×

An assessment of two models for the subgrid scale tensor in the rational LES model. (English) Zbl 1107.76040

Summary: LES models seek to approximate the large scales of a flow which are defined by a space average \((\bar u,\bar p)\) of the velocity u and the pressure \(p\) of the flow. A natural question which arises is: Given reliable data for \((\bar u,\bar p)\), how accurateis the approximation of \((\bar u,\bar p)\) by the solution computed with a LES model? This paper presents numerical studies of this question at a 2d and 3d mixing layer problem for the rational LES model with two types of models for the subgrid scale tensor: the Smagorinsky model and a model proposed by Iliescu and Layton. Whereas in the 2d mixing layer problem the model by Iliescu and Layton showed better results, the behaviour of both models was similar in the 3d mixing layer problem.

MSC:

76F65 Direct numerical and large eddy simulation of turbulence
76F25 Turbulent transport, mixing

Software:

FEATFLOW; MooNMD
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Boersma, B. J.; Kooper, M. N.; Neuwstadt, F. T.M.; Wesseling, P., Local grid refinement in large-eddy simulations, J. Enrg. Math, 32, 161-175 (1997) · Zbl 0911.76052
[2] Clark, R. A.; Ferziger, J. H.; Reynolds, W. C., Evaluation of subgrid-scale models using an accurately simulated turbulent flow, J. Fluid Mech, 91, 1-16 (1979) · Zbl 0394.76052
[4] Comte, P.; Lesieur, M.; Lamballais, E., Large- and small-scale stirring of vorticity and a passive scalar in a 3-d temporal mixing layer, Phys. Fluids A, 4, 12, 2761-2778 (1992)
[6] Fortin, M., Finite element solution of the Navier-Stokes equations, (Iserles, A., Acta Numerica (1993), Cambridge University Press: Cambridge University Press Cambridge), 239-284 · Zbl 0801.76043
[7] Galdi, G. P.; Layton, W. J., Approximation of the larger eddies in fluid motion IIa model for space filtered flow, Math. Model Methods Appl. Sci, 10, 3, 343-350 (2000) · Zbl 1077.76522
[8] Germano, M.; Piomelli, U.; Moin, P.; Cabot, W., A dynamic subgrid-scale eddy viscosity model, Phys. Fluids A, 3, 1760-1765 (1991) · Zbl 0825.76334
[10] Gresho, P. M.; Sani, R. L., Incompressible Flow and the Finite Element Method (2000), Wiley: Wiley Chichester · Zbl 0988.76005
[11] Griebel, M.; Koster, F., Adaptive wavelet solvers for the unsteady incompressible Navier-Stokes equations, (Malek, J.; Nečas, J.; Rokyta, M., Advances in Mathematical Fluid Mechanics (2000), Springer: Springer Berlin), 67-118 · Zbl 0985.35062
[12] Iliescu, T.; John, V.; Layton, W. J.; Matthies, G.; Tobiska, L., A numerical study of a class of LES models, Internat. J. Comput. Fluid Dynamics, 17, 75-85 (2003) · Zbl 1148.76327
[13] Iliescu, T.; Layton, W. J., Approximating the larger eddies in fluid motion IIIthe Boussinesq model for turbulent fluctuations, An. Ştiinţ. Univ. “Al. I. Cuza” Iaşi Tomul XLIV Sect. I.a Mat, 44, 245-261 (1998) · Zbl 1078.76553
[14] John, V., Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D Navier-Stokes equations, Internat. J. Numer. Methods Fluids, 40, 775-798 (2002) · Zbl 1076.76544
[16] John, V.; Layton, W. J., Analysis of numerical errors in large eddy simulation, SIAM J. Numer. Anal, 40, 995-1020 (2002) · Zbl 1026.76028
[17] John, V.; Matthies, G., Higher order finite element discretizations in a benchmark problem for incompressible flows, Internat. J. Numer. Methods Fluids, 37, 885-903 (2001) · Zbl 1007.76040
[18] John, V.; Matthies, G., MooNMD—a program package based on mapped finite element methods, Comput. Visual. Sci, 6, 163-170 (2004) · Zbl 1061.65124
[19] Ladyzhenskaya, O. A., New equations for the description of motion of viscous incompressible fluids and solvability in the large of boundary value problems for them, Proc. Steklov Inst. Math, 102, 95-118 (1967) · Zbl 0202.37802
[20] Layton, W. J.; Lewandowski, R., Analysis of an eddy viscosity model for large eddy simulation of turbulent flows, J. Math. Fluid Mech, 4, 374-399 (2002) · Zbl 1021.76020
[21] Leonard, A., Energy cascade in large eddy simulation of turbulent fluid flows, Adv. Geophys, 18A, 237-248 (1974)
[23] Lesieur, M.; Staquet, C.; Le Roy, P.; Comte, P., The mixing layer and its coherence examined from the point of view of two-dimensional turbulence, J. Fluid Mech, 192, 511-534 (1988)
[24] Lilly, D. K., A proposed modification of the Germano subgrid-scale closure method, Phys. Fluids A, 4, 633-635 (1992)
[25] Michalke, A., On the inviscid instability of the hyperbolic tangent velocity profile, J. Fluid Mech, 19, 543-556 (1964) · Zbl 0129.20302
[26] Nägele, S.; Wittum, G., Large-eddy simulation and multigrid methods, Electon. Trans. Numer. Anal, 15, 152-164 (2003) · Zbl 1201.76093
[27] Rogers, M. M.; Moser, R. D., Direct simulation of a self-similar turbulent flow, Phys. Fluids, 6, 903-923 (1994) · Zbl 0825.76329
[28] Sagaut, P., Large Eddy Simulation for Incompressible Flows (2001), Springer: Springer Berlin, Heidelberg, New York · Zbl 0964.76002
[29] Smagorinsky, J. S., General circulation experiments with the primitive equations, Monthly Weather Rev, 91, 99-164 (1963)
[30] Turek, S., Efficient Solvers for Incompressible Flow Problems: an Algorithmic and Computational Approach, Lecture Notes in Computational Science and Engineering, Vol. 6 (1999), Springer: Springer Berlin · Zbl 0930.76002
[31] Vreman, B.; Guerts, B.; Kuerten, H., Large-eddy simulation of turbulent mixing layer, J. Fluid Mech, 339, 357-390 (1997) · Zbl 0900.76369
[32] Zang, Y.; Street, R. L.; Koseff, J. R., A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows, Phys. Fluids A, 5, 3186-3196 (1993) · Zbl 0925.76242
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.