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

[摘要] ENGLISH ABSTRACT: Shallow water equations (SWEs) are a set of hyperbolic partial differentialequations that describe the flow below a pressure surface in a fluid. They arewidely applicable in the domain of fluid dynamics. To meet the needs of engineersworking on the area of fluid dynamics, a method known as spectral/hpelement method has been developed which is a scheme that can be used withcomplicated geometry. The use of discontinuous Galerkin (DG) discretisationpermits discontinuity of the numerical solution to exist at inter-element surfaces.In the DG method, the solution within each element is not reconstructedby looking to neighbouring elements, thus the transfer information between elementswill be ensured through the numerical fluxes. As a consequence, theaccuracy of the method depends largely on the definition of the numericalfluxes. There are many different type of numerical fluxes computed from Riemannsolvers. Four of them will be applied here respectively for comparisonthrough a 2D Rossby wave test case.

[发布机构] Stellenbosch University