A kinetic scheme for the Saint-Venant system¶with a source term

By Benoit Perthame, Chiara Simeoni. 2001

337 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/68ef9a7e5e446c216c0ea6cfca696fdc41b39892

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

Transport of Pollutant in Shallow Water A Two Time Steps Kinetic Method (2003, methodology): “[1] or [16] for complete proofs on the hydrodynamic part.”
A multilayer Saint-Venant system with mass exchanges for shallow water flows. Derivation and numerical validation* (2009, background): “Notice that an analytical solution exists for this test in the case of a single layer [3,25].”
A CENTRAL SCHEME FOR SHALLOW WATER FLOWS ALONG CHANNELS WITH IRREGULAR GEOMETRY (2009, neutral): “Upwind schemes for the treatment of balance laws include [4,6,17,21], and kinetic approaches include [2,22].”
A SECOND-ORDER WELL-BALANCED POSITIVITY PRESERVING CENTRAL-UPWIND SCHEME FOR THE SAINT-VENANT SYSTEM ∗ (2007, methodology): “Note that (according to [1], where several numerical methods were tested) such under- and overshoots are present in all numerical solutions, computed using the schemes from [2, 3, 21].”
A Survey of High Order Schemes for the Shallow Water Equations (2014, methodology): “A kinetic approach to achieve well-balanced property has been shown in [44].”
Numerical methods for nonconservative hyperbolic systems: a theoretical framework (2006, neutral): “preserve some equilibria: see [2], [3], [5], [7], [10], [11], [12], [17], [18], [23], [24], [27], [29], [31], [32], [36], [37], [38], [39], .”
Numerical modeling of avalanches based on Saint Venant equations using a kinetic scheme (2003, positive): “Recently, kinetic schemes have been extended to include stiff source term [Botchorishvilli et al., 2000; Perthame and Simeoni, 2001].”
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows (2004, neutral): “Key-words: Shallow water equations, finite volume schemes, well-balanced schemes Mathematics Subject Classification: 65M12, 76M12, 35L65”
Convergence of the Upwind Interface Source Method for Hyperbolic Conservation Laws (2003, methodology): “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).”
The generalized Riemann problem method for the shallow water equations with bottom topography (2006, background): “We use the classical example to test our algorithm for transcritical flows, see References [14, 15].”
CENTRAL-UPWIND SCHEMES FOR THE SAINT-VENANT SYSTEM (2002, methodology): “First-order kinetic solvers were proposed by Perthame et al. in [5, 34 ].”
Sediment transport models in Shallow Water equations and numerical approach by high order finite volume methods (2008, neutral): “See [50], [4], [26], [27], [40], [22], [23], [46], [9], [56], [47], [12], [13], [3], [6], [43].”
On the well-balance property of Roe?s method for nonconservative hyperbolic systems (2004, result): “This idea of constructing numerical schemes that preserve some equilibria, which are called in general well-balanced schemes, has been extended in different ways: see [2, 6–9,12, 14, 17–20,24, 26, 27, 34, 37].”
An asymptotic-preserving well-balanced scheme for the hyperbolic heat equations (2002, background): “…(cid:2)x stand for the piecewise constant functions coinciding with u ,v the appropriate (cid:2) (cid:2)x , there holds for all t > 0 and 1 (cid:2) p (cid:2) +∞ : and the scheme (6) is positivity-preserving If moreover u 0 ,v 0 BV ( R ) , under the same conditions, one has (cid:11) (cid:11)”