Geodesic
Relaxation schemes for the multicomponent Euler system
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 6, pp. 909-936

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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.

DOI : 10.1051/m2an:2003061
Classification : 35Q30, 65M06, 76N10, 76T05, 80A15
Keywords: multicomponent Euler system, relaxation scheme, entropic scheme, Chapman-Enskog expansion 
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     author = {Dellacherie, St\'ephane},
     title = {Relaxation schemes for the multicomponent {Euler} system},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {909--936},
     publisher = {EDP-Sciences},
     volume = {37},
     number = {6},
     year = {2003},
     doi = {10.1051/m2an:2003061},
     mrnumber = {2026402},
     zbl = {1070.76037},
     language = {en},
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Dellacherie, Stéphane. Relaxation schemes for the multicomponent Euler system. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 37 (2003) no. 6, pp. 909-936. doi: 10.1051/m2an:2003061

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