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Finite difference approximation to the shallow water equations on a quasi-uniform spherical grid

TitleFinite difference approximation to the shallow water equations on a quasi-uniform spherical grid
Publication TypeArticolo su Rivista peer-reviewed
Year of Publication1995
AuthorsRonchi, C., Iacono Roberto, and Paolucci P.S.
JournalLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
KeywordsEquations of motion, Finite difference approximations, Finite difference method, Massively parallel computers, Performance and scalabilities, Rossby-Haurwitz waves, Shallow water equations, Spectral transform method, Spheres, Spherical geometries, Spherical surface

A new gridding technique for the solution of partial differential equations in spherical geometry is applied to the shallow water equations. The method, named the ‘Cubed-Sphere’, is based on a decomposition of the sphere into six identical regions, obtained by projecting the sides of a circumscribed cube onto a spherical surface. The grids defined on each of the six regions are coupled through an interopolation procedure based on the composite mesh finite difference method. We present results from two test cases: the integration of a steady state zonal geostrophic flow and the evolution of a Rossby-Haurwitz wave. For this latter case, the performance of the ‘Cubed-Sphere’ method will also be compared in terms of accuracy and execution time to those obtained using the spectral transform method. Finally, for the Rossby-Haurwitz test case we also give performance and scalability results obtained with a parallel version of the ‘Cubed-Sphere’ method run on a 25 Gflops (512 nodes) APE100/Quadrics massively parallel computer. © Springer-Verlag Berlin Heidelberg 1995.


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Citation KeyRonchi1995741