Analysis of the numerical solution of the shallow water equations
Hamrick, Thomas A.
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This thesis is concerned with the analysis of various methods for the numerical solution of the shallow water equations along with the stability of these methods. Most of the thesis is concerned with the background and formaulation of the shallow water equations. The derivation of the basic equations will be given, in the primative variable and vorticity divergence formulation. Also the shallow water equations will be written in spherical coordinates. Two main types of methods used in approximating differential equations of this nature will be discussed. The two schemes are finite difference method (FDM) and the finite element method (FEM). After presenting the shallow water equations in several formulations, some examples will be presented. The use of the Fourier transform to find the solution of a semidiscrete analog of the shallow water equations is also demonstrated.
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Giraldo, F.X.; Hesthaven, J. S.; Warburton, T. (2002);We present a high-order discontinuous Galerkin method for the solution of the shallow water equations on the sphere. To overcome well-known problems with polar singularities, we consider the shallow water equations in ...
Lustman, Levi; Neta, Beny (Monterey, California. Naval Postgraduate School, 1992-02); NPS-MA-92-004This report contains the host and node programs for the solution of the shallow water equations with topography on an INTEL iPSC/2 hypercube. Finite difference scheme conserving potential enstrophy and energy is employed ...
Multigrid preconditioners for the hybridised discontinuous Galerkin discretisation of the shallow water equations Gibson, Thomas H.; Müller, Eike H.; Betteridge, Jack; Graham, Ivan G. (Elsevier, 2020-10-26);Numerical climate- and weather-prediction models require the fast solution of the equations of fluid dynamics. Discontinuous Galerkin (DG) discretisations have several advantageous properties. They can be used for arbitrary ...