Numerical investigation of Rossby waves for nonlinear shallow‐water equations on the sphere
Sign Up to like & getrecommendations! Published in 2019 at "Quarterly Journal of the Royal Meteorological Society"
DOI: 10.1002/qj.3504
Abstract: Although Rossby modes of the nonlinear shallow‐water system on the rotating sphere are suspected to be close to their counterpart for the non‐divergent barotropic vorticity equation, little is known about their properties. A numerical procedure… read more here.
Keywords: shallow water; non divergent; rossby; rossby modes ... See more keywords
A Comparison of the Explicit and Implicit Hybridizable Discontinuous Galerkin Methods for Nonlinear Shallow Water Equations
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DOI: 10.1007/s10915-019-01007-z
Abstract: An explicit implementation of the hybridizable discontinuous Galerkin (HDG) method for solving the nonlinear shallow water equations is presented. We follow the common construction of the implicit HDG for nonlinear conservation laws, and then explain… read more here.
Keywords: nonlinear shallow; hybridizable discontinuous; discontinuous galerkin; water equations ... See more keywords
Entropy Stable and Well-Balanced Discontinuous Galerkin Methods for the Nonlinear Shallow Water Equations
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DOI: 10.1007/s10915-020-01248-3
Abstract: The nonlinear shallow water equations (SWEs) are widely used to model the unsteady water flows in rivers and coastal areas, with extensive applications in ocean and hydraulic engineering. In this work, we propose entropy stable,… read more here.
Keywords: entropy stable; nonlinear shallow; water; water equations ... See more keywords
Symmetry Reductions, Dynamical Behavior and Exact Explicit Solutions to a Class of Nonlinear Shallow Water Wave Equation
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DOI: 10.1007/s12346-020-00380-7
Abstract: By using Lie symmetry analysis and dynamical systems method for a class of nonlinear shallow water wave equation, the exact solutions based on the Lie group method are provided. Especially, the bifurcations and exact explicit… read more here.
Keywords: shallow water; nonlinear shallow; equation; water wave ... See more keywords
The dynamic properties of solutions for a nonlinear shallow water equation
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DOI: 10.1186/s13661-019-1281-2
Abstract: The local well-posedness for the Cauchy problem of a nonlinear shallow water equation is established. The wave-breaking mechanisms, global existence, and infinite propagation speed of solutions to the equation are derived under certain assumptions. In… read more here.
Keywords: nonlinear shallow; dynamic properties; water equation; equation ... See more keywords