A comparative study on the impact of different fluxes in a discontinuous Galerkin scheme for the 2D shallow water equations

Rasolofoson, Faraniaina (2014-04)

Thesis (MSc)--Stellenbosch University, 2014.

Thesis

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/86610
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