Derivation of a bilayer model for shallow water equations with viscosity. Numerical validation

Abstract

In this work we present a new two-dimensional bilayer Shallow-Water model including viscosity and friction effects on the bottom and interface level. It is obtained following [[6]] from an asymptotic analysis of non-dimensional and incompressible Navier-Stokes equations with hydrostatic approximation. In order to obtain the viscosity effects into the model we must have into account a second order approximation. To evaluate this model we perform two numerical tests consisting of an internal dam-break problem for both, one and two dimensional cases. In the first one we make a comparison between the model obtained and the NavierStokes simulation.