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http://dx.doi.org/10.3795/KSME-B.2003.27.7.973

On the Suitability of Centered and Upwind-Biased Compact Difference Schemes for Large Eddy Smulation (I) - Numerical Test -  

Park, No-Ma (서울대학교 기계항공공학부)
Yoo, Jung-Yul (서울대학교 기계항공공학부)
Choi, Hae-Cheon (서울대학교 기계항공공학부)
Publication Information
Transactions of the Korean Society of Mechanical Engineers B / v.27, no.7, 2003 , pp. 973-983 More about this Journal
Abstract
The suitability of high-order accurate, centered and upwind-biased compact difference schemes is evaluated for large eddy simulation of turbulent flow. Two turbulent flows are considered: turbulent channel flow at Re = 23000 and flow over a circular cylinder at Re = 3900. The effects of numerical dissipation on the finite differencing and aliasing errors and the subgrid-scale stress are investigated. It is shown through the simulations that compact upwind schemes are not suitable for LES, whereas the fourth order-compact centered scheme is a good candidate for LES provided that proper dealiasing of nonlinear terms is performed. The classical issue on the aliasing error and the treatment of nonlinear terms is revisited with compact difference schemes.
Keywords
Compact Difference Scheme; Large Eddy Simulation; Finite Differencing Error; Aliasing Error;
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Times Cited By KSCI : 5  (Citation Analysis)
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1 Min, T., Yoo, J. Y. and Choi, H., 2001, 'Effect of Spatial Discretization Schemes on Numerical Solutions of Viscoelastic Fluid Flows,' J. Non-Newtonian Fluid Mech., Vol. 100, pp. 27-47   DOI   ScienceOn
2 Anderson, W., Thomas, J., Van Leer, B., 1986, 'Comparison of Finite Volume Flux Vector Splitting for the Euler Equations,' AIAA Journal, Vol. 24, pp. 1453-1460   DOI   ScienceOn
3 Beam, R. M. and Warming, R. F. 1978, 'An Implicit Factored Scheme for the Compressible Navier-Stokes Equations,' AIAA Journal, Vol. 16, pp. 393-402   DOI   ScienceOn
4 Ekaterinaris, J. A., 1999, 'Implicit, High-Resolution, Compact Schemes for Gas Dynamics and Aeroacoustics,' J. Comput. Phys., Vol. 156, pp. 272-299   DOI   ScienceOn
5 Park, N. and Yoo, J. Y., 2000, 'A New Implicit Implementation of Compact Difference Scheme for the Direct Simulation of Compressible Flows,' Bulletin of the American Physical Society, Vol. 45, No. 9, pp. 38-39
6 Pulliam, T. H. and Chaussee, D. S., 1981, 'A Diagonal Form of an Implicit ApproximateFactorization Algorithm,' J. Comput. Phys., Vol. 39, pp. 347-363   DOI   ScienceOn
7 Visbal, M. R. and Gaitonde, D. A., 1999, 'High-Order-Accurate Methods for Complex Unsteady Subsonic Flows,' AIAA Journal, Vol 37, pp. 1231-1239   DOI
8 Gaitonde, D. V. and Visbal, M. R., 2000, 'Padetype Higher-Order Boundary Filters for the Navier-Stokes Equations,' AIAA Journal, Vol. 38, pp. 2103-2112   DOI   ScienceOn
9 Jin, B. J., Park, N. and Yoo, J. Y., 2001, 'Large Eddy Simulation of Boundary Layer Transition on the Axial Turbine Blade by Rotor Induced Wake,' FEDSM2001 -18195, Proceedings of 2001 ASME Fluids Engineering Division Summer Meeting, May 29 June 1, 2001, New Orleans, L.A., USA
10 Lourenco, L. M. & Shih, C., 1993, 'Characteristics of the Plane Tubulent Near Wake of a Circular Cylinder. A, Particle Image Velocimetry study,' Phys. Fluids., Vol. 12, pp. 403-407   DOI   ScienceOn
11 Nicoud, F., Baggett, J. S., Moin, P., Cabot, W., 2001, 'Large Eddy Simulation Wall Modeling Based on Sub optimal Control Theory and Linear Stochastic Estimation,' Phys. Fluids, Vol. 13, pp. 2968-2984   DOI   ScienceOn
12 Choi, H. and Moin, P., 1990, 'On the Space-Time Characteristics of Wall-Pressure Fluctuations,' Phys. Fluid A, Vol. 2, pp. 1450-1460   DOI
13 Norberg, C., 1987, 'Effects of Reynolds Number and Low-Intensity Free-Stream Turbulence on the Flow around a Circular Cylinder,' 'Publ. No. 87/2. Department of Applied Thermosc. And Fluid Mech., Chalmer University of Technology, Gothenburg, Sweden
14 Park, N., Yoo, J. Y. and Choi, H., 2003 'On the Suitability of Centered and Upwind-biased Compact Different Schemes for Large Eddy Simulation: Part II-Static Error Analysis,' Trans. Of the KSME B, Vol. 27, No. 7, pp. 984-994   과학기술학회마을   DOI
15 Park, N., Yoo, J. Y. and Choi, H., 2003, 'On the Suitability of Centered and Upwind-biased Compact Different Schemes for Large Eddy Simulation: Part III-Dynamic Error Analysis,' Trans. Of the KSME B, Vol. Vol. 27, No. 7, pp. 995-1006   과학기술학회마을   DOI
16 Coleman, G. N., Kim, J. and Moser, R. D., 1995, 'A Numerical Study of Turbulent Supersonic Isothermal-Wall Channel Flow,' J. Fluid Mech., Vol. 305, pp. 159-183   DOI
17 Wei, T. and Willmarth, W. W., 1989, 'Reynolds-Number Effects on the Structure of a Turbulent Channel Flow,' J. Fluid Mech., Vol. 204, pp. 57-95   DOI   ScienceOn
18 Kravchenko, G. and Moin, P., 2000, 'Numerical Studies of Flow over a Circular Cylinder at $Re_D=3900$,' Phys. Fluids, vol. 12, pp. 403-417   DOI   ScienceOn
19 Germano, M., Piomelli, U., Moin, P. and Cabot, W., 1991, 'A Dynamic Subgrid-Scale Eddy Viscosity Model,' Phys. Fluids A, vol. 3, pp. 1760-1765   DOI
20 Moin, P., Squires, K., Cabot, W., Lee, S., 1991, 'A Dynamic Subgrid Scale Model for Compressible Turbulence and Scalar Transport,' Phys. Fluids A, Vol. 3, pp. 2746-2757   DOI
21 Dubois, T., Jauberteau, F. and Zhou, Y., 1997, 'Influences of Subgrid Scale Dynamics on Resolvable Scale Statistics in Large-Eddy Simulations,   DOI   ScienceOn
22 Moin, P., 2002, 'Advances in Large Eddy Simulation Methodology for Complex Flows,' Int. J. Heat and Fluid Flow, Vol. 23, pp. 710-720   DOI   ScienceOn
23 Adams, N. A. and Shariff, K., 1996, 'A High Resolution Hybrid Compact-ENO Scheme for Shock Turbulence Interaction Problems,' J. Comput. Phys., Vol. 127, pp. 27-51   DOI   ScienceOn
24 J. Jeong and F. Hussain, 1995, 'On the Identification of a Vortex,' J. Fluid Mech., Vol. 285, pp. 69-94   DOI   ScienceOn
25 Ghosal, S., 1996, 'An Analysis of Numerical Errors in Large-Eddy Simulations of Turbulence,' J. Comput. Phys., Vol. 125, pp. 187-206   DOI   ScienceOn
26 Vreman, B., Geurts, B., Kuerten, H., 1996, 'Comparison of Numerical Schemes in Large-Eddy Simulation of the Temporal Mixing Layer,' Int. J. Numer. met. Fluids, Vol. 22, pp. 297-311   DOI
27 Jiang, G. S. and Shu, C. W., 1996, Efficient Implementation of Weighted ENO Schemes,' J. Comput. Phys., Vol. 126, pp. 202-228   DOI   ScienceOn
28 Hughes, T. J. R., Mazzei, L., Oberai, A. A. and Wray, A. A., 2002, 'The Multiscale Formulation of Large Eddy Simulation: Decay of Homogeneous Isotropic Turbulence,' Phys. Fluids, Vol. 13, pp. 505-512   DOI   ScienceOn
29 Domaradzki, J. A. and Loh, K. C., 1999, 'The Subgrid-Scale Estimation Model in the Physical Space Respresentation,' Phys. Fluids, Vol. 11, pp. 2330-2342   DOI
30 Hahn, S. and CHoi, H., 1997, 'Unsteady Simulation of Jets in a Cross Flow,' J. Comput. Phys., Vol. 134, pp 342-356   DOI   ScienceOn
31 Mittal, R. & Moin, P., 1997, 'Suitability of Upwind-Biased Finite-Difference Schemes for Large-Eddy Simulation of Turbulent Flows,' AIAA Journal, Vol. 35, pp. 1415-1417   DOI   ScienceOn
32 Pirozzoli, S., 2002, 'Conservative Hybrid Compact-WENO Schemes for Shock-Turbulence Interaction,' J. Comput. Phys., Vol. 178, pp. 81-117   DOI   ScienceOn
33 Zhong, X., 1998, 'High-Order Finite-Difference Schemes for Numerical Simulation of Hypersonic Boundary-Layer Transition,' J. Comput. Phys., Vol. 144, pp. 662-709   DOI   ScienceOn
34 Tolstykh, A. I. and Lipavskii, M. V., 1998. 'On Performance of Methods with Third- and Fifth-Order Compact Upwind Differencing,' J. Comput. Phys., Vol. 140, pp. 205-232   DOI   ScienceOn
35 Rai, M. M. and Moin, P., 1993, 'Direct Numerical Simulation of Transition and Turbulence in a Spatially Evolving Boundary Layer,' J. Comput. Phys., Vol. 109, pp. 169-192   DOI   ScienceOn
36 Beaudan, P. and Moin, P., 1994, 'Numerical Experiments on the Flow past a Circular Cylinder at a Sub-Critical Reynolds Number,' Report No. TF-62, Department of mechanical Engineering, Stanford Univ.
37 Ong, L. and Wallace, J., 1996, 'The Velocity Field of the Turbulent Very Near Wake of a Circular Cylinder,' Exp. Fluids, Vol. 20, pp. 441-453   DOI
38 Wang, Z. and Huang, G. P., 2002, 'An Essentially Nonoscillatory High-Order Pade-type(ENO-Pade) Scheme,' J. Comput. Phys., Vol. 177, pp. 37-58   DOI   ScienceOn
39 Mossi, M and Sagaut, P., 2003, 'Numerical Investigation of Fully Developed Channel Flow Using Shock-Capturing Schemes,' Computers & Fluids, Vol. 32, pp. 249-274   DOI   ScienceOn
40 Kravchenko, A. G. and Moin, P., 1997, 'On the Effect of Numerical Errors in Large-Eddy Simulations of Turbulent Flows,' J. Comput. Phys., Vol. 131, pp. 310-322   DOI   ScienceOn
41 Rai, M. M. and Moin, P., 1991, 'Direct Simulations of Turbulent Flow Using Finite-Difference Schemes,' J. Comput. Phys., Vol. 96, pp. 15-53   DOI   ScienceOn
42 Lele, S. K., 1992, 'Compact Finite-Difference Schemes With Spectral-Like Resolution,' J. Comput. Phys., Vol. 103, pp. 16-42   DOI   ScienceOn
43 Breuer, M., 1998, 'Numerical and Modeling Influences on Large Eddy Simulations for the Flow Past a Circular Cylinder,' Int. J. Heat and Fluid Flow, Vol. 19, pp.512-521   DOI   ScienceOn
44 Garnier, E., Mossi, M., Sagaut, P., Comte, P. and Deville, M., 1999, 'On the Use of Shock-Capturing Schemes for Large-Eddy Simulation, J. Comput. Phys., Vol. 153, pp. 273-311   DOI   ScienceOn
45 Zang, T. A., 1991, 'On the Rotation and Skew-Symmetric Forms for Incompressible Flow Simulations,' Appl. Numer. Math., Vol. 7, pp. 27-40   DOI   ScienceOn
46 Ladeinde, F., Cai, X., Visbal, M and Gaitonde, D. V., 2001, 'Turbulence Spectra Characteristics of High Order Schemes for Direct and Large Eddy Simulation,' Appl. Numer. Math., Vol. 36, pp. 447-474   DOI   ScienceOn
47 Meinke, M., Schroder, W., Krause, E. and Rister, Th., 2002, 'A Comparison of Second- and Sixth-order Methods for Large-Eddy Simulations,' Computers & Fluids, Vol. 31, pp. 695-718   DOI   ScienceOn
48 Lilly, D, 1992, 'A Proposed Modification of the Germano Subgrid Scale Closure Method,' Phys. Fluids A, Vol.4, pp. 633-634   DOI
49 Blaisdell, G. A., Spyropoulus, E. T. and Qin, J. H., 1996, 'The Effect of the Formulation of Nonlinear Terms on Aliasing Errors in Spectral Methods,' Appl. Numer. Math., Vol. 21, pp. 207-219   DOI   ScienceOn
50 Fedoiun, I., Lardjane, N. and Gokalp, I., 2001, 'Revisiting Numerical Errors in Direct and Large Eddy Simulations of Turbulence: Physical and Spectral Space Analysis,' J. Comput. Phys., Vol. 174, pp.816-851   DOI   ScienceOn
51 Kim. D., 2001, Numerical Study on Dynamics and Control of Flow over a Sphere up to $Re=10^4$, Ph. D. thesis, Seoul National University
52 Min, T., Yoo, J. Y. and Choi, H., 2000 'Effect of Spatial Discretization Schemes on Numerical Solutions of Viscoelastic Fluid Flows,' KSME Journal B, Vol. 24 (9), pp. 1227-1238   과학기술학회마을