Hybrid Multifluid Algorithms

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Abstract
Extensions of many successful single-component schemes to compute multicomponent gas dynamics suffer from oscillations and other computational inaccuracies near material interfaces that are caused by the failure of the schemes to maintain pressure equilibrium between the fluid components. A new algorithm based on the compressible Euler equations for multicomponent fluids augmented by the pressure evolution equation is presented. The extended set of equations offers two alternative ways to update the pressure field: (i) using the equation of state or (ii) using the pressure evolution equation. In a numerical implementation, these two procedures generally yield different answers. The former is a standard conservative update, but may produce oscillations near material interfaces; the latter is nonconservative, but becomes exact near interfaces and automatically maintains pressure equilibrium. A hybrid scheme which selects from the two pressure update procedures is presented. The scheme perfectly conserves total mass and momentum and conserves total energy everywhere except at a finite (very small) number of grid cells. Computed solutions exhibit oscillation-free interfaces and have {\em negligible} relative conservation errors in total energy even for very strong shocks. The proposed hybrid approach and switching strategies are independent of the numerical implementation and may provide a simple framework within which to extend one's favourite scheme to solve multifluid dynamics.

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