Open Access
Volume 57, Number 2, March-April 2023
Page(s) 1087 - 1110
Published online 12 April 2023
  1. 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. [Google Scholar]
  2. J. Balbás and S. Karni, A central scheme for shallow water flows along channels with irregular geometry. M2AN. Math. Model. Numer. Anal. 43 (2009) 333–351. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  3. 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]
  4. F. Bouchut and T. Morales, A subsonic-well-balanced reconstruction scheme for shallow water flows. SIAM J. Numer. Anal. 48 (2010) 1733–1758. [Google Scholar]
  5. Y. Cao, A. Kurganov, Y. Liu and R. Xin, Flux globalization based well-balanced path-conservative central-upwind schemes for shallow water models. J. Sci. Comput. 92 (2022) 31. [CrossRef] [Google Scholar]
  6. M.J. Castro, T. Morales de Luna and C. Parés, Well-balanced schemes and path-conservative numerical methods, in Handbook of Numerical Methods for Hyperbolic Problems. Vol. 18 of Handb. Numer. Anal. Elsevier/North-Holland, Amsterdam (2017) 131–175. [CrossRef] [Google Scholar]
  7. M.J. Castro Daz, A. Kurganov and T. Morales de Luna, Path-conservative central-upwind schemes for nonconservative hyperbolic systems. ESAIM Math. Model. Numer. Anal. 53 (2019) 959–985. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  8. Y. Cheng and A. Kurganov, Moving-water equilibria preserving central-upwind schemes for the shallow water equations. Commun. Math. Sci. 14 (2016) 1643–1663. [CrossRef] [MathSciNet] [Google Scholar]
  9. Y. Cheng, A. Chertock, M. Herty, A. Kurganov and T. Wu, A new approach for designing moving-water equilibria preserving schemes for the shallow water equations. J. Sci. Comput. 80 (2019) 538–554. [CrossRef] [MathSciNet] [Google Scholar]
  10. A. Chertock, S. Cui, A. Kurganov and T. Wu, Well-balanced positivity preserving central-upwind scheme for the shallow water system with friction terms. Int. J. Numer. Meth. Fluids 78 (2015) 355–383. [CrossRef] [Google Scholar]
  11. A. Chertock, S. Cui, A. Kurganov, S.N. Özcan and E. Tadmor, Well-balanced schemes for the Euler equations with gravitation: conservative formulation using global fluxes. J. Comput. Phys. 358 (2018) 36–52. [CrossRef] [MathSciNet] [Google Scholar]
  12. A. Chertock, M. Herty and C.N. Özcan, Well-balanced central-upwind schemes for 2 × 2 systems of balance laws, in Theory, Numerics and Applications of Hyperbolic Problems. I. Vol. 236 of Springer Proc. Math. Stat. Springer, Cham (2018) 345–361. [CrossRef] [Google Scholar]
  13. A. Chertock, A. Kurganov, X. Liu, Y. Liu and T. Wu, Well-balancing via flux globalization: applications to shallow water equations with wet/dry fronts. J. Sci. Comput. 90 (2022) 21. [CrossRef] [Google Scholar]
  14. G. Dal Maso, P.G. Lefloch and F. Murat, Definition and weak stability of nonconservative products. J. Math. Pures Appl. 74 (1995) 483–548. [Google Scholar]
  15. H. Darcy, Recherches expérimentales relatives au mouvement de l’eau dans les tuyaux. Vol. 1. Mallet-Bachelier (1857). [Google Scholar]
  16. C. Escalante, M.J. Castro and M. Semplice, Very high order well-balanced schemes for non-prismatic one-dimensional channels with arbitrary shape. Appl. Math. Comput. 398 (2021) 16. [Google Scholar]
  17. A. Flamant, Mécanique appliquée: Hydraulique. Baudry éditeur, Paris (France) (1891). [Google Scholar]
  18. J.M. Gallardo, C. Parés and M. Castro, On a well-balanced high-order finite volume scheme for shallow water equations with topography and dry areas. J. Comput. Phys. 227 (2007) 574–601. [CrossRef] [MathSciNet] [Google Scholar]
  19. P. Gauckler, Etudes Théoriques et Pratiques sur l’Ecoulement et le Mouvement des Eaux. Gauthier-Villars (1867). [Google Scholar]
  20. N. Gouta and F. Maurel, A finite volume solver for 1d shallow-water equations applied to an actual river. Int. J. Numer. Meth. Fluids 38 (2002) 1–19. [CrossRef] [Google Scholar]
  21. G. Hernández-Dueñas and S. Karni, Shallow water flows in channels. J. Sci. Comput. 48 (2011) 190–208. [CrossRef] [MathSciNet] [Google Scholar]
  22. S. Jin and X. Wen, Two interface-type numerical methods for computing hyperbolic systems with geometrical source terms having concentrations. SIAM J. Sci. Comput. 26 (2005) 2079–2101. [Google Scholar]
  23. A. Kurganov, Finite-volume schemes for shallow-water equations. Acta Numer. 27 (2018) 289–351. [Google Scholar]
  24. A. Kurganov and C.-T. Lin, On the reduction of numerical dissipation in central-upwind schemes. Commun. Comput. Phys. 2 (2007) 141–163. [Google Scholar]
  25. 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]
  26. 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]
  27. A. Kurganov, S. Noelle and G. Petrova, Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton-Jacobi equations. SIAM J. Sci. Comput. 23 (2001) 707–740. [Google Scholar]
  28. A. Kurganov, Y. Liu and V. Zeitlin, A well-balanced central-upwind scheme for the thermal rotating shallow water equations. J. Comput. Phys. 411 (2020) 24. [Google Scholar]
  29. A. Kurganov, Y. Liu and R. Xin, Well-balanced path-conservative central-upwind schemes based on flux globalization. J. Comput. Phys. 474 (2023) 32. [Google Scholar]
  30. P. LeFloch, Graph solutions of nonlinear hyperbolic systems. J. Hyperbolic Differ. Equ. 1 (2004) 643–689. [CrossRef] [Google Scholar]
  31. P.G. LeFloch, Hyperbolic Systems of Conservation Laws: The Theory of Classical and Nonclassical Shock Waves. Lectures in Mathematics ETH Zürich. Birkhäuser Verlag, Basel (2002). [Google Scholar]
  32. P.G. LeFloch and M.D. Thanh, A Godunov-type method for the shallow water equations with discontinuous topography in the resonant regime. J. Comput. Phys. 230 (2011) 7631–7660. [CrossRef] [MathSciNet] [Google Scholar]
  33. K.-A. Lie and S. Noelle, On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws. SIAM J. Sci. Comput. 24 (2003) 1157–1174. [Google Scholar]
  34. X. Liu, A steady-state-preserving scheme for shallow water flows in channels. J. Comput. Phys. 423 (2020) 22. [Google Scholar]
  35. X. Liu, X. Chen, S. Jin, A. Kurganov and H. Yu, Moving-water equilibria preserving partial relaxation scheme for the Saint-Venant system. SIAM J. Sci. Comput. 42 (2020) A2206–A2229. [CrossRef] [Google Scholar]
  36. R. Manning, On the flow of water in open channel and pipes, in Transactions of the Institution of Civil Engineers of Ireland. Vol. 20 (1891) 161–207. [Google Scholar]
  37. H. Nessyahu and E. Tadmor, Nonoscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. [Google Scholar]
  38. C. Parés, Path-conservative numerical methods for nonconservative hyperbolic systems, in Vol. 24 of Quad. Mat. Dept. Math. Seconda Univ. Napoli, Caserta (2009). [Google Scholar]
  39. M. Ricchiuto, An explicit residual based approach for shallow water flows. J. Comput. Phys. 280 (2015) 306–344. [CrossRef] [MathSciNet] [Google Scholar]
  40. B. Sulistyono, L. Wiryanto and S. Mungkasi, A staggered method for simulating shallow water flows along channels with irregular geometry and friction. Int. J. Adv. Sci. Eng. Inf. Technol. 10 (2020) 952–958. [CrossRef] [Google Scholar]
  41. P.K. Sweby, High resolution schemes using flux limiters for hyperbolic conservation laws. SIAM J. Numer. Anal. 21 (1984) 995–1011. [Google Scholar]
  42. 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]
  43. 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]

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