Multicomponent Flow Calculations by a Consistent Primitive Algorithm

Abstract

The dynamics of inviscid multicomponent fluids may be modelled by the Euler equations, augmented by one (or more) additional species equation(s). Attempts to compute solutions for extended Euler models in conservation form, show strong oscillations and other computational inaccuracies near material interfaces. These are due to erroneous pressure fluctuations generated by the conservative wave model. This problem does not occur in single component computations and arises only in the presence of several species. A nonconservative (primitive) Euler formulation is proposed, which results in complete elimination of the oscillations. The numerical algorithm uses small viscous perturbations to remove leading order conservation errors and is conservative to the order of numerical approximation. Numerical experiments show clean monotonic solution profiles, with acceptably small conservation error for shocks of weak to moderate strengths.