An Efficient Shock-Capturing Algorithm for Compressible Multicomponent Problems

A simple shock-capturing approach to multicomponent flow problems is developed for the compressible Euler equations with a stiffened gas equation of state in multiple space dimensions. The algorithm uses a quasi-conservative formulation of the equations that is derived to ensure the correct fluid mixing when approximating the equations numerically with interfaces. A γ -based model and a volume-fraction model have been described, and both of them are solved using the standard high-resolution wave propagation method for general hyperbolic systems of partial differential equations. Several calculations are presented with a Roe approximate Riemann solver that show accurate results obtained using the method without any spurious oscillations in the pressure near the interfaces. Convergence of the computed solutions to the correct weak ones has been verified for a two-dimensional Richtmyer–Meshkov unstable interface problem where we have performed a mesh-refinement study and also shown front-tracking results for comparison. c © 1998 Academic Press