368 IGPM368.pdf        June 2013
TITLE Viscous Sublayering for Shallow Water Flows
AUTHORS Jörn Thies Frings
ABSTRACT 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