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Comparison of Subgrid-scale Viscosity Models and Selective Filtering Strategy for Large-eddy Simulations

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Abstract

Explicitly filtered large-eddy simulations (LES), combining high-accuracy schemes with the use of a selective filtering without adding an explicit subgrid-scales (SGS) model, are carried out for the Taylor-Green-vortex and the supersonic-boundary-layer cases. First, the present approach is validated against direct numerical simulation (DNS) results. Subsequently, several SGS models are implemented in order to investigate if they can improve the initial filter-based methodology. It is shown that the most accurate results are obtained when the filtering is used alone as an implicit model, and for a minimal cost. Moreover, the tests for the Taylor-Green vortex indicate that the discretization error from the numerical methods, notably the dissipation error from the high-order filtering, can have a greater influence than the SGS models.

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References

  1. Garnier, E., Adams, N., Sagaut, P.: Large Eddy Simulation for Compressible Flows. Springer (2009)

  2. Meyers, J., Sagaut, P.: Is plane channel flow a friendly case for the testing of the large-eddy simulation subgrid-scale models? Phys. Fluids 19, 048105 (2007)

    Article  Google Scholar 

  3. Bose, S.T., Moin, P., You, D.: Grid-independent large-eddy simulation using explicit filtering. Phys. Fluids 22, 105103 (2010)

    Article  Google Scholar 

  4. Radhakrishnan, S., Bellan, J.: Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of compressible single-phase flow. J. Fluid Mech. 697, 399–435 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. De Stefano, G., Vasilyev, O.V.: Sharp cutoff versus smooth filtering in large eddy simulation. Phys. Fluids 14(1), 362–369 (2004)

    Article  Google Scholar 

  6. Yang, X., Fu, S.: The effect of filtering on truncated Navier-Stokes equations. J. Turbul. 8(8), 1–18 (2007)

    MathSciNet  Google Scholar 

  7. Ghosal, S.: An analysis of numerical errors in large-eddy simulations of turbulence. J. Comput. Phys. 125, 187–206 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kravchenko, A.G., Moin, P.: On the effect of numerical errors in large eddy simulations of turbulent flows. J. Comput. Phys. 131, 310–322 (1997)

    Article  MATH  Google Scholar 

  9. Smagorinsky, J.S.: General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weather Rev. 91, 99–163 (1963)

    Article  Google Scholar 

  10. Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3(7), 1760–1765 (1991)

    Article  MATH  Google Scholar 

  11. Bogey, C., Bailly, C.: Decrease of the effective Reynolds number with eddy-viscosity subgrid-scale modelling. AIAA J. 43(2), 437–439 (2005)

    Article  Google Scholar 

  12. Bardina, J., Ferziger, J.H., Reynold, W.C.: Improved subgrid scale models for large eddy simulation. In: 13th AIAA Fluid & Plasma Dynamics Conference, Snowmass, Colorado, 14–16 July 1981. AIAA 2003-4098 (1980)

  13. Hughes, T.J.R., Mazzei, L., Oberai, A.A.: The multiscale formulation of large eddy simulation: decay of homogeneous isotropic turbulence. Phys. Fluids 13(2), 505–512 (2001)

    Article  Google Scholar 

  14. Stolz, S., Adams, N.A., Kleiser, L.: An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows. Phys. Fluids 13(4), 997–1015 (2001)

    Article  Google Scholar 

  15. Stolz, S., Adams, N.A., Kleiser, L.: The approximate deconvolution model for large-eddy simulations of compressible flows and its application to shock-turbulent boundary-layer interaction. Phys. Fluids 13(10), 2985–3001 (2001)

    Article  Google Scholar 

  16. Gullbrand, J., Chow, F.K.: The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering. J. Fluid Mech. 495, 323–341 (2003)

    Article  MATH  Google Scholar 

  17. Borue, V.V., Orszag, S.A.: Self-similar decay of three-dimensional homogeneous turbulence with hyperviscosity. Phys. Rev. E 51(2), R856–R859 (1995)

    Article  Google Scholar 

  18. Cook, A.W., Cabot, W.H.: A high-wavenumber viscosity for high-resolution numerical methods. J. Comput. Phys. 195(2), 594–601 (2004)

    Article  MATH  Google Scholar 

  19. Lamorgese, A.G., Caughtey, D.A., Pope, S.B.: Direct numerical simulation of homogeneous turbulence with hyperviscosity. Phys. Fluids 17, 015106 (2005)

    Article  Google Scholar 

  20. Karamanos, G.-S., Karniadakis, G.E.: A spectral-vanishing viscosity method for large-eddy simulations. J. Comput. Phys. 163, 22–50 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  21. Boris, J.P., Grinstein, F.F., Oran, E.S., Kolbe, R.L.: New insights into large eddy simulation. Fluid Dyn. Res. 10, 199–228 (1992)

    Article  Google Scholar 

  22. Fureby, C., Grinstein, F.F.: Large eddy simulation of high-Reynolds number free and wall-bounded flows. J. Comput. Phys. 181, 68–97 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  23. Domaradzki, J.A., Saiki, E.M.: A subgrid-scale model based on the estimation of unresolved scales of turbulence. Phys. Fluids 9(7), 2148–2164 (1997)

    Article  Google Scholar 

  24. Domaradzki, J.A., Loh, K.-C.: The subgrid-scale estimation model in the physical-space representation. Phys. Fluids 11(8), 2330–2342 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  25. Domaradzki, J.A., Yee, P.P.: The subgrid-scale estimation model for high Reynolds number turbulence. Phys. Fluids 12(1), 193–196 (2000)

    Article  MATH  Google Scholar 

  26. Stolz, S., Adams, N.A.: Large-eddy simulation of high-Reynolds-number supersonic boundary layers using the approximate deconvolution model and rescaling and recycling technique. Phys. Fluids 15(8), 2398–2412 (2003)

    Article  Google Scholar 

  27. Rizzetta, D.P., Visbal, M.R., Blaisdell, G.A.: A time-implicit high-order compact differencing and filtering scheme for large-eddy simulation. Int. J. Numer. Methods Fluids 42, 665–693 (2003)

    Article  MATH  Google Scholar 

  28. Bogey, C., Bailly, C.: Large eddy simulations of round jets using explicit filtering with/without dynamic Smagorinsky model. Int. J. Heat Fluid Flow 27, 603–610 (2006)

    Article  Google Scholar 

  29. Bogey, C., Bailly, C.: Large eddy simulations of transitional round jets: influence of the Reynolds number on flow development and energy dissipation. Phys. Fluids 18, 065101 (2006)

    Article  Google Scholar 

  30. Mathew, J., Lechner, R., Foysi, H., Sesterhenn, J., Friedrich, R.: An explicit filtering method for large eddy simulation of compressible flows. Phys. Fluids 15(8), 2279–2289 (2003)

    Article  Google Scholar 

  31. Visbal, M.R., Morgan, P.E., Rizzetta, D.P.: An implicit LES approach based on high-order compact differencing and filtering schemes. In: 16th AIAA Computational Fluid Dynamics Conference, Orlando, Florida, 23–26 June 2003. AIAA 80-1357 (2003)

  32. Berland, J., Lafon, P., Daude, F., Crouzet, F., Bogey, C., Bailly, C.: Filter shape dependence and effective scale separation in large-eddy simulations based on relaxation filtering. Comput. Fluids 47, 65–74 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  33. Vreman, B., Geurts, B., Kuerten, H.: Large-eddy simulation of the turbulent mixing layer. J. Fluid Mech. 339, 357–390 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  34. Vreman, B., Geurts, B., Kuerten, H.: Subgrid-modelling in LES of compressible flow. Appl. Sci. Res. 54, 181–203 (1995)

    Google Scholar 

  35. Bogey, C., Bailly, C.: A family of low dispersive and low dissipative explicit schemes for noise computation. J. Comput. Phys. 194, 194–214 (2004)

    Article  MATH  Google Scholar 

  36. Bogey, C., De Cacqueray, N., Bailly, C.: A shock-capturing methodology based on adaptative spatial filtering for high-order non-linear computations. J. Comput. Phys. 228(5), 1447–1465 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  37. Yoshizawa, A.: Statistical theory for compressible turbulent shear flows, with the application to subgrid modeling. Phys. Fluids 29, 2152–2164 (1986)

    Article  MATH  Google Scholar 

  38. Erlebacher, G., Hussaini, M.Y., Speziale, C.G., Zang, T.A.: Toward the large-eddy simulation of compressible turbulent flows. J. Fluid Mech. 238, 155–185 (1992)

    Article  MATH  Google Scholar 

  39. Meneveau, C., Katz, J.: Scale-invariance and turbulence models for large-eddy simulation. Ann. Rev. Fluid Mech. 32, 1–32 (2000)

    Article  MathSciNet  Google Scholar 

  40. Visbal, M.R., Rizzetta, D.P.: Large-eddy simulation on curvilinear grids using compact differencing and filtering schemes. ASME J. Fluids Eng. 124, 836–847 (2002)

    Article  Google Scholar 

  41. Hickel, S., Adams, N.A., Domaradzki, J.A.: An adaptive local deconvolution method for implicit LES. J. Comput. Phys. 213(1), 413–436 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  42. Drikakis, D., Fureby, C., Grinstein, F.F., Youngs, D.: Simulation of transition and turbulence decay in the Taylor-Green vortex. J. Turbul. 8(20), 1–12 (2007)

    Google Scholar 

  43. Chandy, A.J., Frankel, S.H.: Regularization-based sub-grid scale (SGS) models for large eddy simulations (LES) of high-Re decaying isotropic turbulence. J. Turbul. 10(25), 1–22 (2009)

    MathSciNet  Google Scholar 

  44. Fauconnier, D., De Langhe, C., Dick, E.: Construction of explicit and implicit dynamic finite difference schemes and application to the large-eddy simulation of the Taylor-Green vortex. J. Comput. Phys. 228, 8053–8084 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  45. Fauconnier, D., Bogey, C., Dick, E.: On the performance of relaxation filtering for large-eddy simulation. J. Turbul. 14(1), 22–49 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  46. Brachet, M.E., Meiron, D.I., Orszag, S.A., Nickel, B.G., Morf, R.H., Frisch, U.: Small-scale structure of the Taylor-Green vortex. J. Fluid Mech. 130, 411–452 (1983)

    Article  MATH  Google Scholar 

  47. Tam, C.K.W., Webb, J.C.: Dispersion-relation-preserving finite difference schemes for computational acoustics. J. Comput. Phys. 107, 262–281 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  48. Berland, J., Bogey, C., Marsden, O., Bailly, C.: High-order, low dispersive and low dissipative explicit schemes for multiple-scale and boundary problems. J. Comput. Phys. 224(2), 637–662 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  49. Thompson, K.W.: Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 68, 1–24 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  50. Gloerfelt, X., Lafon, P.: Direct computation of the noise induced by a turbulent flow through a diaphragm in a duct at low Mach number. Comput. Fluids 37, 388–401 (2008)

    Article  MATH  Google Scholar 

  51. Hopkins, E.J., Inouye, M.: An evaluation of theories for predicting turbulent skin friction and heat transfer on flat plates at supersonic and hypersonic Mach numbers. AIAA J. 9(3), 993–1003 (1971)

    Article  Google Scholar 

  52. Pirozzoli, S., Bernardini, M.: Direct numerical simulation database for impinging shock wave/turbulent boundary-layer interaction. AIAA J. 49(6), 1307–1312 (2011)

    Article  Google Scholar 

  53. Bernardini, M., Pirozzoli, S.: Wall pressure fluctuations beneath supersonic turbulent boundary layers. Phys. Fluids 23, 085102 (2011)

    Article  Google Scholar 

  54. Schlatter, P., Örlü, R.: Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126 (2010)

    Article  MATH  Google Scholar 

  55. Bogey, C., Bailly, C.: Turbulence and energy budget in a self-preserving round jet: direct evaluation using large-eddy simulation. J. Fluid Mech. 627, 129–160 (2009)

    Article  MATH  Google Scholar 

  56. Adams, N.A., Stolz, S.: A subgrid-scale deconvolution approach for shock capturing. J. Comput. Phys. 178, 391–426 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  57. Schlatter, P., Stolz, S., Kleiser, L.: LES of transitional flows using the approximate deconvolution model. Int. J. Heat Fluid Flow 25, 549–558 (2004)

    Article  Google Scholar 

  58. Kawai, S., Shankar, S.K., Lele, S.K.: Assessment of localized artificial diffusivity scheme for large-eddy simulation of compressible turbulent flows. J. Comput. Phys. 229(5), 1739–1762 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  59. Lamballais, E., Fortuné, V., Laizet, S.: Straightforward high-order numerical dissipation via the viscous term for direct and large eddy simulation. J. Comput. Phys. 230, 3270–3275 (2011)

    Article  MATH  Google Scholar 

  60. Honein, A.E., Moin, P.: Higher entropy conservation and numerical stability of compressible turbulence simulations. J. Comput. Phys. 201, 531–545 (2004)

    Article  MATH  Google Scholar 

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Correspondence to X. Gloerfelt.

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Aubard, G., Stefanin Volpiani, P., Gloerfelt, X. et al. Comparison of Subgrid-scale Viscosity Models and Selective Filtering Strategy for Large-eddy Simulations. Flow Turbulence Combust 91, 497–518 (2013). https://doi.org/10.1007/s10494-013-9485-5

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