Relaxation schemes for the multicomponent Euler system

Stéphane Dellacherie
2003 Mathematical Modelling and Numerical Analysis  
We show that it is possible to construct a class of entropic schemes for the multicomponent Euler system describing a gas or fluid homogeneous mixture at thermodynamic equilibrium by applying a relaxation technique. A first order Chapman-Enskog expansion shows that the relaxed system formally converges when the relaxation frequencies go to the infinity toward a multicomponent Navier-Stokes system with the classical Fick and Newton laws, with a thermal diffusion which can be assimilated to a
more » ... t effect in the case of a fluid mixture, and with also a pressure diffusion or a density diffusion respectively for a gas or fluid mixture. We also discuss on the link between the convexity of the entropies of each species and the existence of the Chapman-Enskog expansion. Mathematics Subject Classification. 35Q30, 65M06, 76N10, 76T05, 80A15.
doi:10.1051/m2an:2003061 fatcat:26ytb46cj5gffoh4upcgzosi3u