Nodal high-order discontinuous Galerkin methods for the spherical shallow water equations

JOURNAL OF COMPUTATIONAL PHYSICS

卷:181

Article

Giraldo, FX ; Hesthaven, JS ; Warburton, T

关键词: discontinuous Galerkin method;    filters;    high-order;    icosahedral grid;    shallow water equations;    spectral element method;    spherical geometry;   

DOI  :  10.1006/jcph.2002.7139

来源: Elsevier

【 摘 要 】

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 Cartesian coordinates, augmented with a Lagrange multiplier to ensure that fluid particles are constrained to the spherical surface. The global solutions are represented by a collection of curvilinear quadrilaterals from an icosahedral grid. On each of these elements the local solutions are assumed to be well approximated by a high-order nodal Lagrange polynomial, constructed from a tensor-product of the Legendre-Gauss-Lobatto points, which also Supplies a high-order quadrature. The shallow water equations are satisfied in a local discontinuous element fashion with solution continuity being enforced weakly. The numerical experiments, involving a comparison of weak and strong conservation forms and the impact of over-integration and filtering, confirm the expected high-order accuracy and the potential for using such highly parallel formulations in numerical weather prediction. (C) 2002 Elsevier Science (USA).

【 授权许可】

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