dimensional manifolds as computational degrees of freedom in a numerical algorithm. Its purpose is to improve the resolution of discontinuities or steep gradients in the solution variables or in the laws of physics which describe them. Thermal or concentration discontinuities, and thermodynamic phase discontinuities, often poorly handled by Eulerian advection schemes, may benefit from the use of front tracking. Other examples include discontinuities or strong gradients in opacity, conductivity, permeability and material strength. We present the front-tracking algorithm in a formulation which includes two important recent developments, namely (cell-by-cell) conservation and an application programming interface for ease of insertion of tracking into client codes. Ongoing work to improve the late time robustness of the solution, still in progress, is outlined here. We also present an overview of solved problems, based on the front-tracking algorithm. We discuss in general terms the problem classes for which the algorithm is beneficial as well as those for which it seems to offer little benefit. This important distinction is the topic of ongoing research.