Some approximate Godunov schemes to compute shallow-water equations with topography

By Thierry Gallouët, Jean-Marc Hérard, Nicolas Seguin. 2003

329 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/530f848d05b1ab098f16e3ea213dab2d825b7fee

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A steady-state capturing method for hyperbolic systems with geometrical source terms (2001, background): “Numerical results for similar problems, as shown in [4], typically exhibit oscillations near the shock.”
A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗ (2007, methodology): “The methods that exactly preserve such solutions are called well-balanced, and we refer the reader to [2, 4, 8, 10, 12, 16, 17, 20, 21, 22, 23, 27, 28], where a variety of highorder well-balanced schemes for the Saint-Venant system can be found.”
A Survey of High Order Schemes for the Shallow Water Equations (2014, unknown): “For more related work, see also [17, 20, 22, 24, 25, 28, 35, 37, 49, 66].”
Convergence of the Upwind Interface Source Method for Hyperbolic Conservation Laws (2003, background): “Quite recently, these kinds of numerical processing have been extended to hyperbolic systems of balance laws (like the Saint-Venant system for shallow waters), to obtain stable schemes which preserve the steady states (see [8], [13],[14] and [28], for instance).”
Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows (2006, background): “would also like to mention the finite volume Roe schemes of Gallouët and coworkers [8] and the Norwegian front tracking approach [14].”
A kinetic scheme for the Saint-Venant system¶with a source term (2001, methodology): “Fluids, 23 (1994), no. 8, 1049-1071 [4] Botchorishvili R., Perthame B. and Vasseur A., Equilibrium Schemes for Scalar Conservation Laws with Stiff Sources, INRIA Report RR8931 (2000) [5] Dafermos C.M., Hyperbolic conservation laws in continuum physics, vol. GM 325 Springer-Verlag, Berlin, 1999 [6] E”
Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations (2004, background): “[10] developed the numerical schemes for computation of the shallow water equations with topography, which can preserve the steady-state solutions.”
Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method (2003, background): “Roe [17] to upwind the source terms at the interfaces – see for instance [2,6,9,11] or [13].”
Finite Volume Methods: Foundation and Analysis (2004, background): “Several choices of such matrices exist as discussed in Masella et al., 1999; Brun et al., 2000; Buffard et al., 2000; Gallouët et al., 2002; Gallouët et al., 2003.”
A finite volume scheme for a model coupling free surface and pressurised flows in pipes (2007, methodology): “[10,9], secondly by defining a criterion to follow the evolution of the transition points.”
ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS (2003, methodology): “Notice that this study is close to some works that have been performed to investigate the behavior of the finite volume method applied to (systems of) conservation laws with source terms by Greenberg and Le Roux,11 or Gallouët, Hérard, Seguin.7 A somewhat related subject is the study of a transpor”
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows (2004, unknown): “Key-words: Shallow water equations, finite volume schemes, well-balanced schemes Mathematics Subject Classification: 65M12, 76M12, 35L65”
A well‐balanced Runge–Kutta discontinuous Galerkin method for the shallow‐water equations with flooding and drying (2008, unknown): “In the framework of FV, several techniques have been proposed to preserve steady-states at rest, leading to so-called well-balanced schemes; see [8, 10, 11] where additional terms are included in the flux calculation and [9] where a socalled upwind discretization of the source term is proposed.”