A high‐order element‐based Galerkin method for the barotropic vorticity equation |
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Authors: | Michael N. Levy Ramachandran D. Nair Henry M. Tufo |
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Affiliation: | 1. Department of Applied Mathematics, University of Colorado at Boulder, 526 UCB Boulder, CO 80309‐0526, U.S.A.;2. Institute for Mathematics Applied to Geosciences (IMAGe), The National Center for Atmospheric Research, PO Box 3000 Boulder, CO 80307‐3000, U.S.A.;3. Computational & Information Systems Laboratory (CISL), The National Center for Atmospheric Research, PO Box 3000 Boulder, CO 80307‐3000, U.S.A.;4. Department of Computer Science, University of Colorado at Boulder, 430 UCB Boulder, CO 80309‐0430, U.S.A. |
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Abstract: | A high‐order element‐based Galerkin method is developed to solve the non‐divergent barotropic vorticity equation (BVE). The solution process involves solving a conservative transport equation for the vorticity fields and a Poisson equation for the stream function fields. The discontinuous Galerkin method is employed for solving the transport equation and a spectral element method (continuous Galerkin) is used for the Poisson equation. A third‐order strong stability preserving explicit Runge–Kutta scheme is used for time integration. A series of tests have been performed to validate the model, which include the evolution of an idealized tropical cyclone and interaction of dual vortices in close proximity. The numerical convergence study is performed by solving the BVE on the sphere where the analytic solution is known. The test results are consistent with physical observations, and the model exhibits exponential convergence. Copyright © 2008 John Wiley & Sons, Ltd. |
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Keywords: | barotropic vorticity equation conservative transport cubed sphere discontinuous Galerkin method Poisson problem spectral element method |
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