The spectral element method for the two-dimensional shallow water equations on the sphere is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements obtained from the generalized icosahedral grid introduced previously (Giraldo FX. Lagrange– Galerkin methods on spherical geodesic grids: the shallow water equations. Journal of Computa...

This paper derives an averaged Lagrangian functional for dynamic coupling between rigid-body motion and its interior shallow-water sloshing in three-dimensional rotating translating coordinates; with a time-dependent rotation vector. A new set of variational equations (SWEs) generalized Green–Naghdi the fluid 3-D vector translations, also linear momentum angular containing shallow water, are de...

to control the nonlinear numerical instability, throughout the time evolution of the eulerian form of the nonlinear rotating shallow water equations, it is necessary to add numerical diffusion to the solution. it is clear that, this extra numerical diffusion degrades the accuracy of the numerical solution and should be kept as small as possible. in a conventional approach a hyper-diffusion is u...

Modeling data on the sphere is fundamental to many problems in the geosciences. Classical approaches to these problems are based on expansions of spherical harmonics and/or approximations on latitude/longitude based grids. The former are quite algorithmically complex, while the latter suffer from the notorious pole problem. Additionally, neither of the methods can be easily generalized to other...

The linear shallow water equations on the sphere are discretized on a quasi-uniform, geodesic, icosahedral Voronoi-Delaunay grid with a C-grid variable arrangement and semi-implicit time discretization. A finite volume discretization is employed for the continuity equation in conservation law form, using as control volumes either the hexagonal/pentagonal or the dual triangular cells. A geostrop...