Mathematical balancing of flux gradient and source terms prior to using Roe's approximate Riemann solver

By Benedict D. Rogers, Alistair G. L. Borthwick, Paul H. Taylor. 2003

215 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/ac3704e51e146f10dca4df9eeab34dd2cd336e6d

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Citations in the corpus

Simulation of dam‐ and dyke‐break hydrodynamics on dynamically adaptive quadtree grids (2004, methodology): “Equation (5) ensures that the ux gradient and source terms are balanced mathematically, thus removing any need for additional numerical treatment when implementing an approximate solver in a Riemann scheme (see Reference [32] for details).”
A Survey of High Order Schemes for the Shallow Water Equations (2014, methodology): “Another popular approach is to rewrite the equation in terms of the water surface instead of water height (also referred as the pre-balanced formulation), and well-balanced methods [31, 48, 69] can be designed based on such formulation.”
Comparison between TVD-MacCormack and ADI-type solvers of the shallow water equations (2006, unknown): “[15,25,16,10]).”
Improved implementation of the HLL approximate Riemann solver for one-dimensional open channel flows (2008, methodology): “The numerical imbalance is created when these terms are calculated using different methods, which leads a numerical flow even in a still water test case, as illustrated by Rogers et al. (2003) through a two-dimensional simulation of a circular water basin with uneven bathymetry.”
A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation (2012, background): “The imbalance problem can be solved by a reformulation of this term in terms of deviations from an unforced but separately specified equilibrium state (see general derivations in Rogers et al., 2003 and recent application in Liang and Marche, 2009).”