An adaptive multilayer model for density layered shallow water flows

• Ein adaptives Mehrschicht-Modell für Dichte-geschichtete Flachwasserströmungen

Frings, Jörn Thies; Noelle, Sebastian (Thesis advisor)

München : Hut (2012)
Dissertation / PhD Thesis

In: Mathematik
Page(s)/Article-Nr.: 237 S.

Zugl.: Aachen, Techn. Hochsch., Diss., 2012

Abstract

Multilayer Shallow Water models give rise to an interesting class of partial differential equations, with a mathematical and numerical complexity in between the full Navier-Stokes equations and the Saint-Venant system for Shallow Water flows. The hyperbolic part of these equations equations allows using modified Finite Volume solvers, which are very efficient. The other part of the equations has to be treated differently, but can model either stratification or viscosity of the flow, or both. In the case of stratified flow with two layers of different densities, instabilites can occur at the interface due to large differences in the velocities of the layer. By adaptively introducing new density-layers and using a velocity profile in depth, the model and the corresponding solver presented in this thesis decrease the occurence of large velocity shears, resulting in a more reliable solver.

Institutions

• Department of Mathematics [110000]
• Mathematics Teaching and Research Area [111520]