On Front Tracking for Compressible Flow

Streamline simulation is particularly efficient for incompressible two-phase flow, for which one can use front tracking to solve the 1-D transport problems along streamlines. Here we investigate the extension of this method to compressible (and immiscible) flow and discuss some of the difficulties involved, and in particular the choices one has in writing the 1-D transport equation(s). Our study is motivated by the simulation of CO2 injection, and we therefore also develop methods that are particularly suited for solving compressible flow where one phase is incompressible. Altogether, we present four front-tracking methods that are based on a combination of solving ordinary Riemann problems and Riemann problems with discontinuous flux.