Relaxation schemes for the multicomponent Euler system

Stéphane Dellacherie

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 6, page 909-936
  • ISSN: 0764-583X

Abstract

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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.

How to cite

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Dellacherie, Stéphane. "Relaxation schemes for the multicomponent Euler system." ESAIM: Mathematical Modelling and Numerical Analysis 37.6 (2010): 909-936. <http://eudml.org/doc/194198>.

@article{Dellacherie2010,
abstract = { 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. },
author = {Dellacherie, Stéphane},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Multicomponent Euler system; relaxation scheme; entropic scheme; Chapman–Enskog expansion.; entropic schemes; first-order Chapman-Enskog expansion; hyperbolicity},
language = {eng},
month = {3},
number = {6},
pages = {909-936},
publisher = {EDP Sciences},
title = {Relaxation schemes for the multicomponent Euler system},
url = {http://eudml.org/doc/194198},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Dellacherie, Stéphane
TI - Relaxation schemes for the multicomponent Euler system
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 6
SP - 909
EP - 936
AB - 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.
LA - eng
KW - Multicomponent Euler system; relaxation scheme; entropic scheme; Chapman–Enskog expansion.; entropic schemes; first-order Chapman-Enskog expansion; hyperbolicity
UR - http://eudml.org/doc/194198
ER -

References

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