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

Voir la notice de l'article dans Numdam

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
Mots-clés : multicomponent Euler system, relaxation scheme, entropic scheme, Chapman-Enskog expansion 
@article{M2AN_2003__37_6_909_0,
     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},
     zbl = {1070.76037},
     mrnumber = {2026402},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003061/}
}
TY  - JOUR
AU  - Dellacherie, Stéphane
TI  - Relaxation schemes for the multicomponent Euler system
JO  - ESAIM: Mathematical Modelling and Numerical Analysis 
PY  - 2003
SP  - 909
EP  - 936
VL  - 37
IS  - 6
PB  - EDP-Sciences
UR  - https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003061/
DO  - 10.1051/m2an:2003061
LA  - en
ID  - M2AN_2003__37_6_909_0
ER  - 
%0 Journal Article
%A Dellacherie, Stéphane
%T Relaxation schemes for the multicomponent Euler system
%J ESAIM: Mathematical Modelling and Numerical Analysis 
%D 2003
%P 909-936
%V 37
%N 6
%I EDP-Sciences
%U https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003061/
%R 10.1051/m2an:2003061
%G en
%F M2AN_2003__37_6_909_0
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. https://geodesic-test.mathdoc.fr/articles/10.1051/m2an:2003061/

Cité par Sources :