EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 56 / No 4 (July-August 2022) ESAIM: M2AN, 56 4 (2022) 1327-1360 References
Open Access
Issue
ESAIM: M2AN
Volume 56, Number 4, July-August 2022
Page(s) 1327 - 1360
DOI https://doi.org/10.1051/m2an/2022041
Published online 27 June 2022
  1. L. Arpaia and M. Ricchiuto, r-adaptation for shallow water flows: conservation, well balancedness, efficiency. Comput. Fluids 160 (2018) 175–203. [CrossRef] [MathSciNet] [Google Scholar]
  2. G. Beckett and J. Mackenzie, Convergence analysis of finite difference approximations on equidistributed grids to a singularly perturbed boundary value problem. Appl. Numer. Math. 35 (2000) 87–109. [CrossRef] [MathSciNet] [Google Scholar]
  3. A. Beljadid, A. Mohammadian and A. Kurganov, Well-balanced positivity preserving cell-vertex central-upwind scheme for shallow water flows. Comput. Fluids 136 (2016) 193–206. [CrossRef] [MathSciNet] [Google Scholar]
  4. A. Bollermann, S. Noelle and M. Lukáčová-Medviďová, Finite volume evolution Galerkin methods for the shallow water equations with dry beds. Commun. Comput. Phys. 10 (2011) 371–404. [CrossRef] [MathSciNet] [Google Scholar]
  5. 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. 56 (2013) 267–290. [Google Scholar]
  6. S. Bryson and D. Levy, Balanced central schemes for the shallow water equations on unstructured grids. SIAM J. Sci. Comput. 27 (2005) 532–552. [CrossRef] [MathSciNet] [Google Scholar]
  7. S. Bryson, Y. Epshteyn, A. Kurganov and G. Petrova, Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system. ESAIM: M2AN 45 (2011) 423–446. [CrossRef] [EDP Sciences] [Google Scholar]
  8. H. Ceniceros and T. Hou, An efficient dynamically adaptive mesh for potentially singular solutions. J. Comput. Phys. 172 (2001) 609–639. [CrossRef] [Google Scholar]
  9. G. Chen, H. Tang and P. Zhang, Second-order accurate Godunov scheme for multicomponent flows on moving triangular meshes. J. Sci. Comput. 34 (2008) 64–86. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. de Saint-Venant, Thèorie du mouvement non-permanent des eaux, avec application aux crues des rivière at à l’introduction des marèes dans leur lit. C. R. Acad. Sci. Paris 73 (1871) 147–154. [Google Scholar]
  11. S. Gottlieb, C. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 (2001) 89–112 (electronic). [NASA ADS] [CrossRef] [Google Scholar]
  12. S. Gottlieb, D. Ketcheson and C.-W. Shu, Strong Stability Preserving Runge–Kutta and Multistep Time Discretizations. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ (2011). [CrossRef] [Google Scholar]
  13. W. Huang and R.D. Russell, Adaptive Moving Mesh Methods. Vol. 174 of Applied Mathematical Sciences. Springer, New York (2011). [CrossRef] [Google Scholar]
  14. W. Huang and W. Sun, Variational mesh adaptation II: error estimates and monitor functions. J. Comput. Phys. 184 (2003) 619–648. [CrossRef] [MathSciNet] [Google Scholar]
  15. M.E. Hubbard, On the accuracy of one-dimensional models of steady converging/diverging open channel flows. Int. J. Numer. Methods Fluids 35 (2001) 785–808. [CrossRef] [Google Scholar]
  16. A. Kurganov, Finite-volume schemes for shallow-water equations. Acta Numer. 27 (2018) 289–351. [Google Scholar]
  17. A. Kurganov and D. Levy, Central-upwind schemes for the Saint-Venant system. ESAIM: M2AN 36 (2002) 397–425. [CrossRef] [EDP Sciences] [Google Scholar]
  18. 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. [Google Scholar]
  19. A. Kurganov, Z. Qu, O. Rozanova and T. Wu, Adaptive moving mesh central-upwind schemes for hyperbolic system of PDEs. Applications to compressible Euler equations and granular hydrodynamics. Commun. Appl. Math. Comput. 3 (2021) 445–479. [CrossRef] [MathSciNet] [Google Scholar]
  20. M. Sead, Non-oscillatory relaxation methods for the shallow-water equations in one and two space dimensions. Int. J. Numer. Methods Fluids 46 (2004) 457–484. [CrossRef] [Google Scholar]
  21. H. Shirkhani, A. Mohammadian, O. Seidou and A. Kurganov, A well-balanced positivity-preserving central-upwind scheme for shallow water equations on unstructured quadrilateral grids. Comput. Fluids 126 (2016) 25–40. [CrossRef] [MathSciNet] [Google Scholar]
  22. H. Tang and T. Tang, Adaptive mesh methods for one- and two-dimensional hyperbolic conservation laws. SIAM J. Numer. Anal. 41 (2003) 487–515 (electronic). [CrossRef] [MathSciNet] [Google Scholar]
  23. A. van Dam and P.A. Zegeling, A robust moving mesh finite volume method applied to 1d hyperbolic conservation laws from magnetohydrodynamics. J. Comput. Phys. 216 (2006) 526–546. [CrossRef] [MathSciNet] [Google Scholar]
  24. Y. Xing, Numerical methods for the nonlinear shallow water equations. In: Handbook of Numerical Methods for Hyperbolic Problems. Vol. 18 of Handb. Numer. Anal. Elsevier/North-Holland, Amsterdam (2017) 361–384. [CrossRef] [Google Scholar]
  25. F. Zhou, G. Chen, Y. Huang, J.Z. Yang and H. Feng, An adaptive moving finite volume scheme for modeling flood inundation over dry and complex topography. Water Resour. Res. 49 (2013) 1914–1928. [CrossRef] [Google Scholar]
  26. F. Zhou, G. Chen, S. Noelle and H. Guo, A well-balanced stable generalized Riemann problem scheme for shallow water equations using adaptive moving unstructured triangular meshes. Int. J. Numer. Methods Fluids 73 (2013) 266–283. [CrossRef] [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.

Recommended for you