We present a new high-order front-tracking method for hyperbolic systems of conservation laws for two gases separated by a tracked contact discontinuity, using a combination of a high-order Godunov algorithm and level set methods. Our approach discretizes the moving front and gas domains on a Cartesian grid, with control volumes determined by the intersection of the grid with the front. In cut cells, a combination of conservative and nonconservative finite volume quadratures provide small-cell stability. Global conservation is maintained using redistribution. We demonstrate second-order convergence in smooth flow and first-order convergence in the presence of shocks.
"A front-tracking shock-capturing method for two gases." Commun. Appl. Math. Comput. Sci. 11 (1) 1 - 35, 2016. https://doi.org/10.2140/camcos.2016.11.1