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All issues Volume 59 / No 4 (July-August 2025) ESAIM: M2AN, 59 4 (2025) 2253-2277 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 4, July-August 2025
Page(s) 2253 - 2277
DOI https://doi.org/10.1051/m2an/2025053
Published online 31 July 2025
  1. 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. [Google Scholar]
  2. D.S. Balsara, D. Bhoriya, C.-W. Shu and H. Kumar, Efficient alternative finite difference WENO scheme for hyperbolic systems with non-conservative products. Commun. Appl. Math. Comput. (2024). DOI: 10.1007/s42967-024-00374-1. [Google Scholar]
  3. D.S. Balsara, S. Garain and C.-W. Shu, An efficient class of WENO schemes with adaptive order. J. Comput. Phys. 326 (2016) 780–804. [Google Scholar]
  4. 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) 69. [Google Scholar]
  5. Y. Cao, A. Kurganov, Y. Liu and V. Zeitlin, Flux globalization based well-balanced path-conservative central-upwind scheme for two-layer thermal rotating shallow water equations. J. Comput. Phys. 474 (2023) 111790. [Google Scholar]
  6. V. Caselles, R. Donat and G. Haro, Flux-gradient and source-term balancing for certain high resolution shock-capturing schemes. Comput. Fluids 38 (2009) 16–36. [Google Scholar]
  7. M.J. Castro Díaz, 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. X. Chen, A. Kurganov and Y. Liu, Flux globalization based well-balanced central-upwind schemes for hydrodynamic equations with general free energy. J. Sci. Comput. 95 (2023) 95. [Google Scholar]
  9. Y. Chen, A. Kurganov and M. Na, A flux globalization based well-balanced path-conservative central-upwind scheme for the shallow water flows in channels. ESAIM Math. Model. Numer. Anal. 57 (2023) 1087–1110. [Google Scholar]
  10. 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]
  11. A. Chertock, S. Cui, A. Kurganov, S¸.N. Ozcan 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. Ozcan, 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 Proceedings in Mathematics & Statistics. Springer, Cham (2018) 345–361. [Google Scholar]
  13. A. Chertock, S. Chu and A. Kurganov, Hybrid multifluid algorithms based on the path-conservative central-upwind scheme. J. Sci. Comput. 89 (2021) 48. [Google Scholar]
  14. 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) 9. [Google Scholar]
  15. A. Chertock, S. Chu and A. Kurganov, Adaptive high-order A-WENO schemes based on a new local smoothness indicator. E. Asian. J. Appl. Math. 13 (2023) 576–609. [Google Scholar]
  16. S. Chu, A. Kurganov and M. Na, Fifth-order A-WENO schemes based on the path-conservative central-upwind method. J. Comput. Phys. 469 (2022) 111508. [Google Scholar]
  17. S. Chu, A. Kurganov, S. Mohammadian and Z. Zheng, Fifth-order A-WENO path-conservative central-upwind scheme for behavioral non-equilibrium traffic models. Commun. Comput. Phys. 33 (2023) 692–732. [Google Scholar]
  18. S. Chu, A. Kurganov, M. Na and R. Xin, Local characteristic decomposition of equilibrium variables for hyperbolic systems of balance laws. Preprint arXiv:2412.19791 (2024). [Google Scholar]
  19. S. Chu, A. Kurganov and R. Xin, A well-balanced fifth-order A-WENO scheme based on flux globalization. Beijing J. Pure Appl. Math. Preprint arXiv:2412.19901 (2024). [Google Scholar]
  20. S. Chu, A. Kurganov and R. Xin, New more efficient A-WENO scheme. J. Sci. Comput. 104 (2025) 53 [Google Scholar]
  21. M. Ciallella, D. Torlo and M. Ricchiuto, Arbitrary high order WENO finite volume scheme with flux globalization for moving equilibria preservation. J. Sci. Comput. 96 (2023) 53. [Google Scholar]
  22. A.J.C. 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, 237–240. [Google Scholar]
  23. W.S. Don, R. Li, B.-S. Wang and Y.H. Wang, A novel and robust scale-invariant WENO scheme for hyperbolic conservation laws. J. Comput. Phys. 448 (2022) 110724. [Google Scholar]
  24. D. Donat and A. Martinez-Gavara, Hybrid second order schemes for scalar balance laws. J. Sci. Comput. 48 (2011) 52–69. [Google Scholar]
  25. 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) 125993. [CrossRef] [Google Scholar]
  26. L. Gascón and J.M. Corderán, Construction of second-order TVD schemes for nonhomogeneous hyperbolic conservation laws. J. Comput. Phys. 172 (2001) 261–297. [Google Scholar]
  27. S. Gottlieb, C. Shu and E. Tadmor, Strong stability-preserving high-order time discretization methods. SIAM Rev. 43 (2001) 89–112. [NASA ADS] [CrossRef] [Google Scholar]
  28. S. Gottlieb, D. Ketcheson and C. Shu, Strong Stability Preserving Runge–Kutta and Multistep Time Discretizations. World Scientific Publishing Co. Pte. Ltd., Hackensack (2011). [Google Scholar]
  29. N. Gouta and F. Maurel, A finite volume solver for 1D shallow-water equations applied to an actual river. Int. J. Numer. Methods Fluids 38 (2002) 1–19. [Google Scholar]
  30. G. Hernández-Dueñas and S. Karni, Shallow water flows in channels. J. Sci. Comput. 48 (2011) 190–208. [CrossRef] [MathSciNet] [Google Scholar]
  31. Y. Jiang, C.-W. Shu, and M. Zhang, An alternative formulation of finite difference weighted ENO schemes with Lax-Wendroff time discretization for conservation laws. SIAM J. Sci. Comput. 35 (2013) A1137–A1160. [Google Scholar]
  32. 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) 109414. [Google Scholar]
  33. A. Kurganov, Y. Liu and R. Xin, Well-balanced path-conservative central-upwind schemes based on flux globalization. J. Comput. Phys. 474 (2023) 111773. [CrossRef] [Google Scholar]
  34. 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]
  35. Z. Li, Nonstaggered central scheme with steady-state discretization for solving the open channel flows via the flux globalization. Appl. Numer. Math. 207 (2025) 58–85. [Google Scholar]
  36. Z. Li and D. Li, Nonstaggered central scheme under steady-state discretization for solving the Ripa model. J. Sci. Comput. 99 (2024) 78. [Google Scholar]
  37. P. Li, T.T. Li, W.S. Don and B.-S. Wang, Scale-invariant multi-resolution alternative WENO scheme for the Euler equations. J. Sci. Comput. 94 (2023) 15. [Google Scholar]
  38. H. Liu, A numerical study of the performance of alternative weighted ENO methods based on various numerical fuxes for conservation law. Appl. Math. Comput. 296 (2017) 182–197. [Google Scholar]
  39. X. Liu, A steady-state-preserving scheme for shallow water flows in channels. J. Comput. Phys. 423 (2020) 109803. [Google Scholar]
  40. R. Manning, On the flow of water in open channel and pipes. Trans. Inst. Civ. Eng. Ireland 20 (1891) 161–207. [Google Scholar]
  41. A. Martinez-Gavara and R. Donat, A hybrid second order scheme for shallow water flows. J. Sci. Comput. 48 (2011) 241–257. [Google Scholar]
  42. C.-W. Shu, High order weighted essentially nonoscillatory schemes for convection dominated problems. SIAM Rev. 51 (2009) 82–126. [NASA ADS] [CrossRef] [Google Scholar]
  43. C.-W. Shu, Essentially non-oscillatory and weighted essentially non-oscillatory schemes. Acta Numer. 29 (2020) 701–762. [Google Scholar]
  44. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (1988) 439–471. [Google Scholar]
  45. 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]
  46. M.E. Váazquez-Cendóon, 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]
  47. B.-S. Wang and W.S. Don, Affine-invariant WENO weights and operator. Appl. Numer. Math. 181 (2022) 630–646. [Google Scholar]
  48. B.-S. Wang, P. Li, Z. Gao and W.S. Don, An improved fifth order alternative WENO-Z finite diference scheme for hyperbolic conservation laws. J. Comput. Phys. 374 (2018) 469–477. [Google Scholar]
  49. B.-S. Wang, W.S. Don, N.K. Garg and A. Kurganov, Fifth-order A-WENO finite-diference schemes based on a new adaptive diffusion central numerical flux. SIAM J. Sci. Comput. 42 (2020) A3932–A3956. [Google Scholar]
  50. B.-S. Wang, W.S. Don, A. Kurganov and Y. Liu, Fifth-order A-WENO schemes based on the adaptive diffusion central-upwind Rankine-Hugoniot fluxes. Commun. Appl. Math. Comput. 5 (2023) 295–314. [Google Scholar]

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