Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: Shallow water equations (SWEs) are a set of hyperbolic partial differential
equations that describe the flow below a pressure surface in a fluid. They are
widely applicable in the domain of fluid dynamics. To meet the needs of engineers
working on the area of fluid dynamics, a method known as spectral/hp
element method has been developed which is a scheme that can be used with
complicated geometry. The use of discontinuous Galerkin (DG) discretisation
permits discontinuity of the numerical solution to exist at inter-element surfaces.
In the DG method, the solution within each element is not reconstructed
by looking to neighbouring elements, thus the transfer information between elements
will be ensured through the numerical fluxes. As a consequence, the
accuracy of the method depends largely on the definition of the numerical
fluxes. There are many different type of numerical fluxes computed from Riemann
solvers. Four of them will be applied here respectively for comparison
through a 2D Rossby wave test case. / AFRIKAANSE OPSOMMING: Vlakwatervergelykings (SWEs) is ’n stel hiperboliese parsiële differensiaalvergelykings
wat die vloei onder ’n oppervlak wat druk op ’n vloeistof uitoefen
beskryf. Hulle het wye toepassing op die gebied van vloeidinamika. Om aan die
behoeftes van ingenieurs wat werk op die gebied van vloeidinamika te voldoen
is ’n metode bekend as die spektraal /hp element metode ontwikkel. Hierdie
metode kan gebruik word selfs wanneer die probleem ingewikkelde grenskondisies
het. Die Diskontinue Galerkin (DG) diskretisering wat gebruik word
laat diskontinuïteit van die numeriese oplossing toe om te bestaan by tussenelement
oppervlakke. In die DG metode word die oplossing binne elke element
nie gerekonstrueer deur te kyk na die naburige elemente nie. Dus word die oordrag
van informasie tussen elemente verseker deur die numeriese stroomterme.
Die akkuraatheid van hierdie metode hang dus grootliks af van die definisie
van die numeriese stroomterme. Daar is baie verskillende tipe numeriese strometerme
wat bereken kan word uit Riemann oplossers. Vier van hulle sal hier
gebruik en vergelyk word op ’n 2D Rossby golf toets geval.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/86610 |
| Date | 04 1900 |
| Creators | Rasolofoson, Faraniaina |
| Contributors | Chun, Sehun, Stellenbosch University. Faculty of Science. Dept. of Mathematical Sciences. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 55 p. : ill. |
| Rights | Stellenbosch University |
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