Free Access
Issue |
ESAIM: M2AN
Volume 48, Number 3, May-June 2014
|
|
---|---|---|
Page(s) | 665 - 696 | |
DOI | https://doi.org/10.1051/m2an/2013106 | |
Published online | 20 January 2014 |
- R. Abgrall and S. Karni, Two-layer shallow water system: a relaxation approach. SIAM J. Sci. Comput. 31 (2009) 1603–1627. [CrossRef] [MathSciNet] [Google Scholar]
- L. Armi, The hydraulics of two flowing layers with different densities. J. Fluid Mech. 163 (1986) 27–58. [CrossRef] [MathSciNet] [Google Scholar]
- L. Armi and D.M. Farmer, Maximal two-layer exchange through a contraction with barotropic net flow. J. Fluid Mech. 186 (1986) 27–51. [Google Scholar]
- E. Audusse, F. Bouchut, M.-O. Bristeau, R. Klein and B. Perthame, A fast and stable well-balanced scheme with hydrostatic reconstruction for shallow water flows. SIAM J. Sci. Comput. 25 (2004) 2050–2065. [CrossRef] [MathSciNet] [Google Scholar]
- J. Balbás and S. Karni, A central scheme for shallow water flows along channels with irregular geometry. ESAIM: M2AN 43 (2009) 333–351. [CrossRef] [EDP Sciences] [Google Scholar]
- A. Bollermann, G. Chen, A. Kurganov and S. Noelle, A well-balanced reconstruction of wet/dry fronts for the shallow water equations. J. Sci. Comput. (2011) 1–24. [Google Scholar]
- A. Bollermann, S. Noelle and M. Lukáčová-Medvidóvá, Finite volume evolution Galerkin methods for the shallow water equations with dry beds. Commun. Comput. Phys. 10 (2011) 371–404. [Google Scholar]
- F. Bouchut, Nonlinear stability of finite volume methods for hyperbolic conservation laws and well-balanced schemes for sources. Frontiers in Mathematics. Birkhäuser Verlag, Basel (2004). [Google Scholar]
- M. Castro, J. Macías and C. Parés, A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1-D shallow water system. ESAIM: M2AN 35 (2001) 107–127. [CrossRef] [EDP Sciences] [Google Scholar]
- M.J. Castro, J.A. García-Rodríguez, J.M. González-Vida, J. Macías, C. Parés and M.E. Vázquez-Cendón, Numerical simulation of two-layer shallow water flows through channels with irregular geometry. J. Comput. Phys. 195 (2004) 202–235. [Google Scholar]
- M.J. Castro, A. Pardo Milanés and C. Parés, Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique. Math. Models Methods Appl. Sci. 17 (2007) 2055–2113. [CrossRef] [Google Scholar]
- N. Črnjarić-Žic, S. Vuković and L. Sopta, Balanced finite volume WENO and central WENO schemes for the shallow water and the open-channel flow equations. J. Comput. Phys. 200 (2004) 512–548. [CrossRef] [MathSciNet] [Google Scholar]
- D.M. Farmer and L. Armi, Maximal two-layer exchange over a sill and through the combination of a sill and contraction with barotropic flow. J. Fluid Mech. 164 (1986) 53–76. [CrossRef] [Google Scholar]
- P. Garcia-Navarro and M.E. Vazquez-Cendon, On numerical treatment of the source terms in the shallow water equations. Comput. Fluids 29 (2000) 951–979. [CrossRef] [Google Scholar]
- D.L. George, Augmented Riemann solvers for the shallow water equations over variable topography with steady states and inundation. J. Comput. Phys. 227 (2008) 3089–3113. [CrossRef] [Google Scholar]
- S. Gottlieb, C.-W. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods. SIAM Review 43 (2001) 89–112. [CrossRef] [MathSciNet] [Google Scholar]
- G. Hernández-Dueñas and S. Karni, Shallow water flows in channels. J. Sci. Comput. 48 (2011) 190–208. [CrossRef] [Google Scholar]
- S. Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms. ESAIM: M2AN (2001) 35 631–645. [CrossRef] [EDP Sciences] [Google Scholar]
- S. Karni and G. Hernández-Dueñas, A scheme for the shallow water flow with area variation. AIP Conference Proceedings. Vol. 1168 of International Conference Numer. Anal. Appl. Math., Rethymno, Crete, Greece. American Institute of Physics (2009) 1433–1436. [Google Scholar]
- A. Kurganov and D. Levy, Central-upwind schemes for the Saint-Venant system. ESAIM: M2AN 36 (2002) 397–425. [CrossRef] [EDP Sciences] [Google Scholar]
- A. Kurganov and G. Petrova, A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system. Commun. Math. Sci. 5 (2007) 133–160. [CrossRef] [Google Scholar]
- A. Kurganov and G. Petrova, Central-upwind schemes for two-layer shallow water equations. SIAM J. Sci. Comput. 31 (2009) 1742–1773. [CrossRef] [Google Scholar]
- A. Kurganov and E. Tadmor, New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations. J. Comput. Phys. 160 (2000) 241–282. [Google Scholar]
- R.J. LeVeque, Balancing source terms and flux gradients in high-resolution Godunov methods: the quasi-steady wave-propagation algorithm. J. Comput. Phys. 146 (1998) 346–365. [NASA ADS] [CrossRef] [MathSciNet] [Google Scholar]
- S. Noelle, N. Pankratz, G. Puppo and J.R. Natvig, Well-balanced finite volume schemes of arbitrary order of accuracy for shallow water flows. J. Comput. Phys. 213 (2006) 474–499. [CrossRef] [MathSciNet] [Google Scholar]
- S. Noelle, Y. Xing and C.-W. Shu, High-order well-balanced finite volume WENO schemes for shallow water equation with moving water. J. Comput. Phys. 226 (2007) 29–58. [CrossRef] [MathSciNet] [Google Scholar]
- B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system with a source term. Calcolo 38 (2001) 201–231. [CrossRef] [MathSciNet] [Google Scholar]
- P.L. Roe, Upwind differencing schemes for hyperbolic conservation laws with source terms. Nonlinear hyperbolic problems (St. Etienne, 1986). In vol. 1270 of Lecture Notes in Math. Springer, Berlin (1987) 41–51. [Google Scholar]
- G. Russo, Central schemes for balance laws. Hyperbolic problems: theory, numerics, applications, Vol. I, II (Magdeburg, 2000). In vol. 140 of Internat. Ser. Numer. Math. Birkhäuser, Basel (2001) 821–829. [Google Scholar]
- B. van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 32 (1979) 101–136; J. Comput. Phys. 135 (1997) 227–248. [Google Scholar]
- M. E. Vázquez-Cendón. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comput. Phys. 148 (1999) 497–526. [CrossRef] [MathSciNet] [Google Scholar]
- S. Vuković and L. Sopta, High-order ENO and WENO schemes with flux gradient and source term balancing. In Applied mathematics and scientific computing (Dubrovnik, 2001). Kluwer/Plenum, New York (2003) 333–346. [Google Scholar]
- Yulong Xing, Chi-Wang Shu and Sebastian Noelle, On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations. J. Sci. Comput. 48 (2011) 339–349. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.