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The study of coastal flows based on lattice Boltzmann method: application Oualidia lagoon

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Abstract

The lattice Boltzmann method (LBM) is a recent method widely used in the field of computational fluid dynamics. It was first presented for solving the Navier–Stokes equations. Since then, most of the advances of this method have been published with applications to flows in small-scale domains, but rarely applied to large-scale geophysical flows (flows governed by the shallow equations). The purpose of this paper is then to show that the LBM can be successfully applied for the simulation of large-scale flows such as the propagation of the tidal wave in the Oualidia lagoon (Moroccan Atlantic coast). Before presenting the results of our simulations, we applied the LBM to the classic hydraulic case of a mixed flow in a convergent domain (slightly variable Froude number). This case test has made it possible to measure the performance of the approach. It showed that this method provides solutions with good precision while reproducing the characteristics of a flow as complex as that of a convergent channel flow (change of regime: from subcritical to supercritical). The LBM was then applied to the real case to simulate both the propagation of the \({M}_{2}\)-tidal wave and the estimation of the associated residual velocity in the Oualidia lagoon. As the first results of this numerical modeling, the code developed has shown the capability and the efficiency of reproducing correctly the expected characteristics of tidal circulation in the concerned lagoon. Consequently, the LBM (and especially its GPU parallel version) can now be considered a serious alternative to the classical discretization methods such as the finite differences, finite elements and finite volumes methods.

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References

  1. Boyauzan A, Irzi Z (2015) Impacts of man-made structures on sediment fluxes and water circulation around the barrier island of the Nador lagoon (north-east of Morocco, oriental region). J Mediterr Geogr 125:85–94

    Article  Google Scholar 

  2. Maicu F, Abdellaoui B, Bajo M, Chair A, Hilmi K, Umgiesser G (2021) Modelling the water dynamics of a tidal lagoon: the impact of human intervention in the Nador Lagoon (Morocco). Cont Shelf Res 228:104–115. https://doi.org/10.1016/j.csr.2021.104535

    Article  Google Scholar 

  3. Rharbi N, Ramdani M, Berraho A, Lakhdar JI (2001) Caractéristiques hydrologiques et écologiques de la lagune d’Oualidia, milieu paralique de la côte atlantique marocaine. Marine Life 11(1–2):3–9

    Google Scholar 

  4. Orbi A, Hilmi K, Larissi J, Zidane H, Zizah, El Moussaoui N, Lakhdar JI, Sarf F (1998) Hydrologie et hydrodynamique des côtes marocaines: milieux paraliques et zones côtières. EXPO 98

  5. Carruesco CH (1989) Génèse et évolution à l’holocène de trois lagunes de la façade Atlantique: Moulay Bousselham. Thèse de doctorat d’état Es-Sciences, Univ. de Bordeaux, in french, Oualidia (Maroc) et Arcachon (France), p 485

    Google Scholar 

  6. Sarf F (1999) Dynamique sédimentaire et état de pollution dans la lagune de Oualidia. Thèse de doctorat (in french), Univ, Mohammed V, Faculté des Sciences, Rabat, Maroc, p 121

    Google Scholar 

  7. El Attar J (1998) Contribution à la détermination de l’origine de la contamination fécale dans la lagune d’Oualidia (Maroc) et étude de la contamination bactériologique de l’huître Crassostrea Gigas en conditions naturelles et expérimentales. Thèse de doctorat (in French) Univ, Chouaib Doukkali, Faculté des Sciences, El Jadida, Maroc, p 124

    Google Scholar 

  8. Bennouna A (1999) Etude du phytoplancton du complexe lagunaire Oualidia-Sidi Moussa. Thèse de doctorat (in French) Univ. Chouaib Doukkali, Faculté des Sciences, El Jadida, Maroc p 149

  9. Beaubrun PC (1976) Les huîtres au Maroc et l’ostréiculture dans la lagune de Oualidia. Bulletin Institut des Pêches Maritimes 22:13–143

    Google Scholar 

  10. Hilmi K, Orbi A, Lakhdar IJ, Sarf F (2005) Etude courantologique de la lagune de Oualidia (Maroc) en automne. Bulletin de l’institut scientifique, Rabat, section Sciences de la Terre 36–27:67–71

    Google Scholar 

  11. Hilmi K, Koutitonsky VG, Orbi A, Lakhdar JI, Chagdali M (2005) Oualidia lagoon (Morocco): an estuary without a river. Afr J Aquat Sci 30(1):1–10

    Article  Google Scholar 

  12. McNamara GR, Zanetti G (1988) Use of the Boltzmann equation to simulate lattice-gas automata. Phys Rev Lett 61(20):2332–2335

    Article  Google Scholar 

  13. Chen S, Doolen GD (1998) Lattice Boltzmann method for fluid flows. Annu Rev Fluid Mech 30:329–364

    Article  MathSciNet  Google Scholar 

  14. d’Humieres D, Ginzburg I, Krafczyk M, Lallemand P, Luo LS (2002) Multiple relaxation time lattice Boltzmann models in three dimensions. Philos Trans R Soc London A 360:437–451. https://doi.org/10.1098/rsta.2001.0955

    Article  MathSciNet  Google Scholar 

  15. Sato K, Kawasaki K, Koshimora S (2022) A comparative study of the cumulant lattice Boltzmann method in a single-phase free-surface model of violent flows. Comput Fluids 236(30):105303. https://doi.org/10.1016/j.compfluid.2021.105303

    Article  MathSciNet  Google Scholar 

  16. Geier M, Schönherr M, Pasquali A, Krafczyk M (2015) The cumulant lattice Boltzmann equation in three dimensions: theory and validation. Comput Math Appl 70(4):507–547. https://doi.org/10.1016/j.camwa.2015.05.001

    Article  MathSciNet  Google Scholar 

  17. Watanabe S, Fujisaki S, Hu C (2021) Numerical simulation of dam break flow impact on vertical cylinder by cumulant lattice Boltzmann method. J Hydro 33:185–194. https://doi.org/10.1007/s42241-021-0028-6

    Article  Google Scholar 

  18. Geier M, Greiner A, Korvink JG (2006) Cascaded digital lattice Boltzmann automata for high Reynolds number flow. Phys Rev (E) 73(6):066705. https://doi.org/10.1103/PhysRevE.73.066705

    Article  Google Scholar 

  19. Suzuki K, Inamuro T (2014) An improved lattice kinetic scheme for incompressible viscous fluid flows. Int J Modern Phys C 25(1):1–9. https://doi.org/10.1142/S0129183113400172

    Article  MathSciNet  Google Scholar 

  20. Chen Z (2018) Development of simplified and highly stable lattice Boltzmann method and its applications. PhD thesis, National University of Singapore. p 180

  21. Zhou JG (2004) Lattice Boltzmann methods for shallow water flows, 1st edn. Springer, Berlin

    Book  Google Scholar 

  22. Tubbs KR, Tsai FTC (2019) MRT lattice Boltzmann model for multilayer shallow water flow. Water 11(8):1628. https://doi.org/10.3390/w11081623

    Article  Google Scholar 

  23. Zhou JG, Liu H, Shafiai S, Peng Y, Burrows R (2010) Lattice Boltzmann method for open-channel flows. Proc Inst Civ Eng Eng Comput Mech 163(4):243–249. https://doi.org/10.1680/eacm.2010.163.4.243

    Article  Google Scholar 

  24. Boltzmann L (1878) Weiter Studien über das Wärmegleichgewicht unte Gasmolekülen. Wien Ber 66:275–370

    Google Scholar 

  25. Bhatnagar P, Gross E, Krook M (1954) A model for collision process in gases. I.: small amplitude process in charged and neutral one-component systems. Phys Rev 94(3):511–525

    Article  Google Scholar 

  26. Zhou JG (2001) An elastic-collision scheme for lattice Boltzmann methods. Int J Modern Phys C 12:387–401. https://doi.org/10.1142/S0129183101001833

    Article  Google Scholar 

  27. Dansac VM, Berthon C, Clain S, Foucher F (2016) A well-balanced scheme for the shallow-water equations with topography. Comput Math Appl 72:568–593

    Article  MathSciNet  Google Scholar 

  28. Frisch U, d’Humières D, Hasslacher B, Lallemand P, Pomeau Y, Rivet J-P (1987) Lattice gas hydrodynamics in two and three dimensions. Complex Syst 1:649–707

    MathSciNet  Google Scholar 

  29. Luo L-S (1997) Analytic solutions of linearized lattice Boltzmann equation for simple flows. J Stat Phys 88:913–926

    Article  MathSciNet  Google Scholar 

  30. Guo Z, Shu C (2013) Lattice Boltzmann method and its application in engineering. World Scientific, Singapore, p 404

    Book  Google Scholar 

  31. Aidun CK, Clausen JR (2010) Lattice Boltzmann method for complex flows. Ann Rev Fluid Mech 42:439–472. https://doi.org/10.1146/annurev-fluid-121108-145519

    Article  MathSciNet  Google Scholar 

  32. Kruger T, Kusumaatmaja H, Kuzmin A, Shardt O, Silva G, Viggen EM (2017) The lattice Boltzmann method, principles and practice., 1st edn. Springer, Switzerland

  33. d’Humieres D (1992) Generalized lattice Boltzmann equations. Rarefied gas dynamics: theory and simulations. Prog Aerosp Sci 159:450–458

    Google Scholar 

  34. Lallemand P, Luo LS (2000) Theory of the lattice Boltzmann method: dispersion, dissipa-tion, isotropy, Galilean invariance, and stability. Phys Rev E. https://doi.org/10.1103/PhysRevE.61.6546

    Article  Google Scholar 

  35. Zhou JG (2012) MRT rectangular lattice Boltzmann method. Int J Modern Phys 23(5):1250040. https://doi.org/10.1142/S0129183112500404

    Article  Google Scholar 

  36. Zou Q, He X (1997) On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Phys Fluids. https://doi.org/10.1063/1.869307

    Article  MathSciNet  Google Scholar 

  37. Mohammad AA (2011) Lattice Boltzmann Method, fundamentals and engineering applications with computer codes, 1st edn. Springer- Verlag, London

    Book  Google Scholar 

  38. Rodi W, Constantinescu G, Stoesser T (2013) Large-eddy simulation in hydraulics. CRC Press, London

    Book  Google Scholar 

  39. McDonough JM (2004) Introductory lectures on turbulence, departments of mechanical engineering and mathematics. University of Kentucky

    Google Scholar 

  40. Coles D, Shintaku T (1943) Experimental relation between sudden wall angle change and standing waves in supercritical flow. B.S. thesis, Lehigh University, Bethlehem

  41. Tao Z, Defu C (2016) Double MRT thermal lattice Boltzmann simulation for MHD natural convection of nanofluids in an inclined cavity with four square heat sources. Int J Heat Mass Transf 94:87–100. https://doi.org/10.1016/j.ijheatmasstransfer-.2015.11.071

    Article  Google Scholar 

  42. IPCC (2021) Climate change 2021: the physical science basis. contribution of working group i to the sixth assessment report of the intergovernmental panel on climate change. In: Masson-Delmotte V, Zhai P, Pirani A, Connors SL, Péan C, Berger S, Caud N, Chen Y, Goldfarb L, Gomis MI, Huang M, Leitzell K, Lonnoy E, Matthews JBR, Maycock TK, Waterfield T, Yelekçi O, Yu R, Zhou B (eds) Cambridge University Press. United Kingdom and New York, NY, USA, Cambridge, p 2391

    Google Scholar 

  43. Orbi A, Hilmi K, Idrissi JL, Zizah S (2008) Lagoon ecosystem study trough two cases: Oualidia (Atlantic) and Nador (Mediterranean). Gönenç İE, Vadineanu A, Wolflin JP, Russo RC (eds.) Sustainable use and development of watersheds. NATO Science for peace and security series. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8558-1_17

  44. Egbert GD, Erofeeva SY (2002) Efficient inverse modeling of barotropic ocean tides. J Atmos Ocean Technol 19(2):183–204. https://doi.org/10.1175/1520-0426(2002)019%-3C0183:EIMOBO%3E2.0.CO;2

    Article  Google Scholar 

  45. Roache PJ (1997) Quantification of uncertainty in computational fluid dynamics. Ann Rev Fluid Mech 29(1):123–160. https://doi.org/10.1146/annurev.fluid.29.1.123

    Article  MathSciNet  Google Scholar 

  46. Fred S, Robert VW, Hugh WC, Eric GP (2001) Verification and validation of CFD simulations. Iowa Institute of hydraulic research and propulsion research center, IIHR Report No.407

  47. ITTC (2002) Quality manual CFD general uncertainty analysis in CFD: verification and validation methodology and procedures 12

  48. Celik IB, Ghia U, Roache PJ, Freitas CJ, Coleman H, Raad PE (2008) Procedure for estimation and reporting of uncertainty due to discretization in CFD applications. ASME J Fluids Eng 130(7):078001. https://doi.org/10.1115/1.2960953

    Article  Google Scholar 

  49. Hilmi K, Orbi A, Lakhdar IJ (2009) Hydrodynamisme de la lagune de Oualidia (Maroc) durant l’été et l’automne 2005. Bulletin de l’institut scientifique, Rabat, section Sciences de la Terre 31(29–34):2009

    Google Scholar 

  50. Haddach A, Smaoui H, Radi B (2023) Lattice Boltzmann method for 2D tidal flow: application to the Nador lagoon. Adv. Appl. Math. Mech. Article in press for 2024

  51. Longuet-Higgins MS (1969) On the transport of mass by time-varying ocean currents. Deep-Sea Res 16:431–447. https://doi.org/10.1016/0011-7471(69)90031-X

    Article  Google Scholar 

  52. Zimmerman JTF (1986) The tidal whirlpool: a review of horizontal dispersion by tidal and residual currents. J Sea Res 20(2/3):133–154. https://doi.org/10.1016/0077-7579(86)90037-2

    Article  Google Scholar 

  53. Cheng RT, Casulli V (1982) On lagrangian residual currents with applications in South San Francisco Bay, California. Water Resour Res 18(6):1652–1662. https://doi.org/10.1029/WR018i006p01652

    Article  Google Scholar 

  54. Feng S (1986) A three-dimensional weakly nonlinear dynamic on tide-induced Lagrangian residual current and mass-transport. Chinese J Oceanol Limnol 4(2):139–158. https://doi.org/10.1007/BF02850431

    Article  Google Scholar 

  55. Delhez E (1996) On the residual advection of the passive constituents. J Mar Syst 8:147–169. https://doi.org/10.1016/0924-7963(96)00004-8

    Article  Google Scholar 

  56. Feng S, Xi P, Zhang S (1984) The Baroclinic residual circulation in shallow seas. Chin J Oceanol Limnol 2(1):49–60. https://doi.org/10.1007/BF02888391

    Article  Google Scholar 

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Acknowledgements

The authors warmly thank the anonymous referees who were involved in the evaluation of this paper, by submitting constructive criticism to us which led to the improvement of our paper. Also, the authors would like to thank Engineering, Industrial Management and Innovation (EIMI) Laboratory of Faculty of Science and Technics of Hassan First University of Settat, Morocco, for providing us all the technical instruments used for this research. The numerical computation in this paper was carried out using the computer resource offered by the EIMI Laboratory.

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Authors and Affiliations

  1. Hassan First University of Settat, Faculté des Sciences et Techniques, Laboratory IMII, Settat, Morocco

    Ali Haddach & Bouchaib Radi

  2. Cerema/DTecREM, Margny-lès-Compiègne, France

    Hassan Smaoui

  3. Associate Researcher at Laboratoire Roberval, Université de Technologie de Compiègne, Compiègne, France

    Hassan Smaoui

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  1. Ali Haddach
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Correspondence to Ali Haddach.

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Haddach, A., Smaoui, H. & Radi, B. The study of coastal flows based on lattice Boltzmann method: application Oualidia lagoon. J Braz. Soc. Mech. Sci. Eng. 46, 225 (2024). https://doi.org/10.1007/s40430-024-04812-2

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