Die Runge-Kutta-Discontinuous-Galerkin-Methode zur Lösung konvektionsdominierter tiefengemittelter Flachwasserprobleme

Advances in Computational Fluid Dynamics are only to some extend related to rapidly increasing computer performance, but also to improvement of governing equations and numerical solution algorithms. The focus of this thesis is the numerical solution of the two-dimensional depth-averaged shallow water equations with a Runge-Kutta-Discontinuous-Galerkin finite-element method. As a background, a detailed discussion of the mathematical and physical properties of the governing equations is given with particular attention to discontinuous solutions. Existing numerical schemes are reviewed and discussed. The Runge-Kutta-Discontinuous-Galerkin finite-element method is well suited to handle complicated geometries and requires a simple treatment of boundary conditions and source terms to obtain high-order accuracy. The explicit time integration, together with the use of orthogonal shape functions, makes the method computationally as efficient as comparable finite-volume schemes for transient and transcritical flows. For smooth parts of the solution, the scheme is shown to be second and third order accurate for linear and quadratic shape functions, respectively, both in time and space. Furthermore, shocks are usually captured within only two elements. Several steady transcritical and transient flows are investigated to confirm the accuracy and convergence of the scheme. The results indicate excellent agreement with analytical solutions. Comparison of numerical results with a flume experiment of supercritical open-channel flow shows an evaluation of the shallow water model against experimental data. The method allows very good decoupling of the numerical and mathematical model, resulting in a nearly grid-independent solution. The simulation of the actual Malpasset dam-break demonstrates the outstanding applicability of the scheme to non-trivial bathymetry and wave propagation on a dry bed.

Grantor dc:publisher

Publikationsserver der RWTH Aachen University

Year dc:date

2003

Author dc:creator

• Schwanenberg, Dirk

Contributors dc:contributor

• Köngeter, Jürgen

• info:eu-repo/classification/ddc/710
• Landschaftsgestaltung, Raumplanung
• Flachwassergleichungen
• Finite-Elemente

Statement dc:rights

• info:eu-repo/semantics/openAccess

Language dc:language

ger

Identifier

https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-114618%22

OAI record oai:identifier

https://publications.rwth-aachen.de/oai2d?verb=GetRecord&metadataPrefix=oai_dc&identifier=oai%3Apublications.rwth-aachen.de%3A52390