A high‐order fully explicit flux‐form semi‐Lagrangian shallow‐water model |
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Authors: | Paul Aaron Ullrich Peter Hjort Lauritzen Christiane Jablonowski |
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Affiliation: | 1. Department of Land, Air and Water Resources, University of California, Davis, Davis, CA 95616, USA;2. Climate and Global Dynamics Division, National Center for Atmospheric Research, Boulder, CO, USA;3. Department of Atmospheric, Oceanic and Space Sciences, Space Research Building, University of Michigan, Ann Arbor, MI 48109, USA |
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Abstract: | A new approach is proposed for constructing a fully explicit third‐order mass‐conservative semi‐Lagrangian scheme for simulating the shallow‐water equations on an equiangular cubed‐sphere grid. State variables are staggered with velocity components stored pointwise at nodal points and mass variables stored as element averages. In order to advance the state variables in time, we first apply an explicit multi‐step time‐stepping scheme to update the velocity components and then use a semi‐Lagrangian advection scheme to update the height field and tracer variables. This procedure is chosen to ensure consistency between dry air mass and tracers, which is particularly important in many atmospheric chemistry applications. The resulting scheme is shown to be competitive with many existing numerical methods on a suite of standard test cases and demonstrates slightly improved performance over other high‐order finite‐volume models. Copyright © 2014 John Wiley & Sons, Ltd. |
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Keywords: | high order semi‐lagrangian finite‐volume methods shallow‐water equations |
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