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How to preserve the mass fractions positivity when computing compressible multi-component flows. (English) Zbl 0725.76090

Summary: We are interested in the numerical investigation of the compressible flow of a gaseous mixture. Considering a hyperbolic system including the Euler equations for the mixture and a mass conservation equation for each species, we propose a new approximation scheme for the convective term of the species equations. This approximation relies on some properties of the exact solution of the Riemann problem for the multi-component system, and applies when an upwind Godunov-type scheme is used for the Euler equations. Its main interest lies in the fact that it preserves the positivity and monotonicity of the mass fractions of all species.

MSC:

76T99 Multiphase and multicomponent flows
76N15 Gas dynamics (general theory)
80A20 Heat and mass transfer, heat flow (MSC2010)

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