Theoretical and Computational Multiphysics Group, Department of Mechanical Engineering, FAMU - FSU College of Engineering
"A Front-Tracking Shock-Capturing Method for Two Gases"


We present a high-order front-tracking method for hyperbolic systems of conservation laws for two gases separated by a contact discontinuity. This approach is a generalization of the Embarked Boundary method for time dependent material domains, and applies a combination of a high-order Godunov algorithm and level set methods. We discretize 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 non-conservative finite volume quadratures provides small-cell stability, and the global conservation is maintained using redistribution. We demonstrate test results for second-order convergence in smooth flow, first-order convergence in the presence of shocks, and applications of this approach in shock driven two-gas problems.