Temporal large-eddy simulations of the lid-driven cavity by finite volume method

  • L. CorrêaEmail author
  • G. Mompean
  • F. A. Kurokawa
  • F. S. Sousa
Technical Paper


This paper describes in detail a numerical scheme to predict complex turbulent flows using a recent model based on temporal large-eddy simulations (TLES). To solve the equations a second-order finite volume numerical method coupled with a second-order time integration scheme is used. The numerical scheme is validated and then applied to present new results concerning the prediction of the complex turbulent flow in a cubic lid-driven cavity, at Reynolds numbers \(Re=12{,}000\) and \(Re=18{,}000\). The results obtained with the TLES are compared with direct numerical simulations and experimental data for the mean velocity flow field and for the Reynolds stresses, showing to be very attractive when compared to large-eddy simulations.


Temporal large eddy simulation Lid-driven cavity flow Finite volume method 



We gratefully acknowledge the support provided by FAPESP (Grants 2010/16865-2, 2012/17827-2 and 2015/02649-0).


  1. 1.
    Watson E (1964) The radial spread of a liquid jet over a horizontal plane. J Fluid Mech 20:481–499MathSciNetCrossRefGoogle Scholar
  2. 2.
    Tang Z, Wan D (2015) Numerical simulation of impinging jet flows by modified MPS method. Eng Comput 32:1153–1171CrossRefGoogle Scholar
  3. 3.
    Bhajantri M, Eldho T, Deolalikar P (2007) Numerical modelling of turbulent flow through spillway with gated operation. Int J Numer Methods Eng 72:221–243CrossRefGoogle Scholar
  4. 4.
    Fureby C (2009) Large eddy simulation modelling of combustion for propulsion applications. Phil Trans Roy Soc Lond A—Math Phys Eng Sci 367:2957–2969CrossRefGoogle Scholar
  5. 5.
    Menzies K (2009) Large eddy simulation applications in gas turbines. Phil Trans Roy Soc Lond A—Math Phys Eng Sci 367:2827–2838CrossRefGoogle Scholar
  6. 6.
    Eastwood S, Tucker P, Xia H, Klostermeier C (2009) Developing large eddy simulation for turbomachinery applications. Phil Trans Roy Soc Lond A—Math Phys Eng Sci 367:2999–3013CrossRefGoogle Scholar
  7. 7.
    Bouffanais R (2010) Advances and challenges of applied large-eddy simulation. Comput Fluids 39:735–738CrossRefGoogle Scholar
  8. 8.
    Bouffanais R, Deville M, Fischer M, Leriche E, Weill D (2006) Large-eddy simulation of the lid-driven cubic cavity flow by the spectral element method. J Sci Comput 27:151–162MathSciNetCrossRefGoogle Scholar
  9. 9.
    Pruett C, Gatski T, Grosch C, Thacker W (2003) The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys Fluids 15:2127CrossRefGoogle Scholar
  10. 10.
    Berland J, Lafon P, Daude F, Crouzet F, Bogey C, Bailly C (2011) Filter shape dependence and effective scale separation in large-eddy simulations based on relaxation filtering. Comput Fluids 47:65–74MathSciNetCrossRefGoogle Scholar
  11. 11.
    Arai J, Koshizuka S, Murozono K (2013) Large eddy simulation and a simple wall model for turbulent flow calculation by a particle method. Int J Numer Methods Fluids 71:772–787MathSciNetCrossRefGoogle Scholar
  12. 12.
    Tsang C, Trujillo M, Rutland C (2014) Large-eddy simulation of shear flows and high-speed vaporizing liquid fuel sprays. Comput Fluids 105:262–279MathSciNetCrossRefGoogle Scholar
  13. 13.
    Sagaut P (2006) Large eddy simulation for incompressible flows—an introduction. Springer, BerlinzbMATHGoogle Scholar
  14. 14.
    Frisch U (1995) Turbulence. Cambridge University Press, CambridgeCrossRefGoogle Scholar
  15. 15.
    Pruett C (2008) Temporal large-eddy simulation: theory and implementation. Theor Comput Fluid Dyn 22:275–304CrossRefGoogle Scholar
  16. 16.
    Dakhoul Y, Bedford K (1986) Improved averaging method for turbulent flow simulation. Part I: theoretical development and application to Burgers’ transport equation. Int J Numer Methods Fluids 6:49CrossRefGoogle Scholar
  17. 17.
    Aldama A (1990) Filtering techniques for turbulent flow simulation. Lectures notes in engineering. Springer, BerlinCrossRefGoogle Scholar
  18. 18.
    Meneveau C, Lund T, Cabot W (1996) Lagrangian dynamic subgrid-scale model of turbulence. J Fluid Mech 319:353–385CrossRefGoogle Scholar
  19. 19.
    Pruett CD (2000) Eulerian time-domain filtering for spatial large-eddy simulation. AIAA 38(9):1634–1642CrossRefGoogle Scholar
  20. 20.
    Stolz S, Adams N (1999) An approximate deconvolution procedure for large-eddy simulation. Phys of Fluids 11(7):1699–1701CrossRefGoogle Scholar
  21. 21.
    Tejada-Martínez A, Grosch C, Gatski T (2007) Temporal large-eddy simulation of unstratified and stably stratified turbulent channel flows. Int J Heat Fluid Flow 28:1244–1261CrossRefGoogle Scholar
  22. 22.
    Leriche E, Gavrilakis S (2000) Direct numerical simulation of the flow in a lid-driven cubical cavity. Phys Fluids 12:1363CrossRefGoogle Scholar
  23. 23.
    Bruneau C, Saad M (2006) The 2D lid-driven cavity problem revisited. Comput Fluids 35:326–348CrossRefGoogle Scholar
  24. 24.
    Thais L, Tejada-Martínez A, Gatski T, Mompean G (2010) Temporal large eddy simulations of turbulent viscoelastic drag reduction flows. Phys Fluids 22(013):103zbMATHGoogle Scholar
  25. 25.
    Pruett C, Thomas B, Grosch C, Gatski T (2006) A temporal approximate deconvolution model for large-eddy simulation. Phys Fluids 18(028):104Google Scholar
  26. 26.
    Bell JB, Colella P, Glaz HM (1989) A 2nd-order projection method for the incompressible Navier–Stokes equations. J Comp Phys 85(2):257–283CrossRefGoogle Scholar
  27. 27.
    Liu M, Ren YX, Zhang H (2004) A class of fully second order accurate projection methods for solving the incompressible Navier–Stokes equations. J Comp Phys 200(1):325–346MathSciNetCrossRefGoogle Scholar
  28. 28.
    Guermond JL, Minev P, Shen J (2006) An overview of projection methods for incompressible flows. Comput Method Appl M 195(44–47):6011–6045MathSciNetCrossRefGoogle Scholar
  29. 29.
    Sousa FS, Oishi CM, Buscaglia GC (2015) Spurious transients of projection methods in microflow simulations. Comput Method Appl M 285:659–693MathSciNetCrossRefGoogle Scholar
  30. 30.
    Perot JB (1993) An analysis of the fractional step method. J Comput Phys 108(1):51–58MathSciNetCrossRefGoogle Scholar
  31. 31.
    Strikwerda JC, Lee YS (1999) The accuracy of the fractional step method. SIAM J Numer Anal 37(1):37–47MathSciNetCrossRefGoogle Scholar
  32. 32.
    Codina R (2001) Pressure stability in fractional step finite element methods for incompressible flows. J Comput Phys 170(1):112–140MathSciNetCrossRefGoogle Scholar
  33. 33.
    Armfield S, Street R (2002) An analysis and comparison of the time accuracy of fractional-step methods for the Navier–Stokes equations on staggered grids. Int J Numer Methods Fluids 38(3):255–282CrossRefGoogle Scholar
  34. 34.
    Gervasio P, Saleri F (2006) Algebraic fractional-step schemes for time-dependent incompressible Navier–Stokes equations. J Sci Comput 27(1–3):257–269MathSciNetCrossRefGoogle Scholar
  35. 35.
    Chorin A (1968) Numerical solution of the Navier–Stokes equations. Math Comp 22:745–762MathSciNetCrossRefGoogle Scholar
  36. 36.
    Leonard B (1979) A stable and accurate convective modelling procedure base and quadratic upstream interpolation. Comput Methods Appl Mech Eng 19:59–98CrossRefGoogle Scholar
  37. 37.
    Harris J, Grilli S (2011) A perturbation approach to large eddy simulation of wave-induced bottom boundary layer flows. Int J Numer Methods Fluids 68:1574–1604MathSciNetCrossRefGoogle Scholar
  38. 38.
    Hirt CW, Nichols BD, Romero NC (1975) SOLA numerical solution algorithm for transient fluid flow. Los Alamos Laboratory, Report LA-5852Google Scholar
  39. 39.
    Peric M, Kessler R, Scheuerer G (1988) Comparison of finite-volume numerical-methods with staggered and colocated grids. Comput Fluids 16(4):389–403CrossRefGoogle Scholar
  40. 40.
    Piller M, Stalio E (2004) Finite-volume compact schemes on staggered grids. J Comput Phys 197(1):299–340CrossRefGoogle Scholar
  41. 41.
    Fletcher R (1976) Conjugate gradient methods for indefinite systems. In: Watson GA (ed) Numerical analysis. Lecture notes in mathematics, vol 506. Springer, BerlinGoogle Scholar
  42. 42.
    Kremer F, Bogey C (2015) Large-eddy simulation of turbulent channel flow using relaxation filtering: resolution requirement and Reynolds number effects. Comput Fluids 116:17–28CrossRefGoogle Scholar
  43. 43.
    Deardorff J (1970) A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers. J Fluid Mech 41:453–480CrossRefGoogle Scholar
  44. 44.
    Kim J, Moin P, Moser R (1987) Turbulence statistics in fully developed channel flow at low Reynolds number. J Fluid Mech 177:133–166CrossRefGoogle Scholar
  45. 45.
    Moser R, Kim J, Mansour N (1999) Direct numerical simulation of turbulent channel flow up to \({R}e_{\tau }\)=590. Phys Fluids 11(4):943–945CrossRefGoogle Scholar
  46. 46.
    Thais L, Tejada-Martínez A, Gatski T, Mompean G (2011) A massively parallel hybrid scheme for direct numerical simulation of turbulent viscoelastic channel flow. Comput Fluids 43:134–142MathSciNetCrossRefGoogle Scholar
  47. 47.
    Tabor G, Baba-Ahmadi M (2010) Inlet conditions for large eddy simulation: a review. Comput Fluids 39:553–567MathSciNetCrossRefGoogle Scholar
  48. 48.
    Corrêa L (2016) Simulação de grandes escalas de escoamentos turbulentos com filtragem temporal via método de volumes finitos. Ph.D. thesis, University of São PauloGoogle Scholar
  49. 49.
    Koseff J, Street R (1984) The lid-driven cavity flow: a synthesis of qualitative and quantitative observations. J Fluids Eng 106:390–398CrossRefGoogle Scholar
  50. 50.
    Jordan S, Ragab S (1994) On the unsteady and turbulent characteristics of the three-dimensional shear-driven cavity flow. J Fluids Eng 116:439–449CrossRefGoogle Scholar
  51. 51.
    Shankar P, Desphande M (2000) Fluid mechanics in the driven cavity. Annu Rev Fluid Mech 32:93–136MathSciNetCrossRefGoogle Scholar
  52. 52.
    Kawaguti M (1961) Numerical solution of the Navier–Stokes equations for the flow in a two dimensional cavity. J Phys Soc Japan 16:2307–2327MathSciNetCrossRefGoogle Scholar
  53. 53.
    Burggraf O (1966) Analytical and numerical studies of the structure of steady separated flows. J Fluid Mech 24:113–151CrossRefGoogle Scholar
  54. 54.
    Ghia U, Ghia K, Shin C (1982) High-resolutions for incompressible flow using the Navier–Stokes equations and a multigrid method. J Comput Phys 48:387–411CrossRefGoogle Scholar
  55. 55.
    Shetty D, Fisher T, Chunekar A, Frankel S (2010) High-order incompressible large-eddy simulation of fully inhomogeneous turbulent flows. J Comp Phys 229:8802–8822MathSciNetCrossRefGoogle Scholar
  56. 56.
    Vreman A (2004) An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys Fluids 16:3670–3681CrossRefGoogle Scholar
  57. 57.
    Paraview (2013) Paraview / Line Integral Convolution. URL Accessed 03 Dec 2015

Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2018

Authors and Affiliations

  1. 1.Faculdade de Ciências Exatas e TecnologiasUniversidade Federal da Grande DouradosDouradosBrazil
  2. 2.Unité de Mécanique de Lille, UML EA 7512, Cité ScientifiqueUniversité de LilleVilleneuve d’AscqFrance
  3. 3.Escola Politécnica, Departamento de Engenharia de Construção CivilUniversidade de São PauloSão PauloBrazil
  4. 4.Instituto de Ciências Matemáticas e de Computação, Departamento de Matemática Aplicada e EstatísticaUniversidade de São PauloSão CarlosBrazil

Personalised recommendations