Extension of the two‐component pressure approach for modeling mixed free‐surface‐pressurized flows with the two‐dimensional shallow water equations
Sign Up to like & getrecommendations! Published in 2020 at "International Journal for Numerical Methods in Fluids"
DOI: 10.1002/fld.4902
Abstract: Numerical models based on the two‐dimensional shallow water equations (2D‐SWE) are routinely used in flood risk management and inundation studies. However, most of these models do not adequately account for vertically confined flow conditions that… read more here.
Keywords: shallow water; surface; free surface; two dimensional ... 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
Implicit Discontinuous Galerkin Scheme for Discontinuous Bathymetry in Shallow Water Equations
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DOI: 10.1007/s12205-020-2409-8
Abstract: One important issue in the approach with shallow water equations, which is not restricted to discontinuous Galerkin formulation, is the limitation to step geometries (discontinuous bathymetry), due to the hydrostatic assumption employed for the derivation… read more here.
Keywords: discontinuous galerkin; scheme; water equations; discontinuous bathymetry ... See more keywords
Implicit discontinuous Galerkin scheme for shallow water equations
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Mechanical Science and Technology"
DOI: 10.1007/s12206-019-0625-2
Abstract: The numerical solutions of shallow water equations are presented with implicit discontinuous Galerkin (IDG) method. The motivations for the development of an implicit scheme is stated. Details of the developed model is described including the… read more here.
Keywords: discontinuous galerkin; scheme; water equations; implicit discontinuous ... See more keywords
Discrete-Time Flatness-Based Feedforward Control for the 1D Shallow Water Equations
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DOI: 10.1016/j.ifacol.2019.11.753
Abstract: Abstract Flatness of given outputs for quasilinear 1D hyperbolic systems is conserved under an appropriate port-Hamiltonian spatial discretization. Combining the spatial with a structure-preserving temporal scheme leads to a fully discretized control model of the… read more here.
Keywords: flatness based; based feedforward; discrete time; water equations ... See more keywords
On the standard Galerkin method with explicit RK4 time stepping for the shallow water equations
Sign Up to like & getrecommendations! Published in 2019 at "IMA Journal of Numerical Analysis"
DOI: 10.1093/imanum/drz033
Abstract: We consider a simple initial-boundary-value problem for the shallow water equations in one space dimension. We discretize the problem in space by the standard Galerkin finite element method on a quasiuniform mesh and in time… read more here.
Keywords: time; method; standard galerkin; water equations ... See more keywords
Shallow water equations for equatorial tsunami waves
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DOI: 10.1098/rsta.2017.0100
Abstract: We present derivations of shallow water model equations of Korteweg–de Vries and Boussinesq type for equatorial tsunami waves in the f-plane approximation and discuss their applicability. This article is part of the theme issue ‘Nonlinear… read more here.
Keywords: water; equatorial tsunami; water equations; tsunami waves ... See more keywords
Existence of strong solutions to the rotating shallow water equations with degenerate viscosities
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DOI: 10.1142/s021953051950012x
Abstract: In this paper, we consider the Cauchy problem of a viscous compressible shallow water equations with the Coriolis force term and non-constant viscosities. More precisely, the viscous coefficients are constants multiple of height, the equations… read more here.
Keywords: strong solutions; existence strong; water equations; equations degenerate ... See more keywords
Solving global shallow water equations on heterogeneous supercomputers
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DOI: 10.1371/journal.pone.0172583
Abstract: The scientific demand for more accurate modeling of the climate system calls for more computing power to support higher resolutions, inclusion of more component models, more complicated physics schemes, and larger ensembles. As the recent… read more here.
Keywords: global shallow; equations heterogeneous; heterogeneous supercomputers; water equations ... See more keywords
Finite difference methods for 2D shallow water equations with dispersion
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DOI: 10.1515/rnam-2019-0009
Abstract: Abstract Basic properties of some finite difference schemes for two-dimensional nonlinear dispersive equations for hydrodynamics of surface waves are considered. It is shown that stability conditions for difference schemes of shallow water equations are qualitatively… read more here.
Keywords: difference; difference methods; water equations; finite difference ... See more keywords