A steady-state capturing method for hyperbolic systems with geometrical source terms
By Shi Jin. 2001
211 citations recorded by the source corpus.
Subfields: Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/43ed5e310fcd94fbf9b8185b40fb3b2f665e06b8
How researchers see this paper
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In Computational Mechanics
- Alexander Kurganov
- Benoit Perthame
- Guergana Petrova
- Marie-Odile Bristeau
- Emmanuel Audusse
- Chiara Simeoni
- Guoxian Chen
- Jiequan Li
Citations in the corpus
- 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].”
- A kinetic scheme for the Saint-Venant system¶with a source term (2001, unknown): “Still using the interface values, instead of the cell-averages, for the source terms, Jin proposes in [15] a rather simple method for capturing the steady state solutions with a high order accuracy.”
- Convergence of the Upwind Interface Source Method for Hyperbolic Conservation Laws (2003, methodology): “A more generic scheme, again proposed in [17], is defined by”
- 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 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.”
- The generalized Riemann problem method for the shallow water equations with bottom topography (2006, methodology): “Our discretization of the source term in (10) is an explicit variant of the interface method proposed in a semi-discrete scheme [8].”
- A CENTRAL SCHEME FOR SHALLOW WATER FLOWS ALONG CHANNELS WITH IRREGULAR GEOMETRY (2009, unknown): “Recent years have seen growing interest in developing well-balanced schemes in various numerical frameworks (see, for example, [6,10,12–14,17,19,21,22]).”
- 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].”