High-order well-balanced finite volume schemes for geophysical flows : development and numerical comparisons

Many geophysical flows are merely perturbations of some fundamental equilibrium state. If a numerical scheme shall capture such flows efficiently, it should be able to preserve the unperturbed equilibrium state at the discrete level. In the first part of this thesis we present a class of schemes of any desired order of accuracy which preserve the lake at rest perfectly. These schemes should have an impact for studying important classes of lake and ocean flows. In the Introduction we present some of the key ideas and ingredients of the subsequent sections. We begin with a review of the shallow water equations and their equilibrium states, in particular the lake at rest. Then we show an example of a numerical storm produced by a scheme which is not in discrete equilibrium. Next we review the key ingredient of several of the recent well-balanced schemes, and give some related references. We close with a preview of our new high order well-balanced schemes. In the second part we compare a classical finite-difference and a high order finite-volume scheme for barotropic ocean flows. We compare the schemes with respect to their accuracy, stability, and study various outflow and inflow boundary conditions. We apply the schemes to the problem of eddy formation in shelf slope jets along the Ormen Lange section of the Norwegian shelf. Our results strongly confirm the development of mesoscale eddies caused by instability of the flows.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2007

Author dc:creator

• Pankratz, Normann

Contributors dc:contributor

• Noelle, Sebastian

• info:eu-repo/classification/ddc/510
• Numerische Mathematik
• Finite-Volumen-Methode
• System von partiellen Differentialgleichungen
• Numerische Strömungssimulation
• Mathematik
• Flachwassergleichungen
• shallow-water
• well-balanced
• finite-volume
• high-order
• WENO

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

eng

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-123919%22

OAI identifier oai:identifier

oai:publications.rwth-aachen.de:62348