|Preprint-No.:||< 368 >||Published in:||June 2013||PDF-File:||IGPM368_k.pdf|
|Title:||Viscous Sublayering for Shallow Water Flows|
|Authors:||Jörn Thies Frings|
Analyzing the non-dimensional, incompressible Navier-Stokes 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,  and Audusse, 2005,  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|