HOW TO PRESERVE THE MASS FRACTIONS POSITIVITY WHEN COMPUTING COMPRESSIBLE MULTICOMPONENT FLOWS

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. © 1991.