Multilevel Adaptive Methods for Semi-Implicit Solution of Shallow-Water Equations on a Sphere

John W. Ruge Computational Mathematics Group, University of Colorado at Denver, Denver, Colorado

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Stephen F. McCormick Program in Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado

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Samuel Y. K. Yee Geophysics Directorate, Phillips Laboratory, Hanscom Air Force Base, Bedford, Massachusetts

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Abstract

A multigrid algorithm for local refinement in time and space for an Eulerian formulation of the shallow-water equations on a sphere is presented. It is shown that the accuracy obtainable on a full global grid can be reached using local patches in time and space. Results are presented using a model problem with a large-scale disturbance and a problem with topography and realistic initial conditions.

Abstract

A multigrid algorithm for local refinement in time and space for an Eulerian formulation of the shallow-water equations on a sphere is presented. It is shown that the accuracy obtainable on a full global grid can be reached using local patches in time and space. Results are presented using a model problem with a large-scale disturbance and a problem with topography and realistic initial conditions.

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