A One-Dimensional Conservative Method for Front-Tracking in a Compressible Medium

We present a one-dimensional front-tracking algorithm in a compressible medium that can readily be extended to multiple dimensions. The moving interface cuts out time-varying control volumes and a consistent finite-volume discretization is derived by applying the divergence theorem in space-time. The method is fully conservative, even at discontinuities, and the truncation error is expected to be first-order at the boundary between the two fluids, which is one order higher than conventional methods. Classical benchmark results and convergence studies are presented. Target applications for this work are flames in Type 1A supernovae and gas jet boundaries in plasma-wakefield particle accelerators.