Lagrange—Galerkin methods on spherical geodesic grids: the shallow water equations

By F. Giraldo. 2000

61 citations recorded by the source corpus.

Abstract The weak Lagrange–Galerkin finite element method for the 2D shallow water equations on the sphere is presented. This method offers stable and accurate solutions because the equations are integrated along the characteristics. The equations are written in 3D Cartesian conservation form and the domains are discretized using linear triangular elements. The use of linear triangular elements permits the construction of accurate (by virtue of the second-order spatial and temporal accuracies of the scheme) and efficient (by virtue of the less stringent CFL condition of Lagrangian methods) schemes on unstructured domains. Using linear triangles in 3D Cartesian space allows for the explicit construction of area coordinate basis functions thereby simplifying the calculation of the finite element integrals. The triangular grids are constructed by a generalization of the icosahedral grids that have been typically used in recent papers. An efficient searching strategy for the departure points is also presented for these generalized icosahedral grids which involves very few floating point operations. In addition a high-order scheme for computing the characteristic curves in 3D Cartesian space is presented: a general family of Runge–Kutta schemes. Results for six test cases are reported in order to confirm the accuracy of the scheme.

Subfields: Computational Mechanics, Earth-Surface Processes

View Paper: https://www.semanticscholar.org/paper/ed7481a85c0ad01453bebe155a32f499149fa6e5

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In Computational Mechanics

In Earth-Surface Processes

Citations in the corpus

The Evolution of Dynamical Cores for Global Atmospheric Models(125th Anniversary Issue of the Meteorological Society of Japan) (2007, methodology): “He first tested it for horizontal advection then applied it to the shallow water equations (Giraldo 2000).”
Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations (2002, methodology): “The generation of the grid on the sphere is a challenging problem and in this section we describe the procedure for generation of general high order icosahedral grid proposed in [8, 9].”