Recent years have seen a growing interest in developing numerical algorithms for compressible multifluids. Computations ran into unexpected difficulties due to oscillations generated at material interfaces, and understanding of the underlying mechanisms was needed before these oscillations could be circumvented. This paper reviews some of the recent models and numerical algorithms that have been proposed and points to key ideas that they have in common. Noting the known fact that such oscillations do not arise in single-fluid computations, an extremely simple algorithm is proposed which circumvents the oscillations and amounts to computing two different flux functions across material fronts, to update the different fluids on both sides.

We present a detailed numerical study of the interaction of a weak shock wave with an isolated cylindrical gas inhomogeneity. Such interactions have been studied experimentally in an attempt to elucidate the mechanisms whereby shock waves propagating through random media enhance mixing. Our study concentrates on the early phases of the interaction process which are dominated by repeated refractions and reflections of acoustic fronts at the bubble interface. Specifically, we have reproduced two of the experiments performed by Haas & Sturtevant: a Mach 1.22 planar shock wave, moving through air, impinges on a cylindrical bubble which contains either helium or Refrigerant 22. These flows are modelled using the two-dimensional compressible Euler equations for a two-component fluid (air-helium or air–Refrigerant 22). Utilizing a novel shock-capturing scheme in conjunction with a sophisticated mesh refinement algorithm, we have been able to reproduce numerically the intricate mechanisms that were observed experimentally, e.g. transition from regular to irregular refraction, cusp formation and shock wave focusing, multi-shock and Mach shock structures, and jet formation. The level of agreement lends credibility to a number of observations that can be made using information from the simulations for which there is no experimental counterpart. Thus we can now present an updated description for the dynamics of a shock-bubble interaction which goes beyond that provided by the original experiments.

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