A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows

By Emmanuel Audusse, François Bouchut, Marie-Odile Bristeau, Rupert Klein, Benoit Perthame. SIAM Journal on Scientific Computing, 2004

1,033 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/861c0f61606cc745040842971b3b02089a65e216

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation* (2009, methodology): “For the proof of this proposition, the readers can refer to [5].”
High-order balanced CWENO scheme for movable bed shallow water equations (2007, methodology): “[1] a general technique for the well-balancing of finite volume methods is achieved for first and second-order schemes.”
Numerical Models of Surface Tension (2018, background): “…problem arises for a wide range of equations and applications: hyperbolic systems of conservation laws with source terms (LeVeque 1998), hydrostatic balance in σ-coordinate ocean or atmosphere models (Mesinger 1982), topographic source term in shallow-water equations (Audusse et al. 2004) and more.”
Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods (2008, neutral): “See [2–4,6,9,12,13,22,23, 26,27,37,40,43,44,47,52,57,58,61], etc.”
A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying (2008, background): “Here, W ⋄ D is a modified state, obtained according to the hydrostatic reconstruction of the water height proposed in [29].”
A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗ (2007, methodology): “In our numerical experiments, we have used a one-parameter family of the generalized minmod limiters with 2 [1; 2 ]:”
On the use of Saint Venant equations to simulate the spreading of a granular mass (2005, methodology): “[21] The numerical method used here to solve the hyperbolic system (1)–(3) relies on a finite volume formulation together with the hydrostatic reconstruction scheme developed by Audusse et al. [2004] for Saint Venant models, and on the well-balanced scheme of Bouchut [2004] to deal with friction.”
The generalized Riemann problem method for the shallow water equations with bottom topography (2006, methodology): “Alternative approach in Reference [4] is used to construct numerical fluxes by incorporating the source term effects.”
A limiter-based well-balanced discontinuous Galerkin method for shallow-water flows with wetting and drying: One-dimensional case (2015, methodology): “For shallow water flows limiting in surface elevation generally makes sense, since this quantity is constant for the steady state at rest [1, 33].”