Open Access
Volume 56, Number 6, November-December 2022
Page(s) 2297 - 2338
Published online 08 December 2022
  1. 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. [NASA ADS] [CrossRef] [Google Scholar]
  2. V. Michel-Dansac, C. Berthon, S. Clain and F. Foucher, A well-balanced scheme for the shallow-water equations with topography. Comput. Math. App. 72 (2016) 568–593. [Google Scholar]
  3. L. Gosse, A well-balanced flux-vector splitting scheme designed for hyperbolic systems of conservation laws with source terms. Comput. Math. App. 39 (2000) 135–159. [Google Scholar]
  4. M.J. Castro and C. Parés, Well-balanced high-order finite volume methods for systems of balance laws. J. Sci. Comput. 82 (2020) 1–48. [CrossRef] [MathSciNet] [Google Scholar]
  5. S. Noelle and N. Pankratza, 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]
  6. 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]
  7. B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant systeme with a source term. Calcolo 38 (2001) 201–231. [CrossRef] [MathSciNet] [Google Scholar]
  8. Y. Xing and X. Zhang, Positivity-preserving well-balanced discontinuous galerkin methods for the shallow water equations on unstructured triangular meshes. J. Sci. Comput. 57 (2013) 19–41. [CrossRef] [MathSciNet] [Google Scholar]
  9. J. Dong, D. Fang Li, Exactly well-balanced positivity preserving nonstaggered central scheme for open-channel flows. Int. J. Numer. Methods Fluids 93 (2021) 273–292. [CrossRef] [Google Scholar]
  10. M. Lukáčová-Medvid’ová, S. Noelle and M. Kraft, Well-balanced finite volume evolution galerkin methods for the shallow water equations. J. Comput. Phys. 221 (2007) 122–147. [CrossRef] [MathSciNet] [Google Scholar]
  11. 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: Math. Model. Numer. Anal. 45 (2011) 423–446. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  12. J. Dong and D.F. Li, Well-balanced nonstaggered central schemes based on hydrostatic reconstruction for the shallow water equations with coriolis forces and topography. Math. Methods Appl. Sci. 44 (2021) 1358–1376. [CrossRef] [MathSciNet] [Google Scholar]
  13. P.D. Lax, Weak solutions of nonlinear hyperbolic equations and their numerical computation. Commun. Pure Appl. Math. 7 (1954) 159–193. [Google Scholar]
  14. H. Nessyahu and E. Tadmor, Non-oscillatory central differencing for hyperbolic conservation laws. J. Comput. Phys. 87 (1990) 408–463. [CrossRef] [MathSciNet] [Google Scholar]
  15. G.S. Jiang, D. Levy, C.T. Lin, S. Osher and E. Tadmor, High-resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws. SIAM J. Numer. Anal. 35 (1998) 2147–2168. [CrossRef] [MathSciNet] [Google Scholar]
  16. 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. [NASA ADS] [CrossRef] [Google Scholar]
  17. R.G. Touma and F. Kanbar, Well-balanced central schemes for two-dimensional systems of shallow water equations with wet and dry states. Appl. Math. Modell. 62 (2018) 728–750. [CrossRef] [Google Scholar]
  18. R. Touma, U. Koley and C. Klingenberg, Well-balanced unstaggered central schemes for the Euler equations with gravitation. SIAM J. Sci. Comput. 38 (2016) B773–B807. [CrossRef] [Google Scholar]
  19. H. Tang and T. Tang, Adaptive mesh methods for one-and two-dimensional hyperbolic conservation laws. SIAM J. Numer. Anal. 41 (2003) 487–515. [CrossRef] [MathSciNet] [Google Scholar]
  20. W. Cao, W. Huang and R.D. Russell, Anr-adaptive finite element method based upon moving mesh PDEs. J. Comput. Phys. 149 (1999) 221–244. [CrossRef] [MathSciNet] [Google Scholar]
  21. A. Kurganov, Z. Qu, O.S. 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. [Google Scholar]
  22. X. Xu, G. Ni and S. Jiang, A high-order moving mesh kinetic scheme based on WENO reconstruction for compressible flows on unstructured meshes. J. Sci. Comput. 57 (2013) 278–299. [CrossRef] [MathSciNet] [Google Scholar]
  23. J. Han and H. Tang, An adaptive moving mesh method for two-dimensional ideal magnetohydrodynamics. J. Comput. Phys. 220 (2007) 791–812. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Gaburro, M.J. Castro and M. Dumbser, Well-balanced Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming meshes for the Euler equations of gas dynamics with gravity. Mon. Not. R. Astron. Soc. 477 (2018) 2251–2275. [CrossRef] [Google Scholar]
  25. L. Arpaia and M. Ricchiuto, Well balanced residual distribution for the ALE spherical shallow water equations on moving adaptive meshes. J. Comput. Phys. 405 (2020) 109173. [CrossRef] [MathSciNet] [Google Scholar]
  26. L. Pareschi, G. Puppo and G. Russo, Central Runge-Kutta schemes for conservation laws. SIAM J. Sci. Comput. 26 (2005) 979–999. [CrossRef] [MathSciNet] [Google Scholar]
  27. F. Kanbar, R. Touma and C. Klingenberg, Well-balanced central schemes for the one and two-dimensional Euler systems with gravity. Appl. Numer. Math. 156 (2020) 608–626. [CrossRef] [MathSciNet] [Google Scholar]
  28. J. Dong, D. Li, X. Qian and S. Song, Stationary and positivity preserving unstaggered central schemes for two-dimensional shallow water equations with wet-dry fronts, submitted. [Google Scholar]
  29. S. Gottlieb, D.I. Ketcheson and C.-W. Shu, Strong Stability Preserving Runge-Kutta and Multistep Time Discretizations. World Scientific (2011). [CrossRef] [Google Scholar]
  30. C.-W. Shu and S. Osher, Efficient implementation of essentially non-oscillatory shock-capturing schemes. J. Comput. Phys. 77 (1988) 439–471. [Google Scholar]
  31. R. Touma, Central unstaggered finite volume schemes for hyperbolic systems: applications to unsteady shallow water equations. Appl. Math. Comput. 213 (2009) 47–59. [CrossRef] [MathSciNet] [Google Scholar]
  32. G. Russo, Central Schemes for Conservation Laws with Application to Shallow Water Equations. Springer Milan (2005). [Google Scholar]
  33. X. Liu, A. Chertock and A. Kurganov, An asymptotic preserving scheme for the two-dimensional shallow water equations with coriolis forces. J. Comput. Phys. 391 (2019) 259–279. [CrossRef] [MathSciNet] [Google Scholar]
  34. J.G. Zhou, D.M. Causon, C.G. Mingham and D.M. Ingram, The surface gradient method for the treatment of source terms in the shallow-water equations. J. Comput. Phys. 168 (2001) 1–25. [CrossRef] [MathSciNet] [Google Scholar]
  35. Y. Xing, X. Zhang and C.W. Shu, Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations. Adv. Water Res. 33 (2010) 1476–1493. [CrossRef] [Google Scholar]
  36. 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]
  37. M.T. Capilla and A. Balaguer-Beser, A new well-balanced non-oscillatory central scheme for the shallow water equations on rectangular meshes. J. Comput. Appl. Math. 252 (2013) 62–74. [CrossRef] [MathSciNet] [Google Scholar]
  38. E.F. Toro, Shock-capturing Methods for Free-Surface Shallow Flows. Wiley-Blackwell (2001). [Google Scholar]

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