We consider binary gas mixture flows with viscous compressible components in the absence of chemical reactions. We aggregate the previously derived regularized equations for inhomogeneous mixtures and thus derive new simpler regularized equations for homogeneous ones (i.e., with the common velocity and temperature). The entropy balance equation with the non-negative entropy production is stated for the new equations. They are constructed for numerical simulations of flows.

1.
R. I.
Nigmatulin
,
Dynamics of Multiphase Media
, Vol.
1
(
CRC Press
,
Boca Rayton
,
1990
).
2.
Yu. P.
Golovachev
,
Numerical Simulation of Viscous Gas Flows in a Shock Layer
(
Nauka
,
Moscow
,
1996
) [in Russian].
3.
V.
Giovangigli
,
Multicomponent Flow Modeling
(
Birkhäuser
,
Boston
,
1999
).
4.
I. G.
Lebo
and
V. F.
Tishkin
,
Investigation of Hydrodynamic Instability in Problems of Laser Thermonuclear Fusion
(
Fizmatlit
,
Moscow
,
2006
) [in Russian].
5.
T. G.
Elizarova
,
I. A.
Graur
and
J.-C.
Lengrand
, “
Two fluid computational model for a binary gas mixture
”,
European J. Mech. B/Fluids
20
,
351
369
(
2001
).
6.
T. G.
Elizarova
,
Quasi-Gas Dynamic Equations
(
Springer
,
Berlin-Heidelberg
,
2009
).
7.
B. N.
Chetverushkin
,
Kinetic Schemes and Quasi-Gasdynamic System of Equations
(
CIMNE
,
Barcelona
,
2008
).
8.
M. V.
Kraposhin
,
E. V.
Smirnova
,
T. G.
Elizarova
and
M. A.
Istomina
, “
Development of a new OpenFOAM solver using regularized gas dynamic equations
”,
Comput. Fluids
166
,
163
175
(
2018
).
9.
G. A.
Bird
,
Molecular Gas Dynamic and the Direct Simulation of Gas Flows
(
Clarendon Press
,
Oxford
,
1994
).
10.
T. G.
Elizarova
,
A. A.
Zlotnik
and
B. N.
Chetverushkin
, “
On quasi-gasdynamic and quasi-hydrodynamic equtions for binary mixtures of gases
”,
Dokl. Math.
90
,
1
5
(
2014
).
11.
T. G.
Elizarova
and
J.-C.
Lengrand
, “
Free parameters for the modelization of nonmonatomic binary gas mixtures
”,
J. Thermophys. Heat Transfer
30
,
695
697
(
2016
).
12.
Y.
Zhou
, “
Rayleigh-Taylor and Richtmyer-Meshkov instability induced flow, turbulence, and mixing. II
”,
Phys. Reports
723–725
,
1
160
(
2017
).
13.
A.
Zlotnik
and
V.
Gavrilin
, “
On quasi-gasdynamic system of equations with general equations of state and its application
”,
Math. Model. Anal.
16
,
509
526
(
2011
).
14.
B. N.
Chetverushkin
and
A. A.
Zlotnik
, “
On some properties of multidimensional hyperbolic quasigasdynamic systems of equations
”,
Russ. J. Math. Phys.
24
,
299
309
(
2017
).
This content is only available via PDF.
You do not currently have access to this content.