New icosahedral grid-point discretizations of the shallow water equations on the sphere.

*(English)*Zbl 0930.76067From the summary: We describe the implementation of numerical models of shallow water flow on the surface of the sphere, models which include the nondivergent barotropic limit as a special case. All of these models are specified in terms of a new grid-point-based methodology which employs an hierarchy of tessellations derivative of successive dyadic refinements of the spherical icosahedron. Using the new methodology, we have implemented two different formulations of each of the barotropic and shallow water dynamical systems. In one formulation, the vector velocity field is directly advanced in time; in the other, time integration is carried out entirely in terms of scalar quantities (i.e., absolute vorticity in the barotropic model and, in the more general shallow water model, height and velocity potential).

##### MSC:

76M25 | Other numerical methods (fluid mechanics) (MSC2010) |

76B15 | Water waves, gravity waves; dispersion and scattering, nonlinear interaction |

65M55 | Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs |

##### Keywords:

nondivergent barotropic limit; grid-point-based methodology; hierarchy of tesselations; absolute vorticity; barotropic model##### Software:

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\textit{G. R. Stuhne} and \textit{W. R. Peltier}, J. Comput. Phys. 148, No. 1, 23--58 (1999; Zbl 0930.76067)

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