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Relaxation schemes for the multicomponent Euler system

Published online by Cambridge University Press:  15 November 2003

Stéphane Dellacherie
Stéphane Dellacherie*
Affiliation:
Commissariat à l'Énergie Atomique, 91191 Gif-sur-Yvette, France. stephane.dellacherie@cea.fr.
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Abstract

We show that it is possible to construct a class of entropicschemes for the multicomponent Euler system describing a gas or fluidhomogeneous mixture at thermodynamic equilibrium by applying a relaxation technique. Afirst order Chapman–Enskog expansion shows that the relaxed systemformally converges when the relaxation frequencies go to the infinitytoward a multicomponent Navier–Stokes system with the classical Fick andNewton 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.

Keywords

Multicomponent Euler systemrelaxation schemeentropic schemeChapman–Enskog expansion.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 6 , November 2003 , pp. 909 - 936
Copyright
© EDP Sciences, SMAI, 2003

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