EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 59 / No 4 (July-August 2025) ESAIM: M2AN, 59 4 (2025) 1863-1908 References
Open Access
Issue
ESAIM: M2AN
Volume 59, Number 4, July-August 2025
Page(s) 1863 - 1908
DOI https://doi.org/10.1051/m2an/2025038
Published online 14 July 2025
  1. S. Allgeyer, M.O. Bristeau, D. Froger, R. Hamouda, V. Jauzein, A. Mangeney, J. Sainte-Marie, F. Souillé and M. Valée, Numerical approximation of the 3d hydrostatic Navier–Stokes system with free surface. ESAIM: Math. Model. Numer. Anal. 53 (2019) 1981–2024. [Google Scholar]
  2. K. Arun, A. Das Gupta and S. Samantaray, Analysis of an asymptotic preserving low mach number accurate imex-rk scheme for the wave equation system. Appl. Math. Comput. 411 (2021) 126469. https://www.sciencedirect.com/science/article/pii/S0096300321005580. [Google Scholar]
  3. E. Audusse and M.O. Bristeau, A 2d well-balanced positivity preserving second order scheme for shallow water flows on unstructured meshes. Research Report RR-5260, INRIA (2004). https://inria.hal.science/inria-00070738. [Google Scholar]
  4. E. Audusse and M.O. Bristeau, A well-balanced positivity preserving “second-order” scheme for shallow water flows on unstructured meshes. J. Comput. Phys. 206 (2005) 311–333. [CrossRef] [MathSciNet] [Google Scholar]
  5. 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]
  6. E. Audusse, F. Bouchut, M.O. Bristeau and J. Sainte-Marie, Kinetic entropy inequality and hydrostatic reconstruction scheme for the Saint-Venant system. Math. Comput. 85 (2016) 2815–2837. [Google Scholar]
  7. F. Berthelin and F. Bouchut, Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy. Methods Appl. Anal. 9 (2002) 313–327. [Google Scholar]
  8. G. Bispen, K.R. Arun, M. Lukàcˇovà-Medvid’ovà and S. Noelle, IMEX large time step finite volume methods for low froude number shallow water flows. Commun. Comput. Phys. 16 (2014) 307–347. [Google Scholar]
  9. F. Bouchut, Construction of BGK models with a family of kinetic entropies for a given system of conservation laws. J. Stat. Phys. 95 (1999) 113–170. [Google Scholar]
  10. F. Bouchut, Entropy satisfying flux vector splittings and kinetic BGK models. Numer. Math. 94 (2003) 623–672. [Google Scholar]
  11. F. Bouchut, Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-Balanced Schemes for Sources. Springer Science & Business Media (2004). [Google Scholar]
  12. F. Bouchut and X. Lhébrard, Convergence of the kinetic hydrostatic reconstruction scheme for the Saint-Venant system with topography. Math. Comput. 90 (2021) 1119–1153. hal-upec-upem.archives-ouvertes.fr/hal-01515256v3/file/kin-hydrost_conv.pdf. [Google Scholar]
  13. M.O. Bristeau and B. Coussin, Boundary conditions for the shallow water equations solved by kinetic schemes. Research Report RR-4282, INRIA (2001). https://hal.inria.fr/inria-00072305. [Google Scholar]
  14. M.O. Bristeau, N. Goutal and J. Sainte-Marie, Numerical simulations of a non-hydrostatic shallow water model. Comput. Fluids 47 (2011) 51–64. www.sciencedirect.com/science/article/pii/S0045793011000727. [Google Scholar]
  15. F. Coron and B. Perthame, Numerical passage from kinetic to fluid equations. SIAM J. Numer. Anal. 28 (1991) 26–42. [Google Scholar]
  16. D. Coulette, E. Franck, P. Helluy, M. Mehrenberger and L. Navoret, High-order implicit palindromic discontinuous galerkin method for kinetic-relaxation approximation. Comput. Fluids 190 (2019) 485–502. https://www.sciencedirect.com/science/article/pii/S0045793019301835. [CrossRef] [MathSciNet] [Google Scholar]
  17. O. Delestre, C. Lucas, P.A. Ksinant, F. Darboux, C. Laguerre, T.N.T. Vo, F. James and S. Cordier, SWASHES: a compilation of shallow water analytic solutions for hydraulic and environmental studies. Int. J. Numer. Methods Fluids 72 (2013) 269–300. [Google Scholar]
  18. J.F. Gerbeau and B. Perthame, Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation. Discrete Contin. Dyn. Syst. Ser. B 1 (2001) 89–102. [MathSciNet] [Google Scholar]
  19. I. Gómez-Bueno, S. Boscarino, M. Castro, C. Parés and G. Russo, Implicit and semi-implicit well-balanced finite-volume methods for systems of balance laws. Appl. Numer. Math. 184 (2023) 18–48. [Google Scholar]
  20. L. Gosse, Computing Qualitatively Correct Approximations of Balance Laws. Exponential-fit, Well-balanced and Asymptotic-preserving. SIMAI Springer Series Vol. 2. Springer, Milano (2013). [Google Scholar]
  21. N. Goutal and J. Sainte-Marie, A kinetic interpretation of the section-averaged Saint-Venant system for natural river hydraulics. Int. J. Numer. Methods Fluids 67 (2011) 914–938. [Google Scholar]
  22. J. Haack, S. Jin and J.G. Liu, An all-speed asymptotic-preserving method for the isentropic Euler and Navier–Stokes equations. Commun. Comput. Phys. 12 (2012) 955–980. [Google Scholar]
  23. S. Jin and L. Pareschi, Asymptotic-preserving (AP) schemes for multiscale kinetic equations: a unified approach, in Hyperbolic Problems: Theory, Numerics, Applications, edited by H. Freistühler and G. Warnecke. Birkh¨auser Basel, Basel (2001) 573–582. [Google Scholar]
  24. B. Perthame, Boltzmann type schemes for gas dynamics and the entropy property. SIAM J. Numer. Anal. 27 (1990) 1405–1421. [Google Scholar]
  25. B. Perthame, Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions. SIAM J. Numer. Anal. 29 (1992) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  26. B. Perthame, Kinetic Formulation of Conservation Laws. Oxford Lecture Series in Mathematics and its Applications. Vol. 21. Oxford University Press, Oxford (2002). [Google Scholar]
  27. B. Perthame and C. Simeoni, A kinetic scheme for the Saint-Venant system with a source term. Calcolo 38 (2001) 201–231. [Google Scholar]
  28. Saint-Venant, Théorie du mouvement non permanent des eaux, avec application aux crues des rivières et à l’introduction des marées dans leur lit. C. R. Acad. Sci. Paris 73 (1871) 147–154. [Google Scholar]
  29. A. Thomann, G. Puppo and C. Klingenberg, An all speed second order well-balanced imex relaxation scheme for the euler equations with gravity. J. Comput. Phys. 420 (2020) 109723. https://www.sciencedirect.com/science/article/pii/S0021999120304976. [Google Scholar]
  30. Y. Xing and C.W. Shu, A survey of high order schemes for the shallow water equations. J. Math. Study 47 (2014) 221–249. semanticscholar.org/paper/0b3a29cd823dceb85e3a0a1f9622a306bc62591c. [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