Relaxation schemes for the multicomponent Euler system
Commissariat à l'Énergie Atomique, 91191 Gif-sur-Yvette, France.
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 Soret 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
Key words: Multicomponent Euler system / relaxation scheme / entropic scheme / Chapman–Enskog expansion.
© EDP Sciences, SMAI, 2003