A flux-split algorithm applied to conservative models for multicomponent compressible flows

In this paper we consider a conservative extension of the Euler equations for gas dynamics to describe a two-component compressible flow in Cartesian coordinates. It is well known that classical shock-capturing schemes applied to conservative models are oscillatory near the interface between the two gases. Several authors have addressed this problem proposing either a primitive consistent algorithm [J. Comput. Phys. 112 (1994) 31] or Lagrangian ingredients (Ghost Fluid Method by Fedkiw et al. [J. Comput. Phys. 152 (1999) 452] and [J. Comput. Phys. 169 (2001) 594]). We solve directly this conservative model by a flux-split algorithm, due to the first author (see [J. Comput. Phys. 125 (1996) 42]), together with a high-order (WENO5) flux reconstruction [J. Comput. Phys. 115 (1994) 200; 83 (1989) 32]. This algorithm seems to reduce the oscillations near the interfaces in a way that does not affect the physics of the experiments. We validate our algorithm with the numerical simulation of the interaction of a Mach 1.22 shock wave impinging a helium bubble in air, under the same conditions studied by Haas and Sturtevant [J. Fluid Mech. 181 (1987) 41] and successfully simulated by Quirk and Karni [J. Fluid Mech. 318 (1996) 129].