Abstract
Turbulence modeling and the numerical discretization of the Navier- Stokes equations are strongly coupled in large-eddy simulations. The truncation error of common approximations for the convective terms can outweigh the effect of a physically sound subgrid-scale model. The subject of this thesis is the analysis and the control of local truncation errors in large-eddy simulations. We show that physical reasoning can be incorporated into the design of discretization schemes. Using systematic procedures, a nonlinear discretization method has been developed where numerical and turbulence-theoretical modeling are fully merged. The truncation error itself functions as an implicit turbulence model accurately representing the effects of unresolved scales. Various applications demonstrate the efficiency and reliability of the new method as well as the superiority of an holistic approach.
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References
Adams, N.A., Hickel, S., Franz, S.: Implicit subgrid-scale modeling by adaptive deconvolution. J. Comp. Phys. 200, 412–431 (2004)
Almeida, G.P., Durao, D.F.G., Heitor, M.V.: Wake flows behind two dimensional model hills. Exp. Thermal and Fluid Science 7, 87–101 (1993)
Breuer, M.: New reference data for the hill flow test case (2005), http://www.hy.bv.tum.de/DFG-CNRS/
Castillo, L., George, W.K.: Similarity analysis for turbulent boundary layer with pressure gradient: Outerflow. AIAA Journal 39(1), 41–47 (2001)
Castillo, L.: XiaWang, and W. K. George. Separation criterion for turbulent boundary layers via similarity analysis. Journal of Fluids Engineering 126(1), 297–303 (2004)
Chollet, J.-P.: Two-point closures as a subgrid-scale modeling tool for large-eddy simulations. In: Durst, F., Launder, B. (eds.) Turbulent Shear Flows IV, pp. 62–72. Springer, Heidelberg (1984)
Clauser, F.H.: Turbulent boundary layers in adverse pressure gradient. J. Aeronaut. Sci. 21, 91–108 (1954)
Comte-Bellot, G., Corrsin, S.: Simple Eulerian time correlation of full and narrow-band velocity signals in grid-generated ‘isotropic’ turbulence. J. Fluid Mech. 48, 273–337 (1971)
del Álamo, J., Jiménez, J., Zandonade, P., Moser, R.: Scaling of the energy spectra of turbulent channels. J. Fluid Mech. 500, 135–144 (2004)
Fröhlich, J., Mellen, C., Rodi, W., Temmerman, L., Leschziner, M.: Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions. J. Fluid Mech. 526, 19–66 (2005)
Germano, M., Piomelli, U., Moin, P., Cabot, W.H.: A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3, 1760–1765 (1991)
Hickel, S., Adams, N.A.: Efficient implementation of nonlinear deconvolution methods for implicit large-eddy simulation. In: Nagel, W., Jäger, W., Resch, M. (eds.) High Performance Computing in Science and Engineering. Transactions of the High Performance Computing Center, Stuttgart (HLRS), pp. 293–306. Springer, Heidelberg (2006)
Hickel, S., Adams, N.A.: On implicit subgrid-scale modeling in wall-bounded flows. Phys. Fluids 19, 105106 (2007)
Hickel, S., Adams, N.A.: Implicit LES applied to zero-pressure-gradient and adverse-pressure-gradient boundary-layer turbulence. Int. J. Heat and Fluid Flow 29, 626–639 (2008)
Hickel, S., Adams, N.A., Domaradzki, J.A.: An adaptive local deconvolution method for implicit LES. J. Comp. Phys. 213, 413–436 (2006)
Hickel, S., Adams, N.A., Mansour, N.N.: Implicit subgrid-scale modeling for large-eddy simulation of passive-scalar mixing. Phys. Fluids 19, 095102 (2007)
Hickel, S., Kempe, T., Adams, N.A.: Implicit large-eddy simulation applied to turbulent channel flow with periodic constrictions. Theoret. Comput. Fluid Dynamics 22, 227–242 (2008)
Hickel, S., Weynans, L., Adams, N.A., Cottet, G.-H.: Towards implicit subgrid-scale modeling by particle methods. In: ESAIM: Proceedings, vol. 16, pp. 77–88 (2007)
Indinger, T.: Einfluss eines positiven Druckgradienten auf turbulente Grenzschichten an glatten und gerillten Oberflächen. PhD thesis, TU München (2005)
Lesieur, M.: Turbulence in Fluids, 3rd edn. Kluwer Academic Publishers, Dordrecht (1997)
Lilly, D.K.: On the application of the eddy viscosity concept in the inertial subrange of turbulence. National Center for Atmospheric Research, Boulder, Colorado. NCAR MS 123 (1966)
Lilly, D.K.: The representation of small-scale turbulence in numerical simulation experiments. In: Goldstein, H.H. (ed.) Proc. IBM Scientific Computing Symposium on Environmental Sciences, pp. 195–201. IBM (1967)
Lilly, D.K.: A proposed modification of the Germano subgrid-scale closure model. Phys. Fluids A 4, 633–635 (1992)
Lund, T., Wu, X., Squires, K.: Generation of turbulent inflow data for spatially-developing boundary layer simulations. J. Comp. Phys. 140, 233–258 (1998)
Mellen, C., Fröhlich, J., Rodi, W.: Large eddy simulation of the flow over periodic hills. In: Deville, M., Owens, R. (eds.) Proccedings of the 16th IMACS World Congress, Lausanne, Switzerland (2000)
Mittal, R., Iaccarino, G.: Immersed boundary methods. Annu. Rev. Fluid Mech. 37, 239–261 (2005)
Moser, R.D., Kim, J., Mansour, N.: Direct numerical simulation of turbulent channel flow up to \(\text{Re}_\tau=590\). Phys. Fluids 11, 943–945 (1999)
Peller, N., Manhart, M.: Turbulent channel flow with periodic hill constrictions. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design. Springer, Heidelberg (2005)
Schumann, U.: Subgrid scale model for finite-difference simulations of turbulence in plane channels and annuli. J. Comp. Phys. 18, 376–404 (1975)
Simpson, R.L.: A review of some phenomena in turbulent flow separation. J. Fluids Eng. 102, 520–533 (1981)
Simpson, R.L.: Turbulent boundary-layer separation. Ann. Rev. Fluid Mech. 21, 205–234 (1989)
Smagorinsky, J.: General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99–164 (1963)
Spalart, P.R.: Direct simulation of a turbulent boundary layer up to Re θ = 1410. J. Fluid Mech. 187, 61–98 (1988)
Yeung, P., Zhou, Y.: On the universality of the Kolmogorov constant in numerical simulations of turbulence. Technical Report 97-64, ICASE, NASA Langley Research Center, Hampton, Virginia (1997)
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Hickel, S., Devesa, A., Adams, N.A. (2009). Implicit Turbulence Modeling by Finite Volume Methods. In: Brun, C., Juvé, D., Manhart, M., Munz, CD. (eds) Numerical Simulation of Turbulent Flows and Noise Generation. Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol 104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89956-3_7
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DOI: https://doi.org/10.1007/978-3-540-89956-3_7
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