On numerical treatment of the source terms in the shallow water equations

By Pilar García-Navarro, M. Vázquez-Cendón. 2000

281 citations recorded by the source corpus.

Subfields: Atmospheric Science, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/587ab12140b3c39785801e0562a9a8f11e35d146

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In Atmospheric Science

In Computational Mechanics

Citations in the corpus

On the well-balance property of Roe?s method for nonconservative hyperbolic systems (2004, methodology): “This last numerical scheme is similar to the one introduced in [14] for a more general problem corresponding to a symmetric channel with an arbitrary cross-section.”
Simulation of rapidly varying flow using an efficient TVD–MacCormack scheme (2007, unknown): “References [9, 19, 20]).”
A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography (2008, methodology): “Bermúdez and Vázquez-Cendón [8] applied this treatment to first order Roe’s scheme and defined the fundamental notion of C-property, that is the capability of replicating the exact solution for the stationary flow problem.”
Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations (2006, unknown): “[6,19,20]).”
Some approximate Godunov schemes to compute shallow-water equations with topography (2003, methodology): “Some approximate Godunov schemes to compute shallow-water equations with topography”
Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flows (2008, methodology): “(22) Figure A1 Comparisons between numerical solutions of water depth from the second-order HLL-B scheme with Eqs (22) and (23).”
Godunov-type methods for free-surface shallow flows: A review (2007, methodology): “…in the last decades and various computational techniques using finite difference, finite element and finite volume methods have been reported (Alcrudo and Garcia-Navarro, 1993; Bermúdez et al., 1998; Cunge et al., 1980; Garcia-Navarro and Vazquez-Cendon, 2000; Sleigh et al., 1998; Toro, 1989).”
Source term treatment of SWEs using surface gradient upwind method (2012, methodology): “As described by the UM of Bermudez and VazquezCendon (1994) and Garcia-Navarro and Vazquez-Cendon (2000), the forward-difference scheme is used for the time discretization in Eq.”