The surface gradient method for the treatment of source terms in the shallow-water equations

By J. Zhou, D. Causon, C. Mingham, D. Ingram. 2001

607 citations recorded by the source corpus.

Subfields: Atmospheric Science, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/85e6d3375f8c9ad88e082623f9ab0c89b60638e4

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In Atmospheric Science

In Computational Mechanics

Citations in the corpus

Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations (2006, background): “[24,16]) found that the numerical imbalance could be alleviated by using the deviatoric form of SWEs, where the water level and discharge are taken as the unknown variables.”
Source term treatment of SWEs using surface gradient upwind method (2012, methodology): “Starting from Bermudez and Vazquez-Cendon (1994) and Greenberg and Leroux (1996), the conservative property of a flow becomes a standard proof for the preservation of the numerical fluxes.”
Numerical Simulation of the 2011 Tohoku Tsunami Based on a New Transient FEM Co-seismic Source: Comparison to Far- and Near-Field Observations (2013, methodology): “The model uses a second-order Godunov-type TVD method (ZHOU et al. 2001; LIANG and MARCHE 2009) for horizontal gridding, applied on multiple vertical levels defined by a standard bottomand surface-following r-coordinate formulation.”
Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flows (2008, methodology): “(1) as the governing equation automatically incorporates the SGM balancing technique (Zhou et al., 2001) into the model formulation.”
The generalized Riemann problem method for the shallow water equations with bottom topography (2006, methodology): “MIDPOINT VALUES ON CELL INTERFACES There are several methods to calculate midpoint values Un+1/2 j+1/2 such as the MUSCL-Hancock finite-volume method adopted in Reference [15].”
Depth‐integrated, non‐hydrostatic model with grid nesting for tsunami generation, propagation, and run‐up (2010, methodology): “The finite volume method based on the conservative form of the nonlinear shallow-water equations captures flow discontinuities and conserves flow volume through a Riemann solver (e.g., Dodd, 1998; Zhou et al., 2001; Wei et al., 2006; Wu and Cheung, 2008; and George, 2010).”
A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation (2012, methodology): “To eliminate errors introduced by the traditional depth gradient method (DGM), a so-called surface gradient method (SGM) proposed by Zhou et al. (2001) was adopted in the TVD based-Boussinesq models in the recent literatures.”
High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms (2006, methodology): “[38] used the surface gradient method for the treatment of the source terms.”
A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: One-dimensional case (2015, background): “For shallow water flows limiting in surface elevation generally makes sense, since this quantity is constant for the steady state at rest [1, 33].”
Depth‐integrated, non‐hydrostatic model for wave breaking and run‐up (2009, methodology): “Their approach approximates flow discontinuities as bores or hydraulic jumps as in a finite volume model, using a Riemann solver [8–10].”
A weighted surface-depth gradient method for the numerical integration of the 2D shallow water equations with topography (2008, methodology): “where the bed slope source term is discretized with a centered scheme [34]: 2 3”