IJPAM: Volume 68, No. 3 (2011)

DERIVATION AND NUMERICAL STUDY OF
A NEW VISCOUS SHALLOW WATER BIFLUID MODEL

Christian Bourdarias$^1$, Timack Ngom$^2$, Marguerite Gisclon$^3$
$^{1,3}$Laboratorie de Mathematiques - LAMA, UMR 5127 CNRS
Université de Savoie
Le Bourget du Lac Cedex, 73376, FRANCE
$^1$e-mail: christian.bourdarias@univ-savoie.fr
$^3$e-mail: marguerite.gisclons@univ-savoie.fr
$^2$LANI
Université de Gaston Berger
UFR SAT BP 234 Saint-Louis, SÉNÉGAL
e-mail: leontimack@yahoo.fr


Abstract. We consider the flow of two Newtonian, incompressible and nonmiscible fluids in a 2D thin domain. Starting from the Navier-Stokes equations and using the method of asymptotic expansions we derive a 1D viscous shalow water bifluid model. Numerical simulations are performed using a finite volume method.

Received: September 12, 2010

AMS Subject Classification: 35Q30, 35Q35, 65N08, 76D05, 76D50

Key Words and Phrases: bifluid model, thin domain, viscous shalow water model, Navier-Stokes equations, asymptotic expansion

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 3