368

RWTH Publication No: 230483 2013 IGPM368.pdf 
TITLE 
Viscous Sublayering for Shallow Water Flows 
AUTHORS 
Jörn Thies Frings 
ABSTRACT 
Analyzing the nondimensional, incompressible NavierStokes equations assum ing mostly laminar Shallow Water flow we deduct a set of equations modeling the evolution of mass and discharge including the effects of advection, pressure and viscosity. A numerical scheme for this system of equations is defined, where advection and pressure are dealt with by a Finite Volume approach based on the Roe solver and the viscous effects give rise to discrete velocity profiles influencing the propagation of discharge. Compared to similar works of Gerbeau/Perthame, 2001, [15] and Audusse, 2005, [2] on viscous shallow water flows we seek low numerical cost without prescribing the general shape of the velocity profiles. 
KEYWORDS 
multilayer flows, shallow water, approximate Riemann solvers, finite volume method, viscosity, friction 