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All issues Volume 58 / No 4 (July-August 2024) ESAIM: M2AN, 58 4 (2024) 1263-1299 References
Open Access
Issue
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
Page(s) 1263 - 1299
DOI https://doi.org/10.1051/m2an/2024035
Published online 19 July 2024
  1. A. Arakawa and V.R. Lamb, Computational design of the basic dynamical processes of the UCLA general circulation model. Methods Comput. Phys.: Adv. Res. Appl. 17 (1977) 173–265. [CrossRef] [Google Scholar]
  2. A. Arakawa and V.R. Lamb, A potential enstrophy and energy conserving scheme for the shallow water equations. Mon. Weather Rev. 109 (1981) 18–36. [CrossRef] [Google Scholar]
  3. 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]
  4. E. Audusse, F. Bouchut 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, C. Chalons and P. Ung, A simple well-balanced and positive numerical scheme for the shallow-water system. Commun. Math. Sci. 13 (2015) 1317–1332. [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. D. Benson, Computational methods in lagrangian and eulerian hydrocodes. Comput. Methods Appl. Mech. Eng. 99 (1992) 235–394. [CrossRef] [Google Scholar]
  8. M.V.A. Bermudez, Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids 23 (1994) 1049–1071. [CrossRef] [MathSciNet] [Google Scholar]
  9. O. Bernard, M. Bestard, T. Goudon, L. Meyer, S. Minjeaud, F. Noisette and B. Polizzi, Numerical schemes for mixture theory models with filling constraint: application to biofilm ecosystems, Technical report, Univ. Côte d’Azur, CNRS, Inria, 2023. CEMRACS (2022). [Google Scholar]
  10. F. Berthelin, T. Goudon and S. Minjeaud, Consistency analysis of a 1D finite volume scheme for barotropic Euler models. In Finite volumes for complex applications VII. Methods and theoretical aspects, Vol. 77 of Springer Proc. Math. Stat. Springer, Cham (2014) 97–105. [Google Scholar]
  11. F. Berthelin, T. Goudon and S. Minjeaud, Kinetic schemes on staggered grids for barotropic Euler models: entropystability analysis. Math. Comput. 84 (2015) 2221–2262. [CrossRef] [Google Scholar]
  12. F. Berthelin, T. Goudon and S. Minjeaud, Multifluid flows: a kinetic approach. J. Sci. Comput. 66 (2016) 792–824. [CrossRef] [MathSciNet] [Google Scholar]
  13. C. Berthon, A. Duran, F. Foucher, K. Saleh and J. de Dieu Zabsonré, Improvement of the hydrostatic reconstruction scheme to get fully discrete entropy inequalities. J. Sci. Comput. 80 (2019) 924–956. [CrossRef] [MathSciNet] [Google Scholar]
  14. R. Botchorishvili, B. Perthame and A. Vasseur, Equilibrium schemes for scalar conservation laws with stiff sources. Math. Comput. 72 (2003) 131–157. [Google Scholar]
  15. F. Bouchut, Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws and Well-balanced Schemes for Sources. Frontiers in Mathematics, Birkh¨auser (2004). [CrossRef] [Google Scholar]
  16. CALIF3S, A software components library for the computation of reactive turbulent flows. [Google Scholar]
  17. P. Cargo and A.-Y. LeRoux, Un schéma équilibre adapté au modèle d’atmosphère avec termes de gravité. C. R. Acad. Sci. Paris Sér. I Math. 318 (1994) 73–76. [MathSciNet] [Google Scholar]
  18. M. Castro, A. Milanes and C. Pares, Well-balanced numerical schemes based on a generalized hydrostatic reconstruction technique. Math. Models Methods Appl. Sci. 17 (2007) 2055–2113. [CrossRef] [MathSciNet] [Google Scholar]
  19. M.J. Castro, A. Pardo, C. Parés and E.F. Toro, On some fast well-balanced first order solvers for nonconservative systems. Math. Comput. 79 (2010) 1427–1472. [Google Scholar]
  20. F. Coron and B. Perthame, Numerical passage from kinetic to fluid equations. SIAM J. Numer. Anal. 28 (1991) 26–42. [Google Scholar]
  21. C. Dafermos, Hyperbolic conserrvation laws in continuum physics, 3rd edition. In Vol. 325 of Grundlehren der Mathematischen Wissenschaften. Springer, 2010. [CrossRef] [Google Scholar]
  22. G. Dakin, B. Després and S. Jaouen, High-order staggered schemes for compressible hydrodynamics weak consistency and numerical validation. J. Comput. Phys. 376 (2019) 339–364. [CrossRef] [MathSciNet] [Google Scholar]
  23. O. Delestre, Simulation du ruissellement d’eau de pluie sur des surfaces agricoles. Ph.D. thesis, Université d’Orléans (2010). [Google Scholar]
  24. 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 in Fluids 72 (2013) 269–300. [CrossRef] [Google Scholar]
  25. S.M. Deshpande, Kinetic theory based new upwind methods for inviscid compressible flows. In: AIAA 24th Aerospace Science Meeting, Jan 6–9, 1986, Nevada, USA. AIAA paper (1986) 86–0275. [Google Scholar]
  26. S.M. Deshpande, On the Maxwellian distribution, symmetric form and entropy conservation for the Euler equations. Technical report, NASA Langley Research Centre, Hampton, VA (1986). NASA TP2613. [Google Scholar]
  27. D. Doyen and P.H. Gunawan, An explicit staggered finite volume scheme for the shallow water equations. In: Finite Volumes for Complex Applications VII-Methods and Theoretical Aspects, Vol. 77 of Springer Proceedings in Mathematics & Statistics. Springer (2014). [Google Scholar]
  28. T. Gallouët, J.-M. Hérard and N. Seguin, Some approximate Godunov schemes to compute shallow water equations with topography. Comput. Fluids 32 (2003) 479–513. [CrossRef] [MathSciNet] [Google Scholar]
  29. T. Gallouët, R. Herbin and J.-C. Latché, Lax–wendroff consistency of finite volume schemes for systems of non linear conservation laws: extension to staggered schemes. SeMA 79 (2022) 333–354. [CrossRef] [MathSciNet] [Google Scholar]
  30. L. Gastaldo, R. Herbin, W. Kheriji, C. Lapuerta and J.-C. Latché, Staggered discretizations, pressure correction schemes and all speed barotropic flows. In Vol. 4 Finite Volumes for Complex Applications VI, Problems and Perspectives, Prague, Czech Republic (2011) 839–855. [Google Scholar]
  31. L. Gastaldo, R. Herbin, J.-C. Latché and N. Therme, A MUSCL-type segregated-explicit staggered scheme for the Euler equations. Comput. Fluids 175 (2018) 91–110. [CrossRef] [MathSciNet] [Google Scholar]
  32. E. Godlewski and P.-A. Raviart, Numerical approximation of hyperbolic systems of conservation laws. In Vol. 118 of Applied Mathematical Sciences. Springer, New-York (1996). [CrossRef] [Google Scholar]
  33. L. Gosse, Computing qualitatively correct approximations of balance laws. In Vol. 2 of SIMAI Springer Series. Spinger (2013). [CrossRef] [Google Scholar]
  34. T. Goudon, J. Llobell and S. Minjeaud, An asymptotic preserving scheme on staggered grids for the barotropic Euler system in low Mach regimes. Numer. Methods PDE 36 (2020) 1098–1128. [CrossRef] [Google Scholar]
  35. T. Goudon, J. Llobell and S. Minjeaud, An explicit MUSCL scheme on staggered grids with kinetic-like fluxes for the barotropic and full Euler system. Commun. Comput. Phys. 27 (2020) 672–724. [CrossRef] [MathSciNet] [Google Scholar]
  36. T. Goudon, J. Llobell and S. Minjeaud, An explicit finite volume scheme on staggered grids for the Euler equations: unstructured meshes, stability analysis, and energy conservation. Int. J. Numer. Methods Fluids 94 (2022) 76–119. [CrossRef] [Google Scholar]
  37. J.M. Greenberg and A.-Y. Leroux, A well-balanced scheme for the numerical processing of source terms in hyperbolic equations. SIAM J. Numer. Anal. 33 (1996) 1–16. [CrossRef] [MathSciNet] [Google Scholar]
  38. H. Guillard and C. Viozat, On the behavior of upwind schemes in the low Mach number limit. Comput. Fluids 28 (1999) 63–86. [CrossRef] [MathSciNet] [Google Scholar]
  39. H. Guillard and B. Nkonga, Chapter 8 – on the behaviour of upwind schemes in the low mach number limit: A review. In Vol. 18 of Handbook of Numerical Analysis, edited by R. Abgrall and C.-W. Shu. Handbook of Numerical Methods for Hyperbolic Problems. Elsevier (2017) 203–231. [Google Scholar]
  40. F.H. Harlow and J.E. Welch, Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface. Phys. Fluids 8 (1965) 2182–2189. [CrossRef] [MathSciNet] [Google Scholar]
  41. F.H. Harlow and A.A. Amsden, Numerical calculation of almost incompressible flow. J. Comput. Phys. 3 (1968) 80–93. [CrossRef] [Google Scholar]
  42. F.H. Harlow and A.A. Amsden, A numerical fluid dynamics calculation method for all flow speeds. J. Comput. Phys. 8 (1971) 197–213. [CrossRef] [Google Scholar]
  43. R. Herbin, W. Kheriji and J.-C. Latché, Staggered schemes for all speed flows. ESAIM: Proc. 35 (2012) 122–150. [CrossRef] [EDP Sciences] [Google Scholar]
  44. R. Herbin, J.-C. Latché and T.T. Nguyen, Explicit staggered schemes for the compressible Euler equations. In Applied mathematics in Savoie—AMIS 2012: Multiphase flow in industrial and environmental engineering, Vol. 40 of ESAIM Proc., EDP Sciences (2013) 83–102. [Google Scholar]
  45. R. Herbin, J.-C. Latché and T.T. Nguyen, Consistent segregated staggered schemes with explicit steps for the isentropic and full Euler equations. ESAIM:M2AN 52 (2018) 893–944. [CrossRef] [EDP Sciences] [Google Scholar]
  46. R. Herbin, J.-C. Latché, S. Minjeaud and N. Therme, Conservativity and weak consistency of a class of staggered finite volume methods for the Euler equations. Math. Comput. 90 (2021) 1155–1177. [Google Scholar]
  47. R. Herbin, J.-C. Latché and K. Saleh, Low Mach number limit of some staggered schemes for compressible barotropic flows. Math. Comput. 90 (2021) 1039–1087. [CrossRef] [Google Scholar]
  48. D.D. Houghton and A. Kasahara, Nonlinear shallow fluid flow over an isolated ridge. NCAR Manuscript 259a (1967). [Google Scholar]
  49. S. Kaniel and J. Falcovitz, Approximation of the hydrodynamic equations by a transport process, edited by R. Rautman. In: Proceedings of IUTAM Symposium on Approximation Methods for Navier-Stokes Problems, Vol. 771 of Lecture Notes in Math. Springer-Verlag (1980). [Google Scholar]
  50. W. Kheriji, R. Herbin and J.-C. Latché, Pressure correction staggered schemes for barotropic one-phase and two-phase flows. Comput. Fluids 88 (2013) 524–542. [CrossRef] [MathSciNet] [Google Scholar]
  51. C. Klingenberg, G. Puppo and M. Semplice, Arbitrary order finite volume well-balanced schemes for the Euler equations with gravity. SIAM J. Sci. Comput. 41 (2019) A695–A721. [CrossRef] [Google Scholar]
  52. F. Lespagnol and G. Dakin, High order accurate schemes for Euler and Navier-Stokes equations on staggered Cartesian grids. J. Comput. Phys. 410 (2020) 109314. [CrossRef] [MathSciNet] [Google Scholar]
  53. R. LeVeque, Balancing source terms and flux gradients in high-resolution godunov methods: The quasi-steady wave-propagation algorithm. J. Comput. Phys. 146 (1998) 346–365. [CrossRef] [MathSciNet] [Google Scholar]
  54. R.J. LeVeque, Finite volume methods for hyperbolic problems. Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge (2002). [CrossRef] [Google Scholar]
  55. V. Michel-Dansac, C. Berthon, S. Clain and F. Foucher, A well-balanced scheme for the shallow-water equations with topography. Comput. Math. Appl. 72 (2016) 568–593. [CrossRef] [MathSciNet] [Google Scholar]
  56. B. Perthame, Second order Boltzmann schemes for compressible Euler equations in one and two space dimension. SIAM J. Numer. Anal. 29 (1992) 1–19. [CrossRef] [MathSciNet] [Google Scholar]
  57. B. Perthame, Kinetic Formulation of Conservation Laws. Oxford Lecture Series in Math. and its Appl. Oxford University Press (2003). [Google Scholar]
  58. B. Polizzi, O. Bernard and M. Ribot, A time-space model for the growth of microalgae biofilms for biofuel production. J. Theor. Biol. 432 (2017) 55–79. [CrossRef] [Google Scholar]
  59. G. Stelling and S. Duinmeijer, A staggered conservative scheme for every Froude number in rapidly varied shallow water flows. Int. J. Numer. Methods Fluids 43 (2003) 1329–1354. [CrossRef] [Google Scholar]
  60. W.C. Thacker, Some exact solutions to the nonlinear shallow-water wave equations. J. Fluid Mech. 107 (1981) 499–508. [CrossRef] [MathSciNet] [Google Scholar]
  61. E.F. Toro, Riemann Solvers and Numerical Methods for Fluid Dynamics, 3rd edition. Springer-Verlag, Berlin (2009). [Google Scholar]
  62. D.R. van der Heul, C. Vuik and P. Wesseling, A conservative pressure-correction method for flow at all speeds. Comput. Fluids 32 (2003) 1113–1132. [CrossRef] [MathSciNet] [Google Scholar]
  63. B. van Leer, Towards the ultimate conservative difference scheme. V. A second-order sequel to Godunov’s method. J. Comput. Phys. 135 (1997) 227–248. [Google Scholar]
  64. B. van’t Hof and A.E.P. Veldman, Mass, momentum and energy conserving (MaMEC) discretizations on general grids for the compressible Euler and shallow water equations. J. Comput. Phys. 231 (2012) 4723–4744. [CrossRef] [MathSciNet] [Google Scholar]
  65. J. VonNeumann and R.D. Richtmyer, A method for the numerical calculation of hydrodynamic shocks. J. Appl. Phys. 21 (1950) 232–237. [NASA ADS] [CrossRef] [Google Scholar]
  66. I. Wenneker, A. Segal and P. Wesseling, A Mach-uniform unstructured staggered grid method. Int. J. Numer. Methods Fluids 40 (2002) 1209–1235. [Google Scholar]
  67. I. Wenneker, A. Segal and P. Wesseling, Conservation properties of a new unstructured staggered scheme. Comput. Fluids 32 (2003) 139–147. [CrossRef] [MathSciNet] [Google Scholar]
  68. P. Wesseling, Principles of computational fluid dynamics. In Vol. 29 of Springer Series in Computational Mathematics. Springer (2001). [CrossRef] [Google Scholar]
  69. P. Woodward and P. Colella, The numerical simulation of two-dimensional fluid flow with strong shocks. J. Comput. Phys. 54 (1984) 115–173. [Google Scholar]

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