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RISDiffusion Experiments with a Global Discontinuous Galerkin Shallow-Water Model
Publisher: American Meteorological Society
Abstract: A second-order diffusion scheme is developed for the discontinuous Galerkin (DG) global shallow-water model. The shallow-water equations are discretized on the cubed sphere tiled with quadrilateral elements relying on a ...
Quadrature-Free Implementation of a Discontinuous Galerkin Global Shallow-Water Model via Flux Correction Procedure
Publisher: American Meteorological Society
Abstract: he discontinuous Galerkin (DG) discretization relies on an integral (weak) formulation of the hyperbolic conservation law, which leads to the evaluation of several surface and line integrals for multidimensional problems. ...
Extension of a Conservative Cascade Scheme on the Sphere to Large Courant Numbers
Publisher: American Meteorological Society
Abstract: The conservative cascade scheme (CCS) combines a one-dimensional mass-conserving finite-volume method with an efficient semi-Lagrangian scheme over the sphere. Major limitations of this scheme are a breakdown in the polar ...
The Mass-Conservative Cell-Integrated Semi-Lagrangian Advection Scheme on the Sphere
Publisher: American Meteorological Society
Abstract: A mass-conservative cell-integrated semi-Lagrangian (CISL) scheme is presented and tested for 2D transport on the sphere. The total mass is conserved exactly and the mass of each individual grid cell is conserved in general. ...
A Nonoscillatory Discontinuous Galerkin Transport Scheme on the Cubed Sphere
Publisher: American Meteorological Society
Abstract: he discontinuous Galerkin (DG) method is high order, conservative, and offers excellent parallel efficiency. However, when there are discontinuities in the solution, the DG transport scheme generates spurious oscillations ...
Moving Vortices on the Sphere: A Test Case for Horizontal Advection Problems
Publisher: American Meteorological Society
Abstract: A new two-dimensional advection test on the surface of the sphere is proposed. The test combines a solid-body rotation and a deformational flow field to form moving vortices over the surface of the sphere. The resulting ...
Monotone and Conservative Cascade Remapping between Spherical Grids (CaRS): Regular Latitude–Longitude and Cubed-Sphere Grids
Publisher: American Meteorological Society
Abstract: A high-order monotone and conservative cascade remapping algorithm between spherical grids (CaRS) is developed. This algorithm is specifically designed to remap between the cubed-sphere and regular latitude?longitude grids. ...
Discontinuous Galerkin Transport on the Spherical Yin–Yang Overset Mesh
Publisher: American Meteorological Society
Abstract: discontinuous Galerkin (DG) transport scheme is presented that employs the Yin?Yang grid on the sphere. The Yin?Yang grid is a quasi-uniform overset mesh comprising two notched latitude?longitude meshes placed at right ...
Inherently Conservative Nonpolynomial-Based Remapping Schemes: Application to Semi-Lagrangian Transport
Publisher: American Meteorological Society
Abstract: A group of new conservative remapping schemes based on nonpolynomial approximations is proposed. The remapping schemes rely on the conservative cascade scheme (CCS), which employs an efficient sequence of 1D remapping ...
A Potential Enstrophy and Energy Conserving Scheme for the Shallow-Water Equations Extended to Generalized Curvilinear Coordinates
Publisher: American Meteorological Society
Abstract: n energy and potential enstrophy conserving finite-difference scheme for the shallow-water equations is derived in generalized curvilinear coordinates. This is an extension of a scheme formulated by Arakawa and Lamb for ...