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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, [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