A modified leapfrog scheme for shallow water equations
Date
2011-01-25Metadata
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https://hdl.handle.net/1912/4964As published
https://doi.org/10.1016/j.compfluid.2011.08.019Keyword
Shallow Water Equations; Leapfrog scheme; Courant number; Eigenvalue; Semi-implicit; Finite-volume; StabilityAbstract
In the 1D linearized shallow water equations, the Courant number should be < 0.5 for stability in the original Leapfrog (LF) scheme. Here, we propose using the time-averaged heights in the pressure gradient force in the momentum equations. The stability analysis shows that the new scheme is neutral when Courant number <1. The scheme is 2nd order accurate in both time and space. It does not require iterations and can be easily applied in 2D or 3D wave equations. The numerical simulations for 2-D linearized shallow water equations are consistent with those obtained from a 2-time-step semi-implicit scheme.
Description
Author Posting. © The Author(s), 2011. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Computers & Fluids 52 (2011): 69-72, doi:10.1016/j.compfluid.2011.08.019.
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Suggested Citation
Preprint: Sun, Wen-Yih, Sun, Oliver M. T., "A modified leapfrog scheme for shallow water equations", 2011-01-25, https://doi.org/10.1016/j.compfluid.2011.08.019, https://hdl.handle.net/1912/4964Related items
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