A dynamic nonlinear subgrid-scale stress model

Physics of Fluids

Volumn 17, Issue 3, 2005, Pages

  Wang, Bing Chen ^a   Bergstrom, Donald J ^a  

^a UNIVERSITY OF SASKATCHEWAN   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ANISOTROPY; APPROXIMATION THEORY; COMPUTER SIMULATION; FLUID DYNAMICS; KINETIC ENERGY; MATHEMATICAL MODELS; REYNOLDS NUMBER; STRESSES; TENSORS; TURBULENCE;

FIRST-ORDER APPROXIMATION; STRESS TENSORS; SUBGRID-SCALE (SGS) STRESS MODEL; VELOCITY GRADIENTS;

QUADRATIC PROGRAMMING;

MODEL;

EID: 15844390609     PISSN: 10706631     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1858511     Document Type: Article

References (83)

1. S. B. Pope, Turbulent Flows (Cambridge University Press, Cambridge, 2000).
2. J. Smagorinsky, "General circulation experiments with the primitive equations, I. the basic experiment," Mon. Weather Rev. MWREAB0027-0644 91, 99 (1963).
3. M. Germano, U. Piomelli, P. Moin, and W. H. Cabot, "A dynamic subgrid-scale eddy viscosity model," Phys. Fluids APFADEB0899-821310.1063/1.857955 3, 1760 (1991).
4. D. K. Lilly, "A proposed modification of the Germano subgrid-scale closure method," Phys. Fluids APFADEB0899-821310.1063/1.858280 4, 633 (1992).
5. U. Piomelli, "High Reynolds number calculations using the dynamic subgrid-scale stress model," Phys. Fluids APFADEB0899-821310.1063/ 1.858586 5, 1484 (1993).
6. U. Piomelli and J. Liu, "Large-eddy simulation of rotating channel flows using a localized dynamic model," Phys. FluidsPHFLE61070-663110.1063/1.868607 7, 839 (1995).
7. P. Sagaut, Large Eddy Simulation for Incompressible Flows: An Introduction, 2nd ed. (Springer, Berlin, 2002).
8. M. V. Salvetti and S. Banerjee, "A priori tests of a new dynamic subgrid-scale model for finite-difference large-eddy simulations," Phys. FluidsPHFLE61070-663110.1063/1.868779 7, 2831 (1995).
9. P. Moin, K. Squires, W. Cabot, and S. Lee, "A dynamic subgrid-scale model for compressible turbulence and scalar transport," Phys. Fluids APFADEB0899-821310.1063/1.858164 3, 2746 (1991).
10. Y. Morinishi and O. V. Vasilyev, "A recommended modification to the dynamic two-parameter mixed subgrid scale model for large eddy simulation of wall bounded turbulent flow," Phys. FluidsPHFLE61070-663110.1063/1.1404396 13, 3400 (2001).
11. R. S. Rivlin, "The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids," Q. Appl. Math.QAMAAY0033-569X 15, 212 (1957).
12. J. L. Lumley, "Toward a turbulent constitutive relation," J. Fluid Mech.JFLSA70022-1120 41, 413 (1970).
13. A. J. M. Spencer, "Part III: Theory of invariants," in Continuum Physics, Volume I-Mathematics, edited by A. C. Eringen (Academic, New York, 1971).
14. S. B. Pope, "A more general effective-viscosity hypothesis," J. Fluid Mech.JFLSA70022-1120 72, 331 (1975).
15. D. B. Taulbee, "An improved algebraic Reynolds stress model and corresponding nonlinear stress model," Phys. Fluids APFADEB0899-821310.1063/1.858442 4, 2555 (1992).
16. T. B. Gatski and C. G. Speziale, "On explicit algebraic stress models for complex turbulent flows," J. Fluid Mech.JFLSA70022-1120 254, 59 (1993).
17. A. Yoshizawa, "Statistical analysis of the deviation of the Reynolds stress from its eddy-viscosity representation," Phys. FluidsPFLDAS0031-917110.1063/1.864780 27, 1377 (1984).
18. C. G. Speziale, "On nonlinear K-l and K-ε models of turbulence," J. Fluid Mech.JFLSA70022-1120 178, 459 (1987).
19. K. Horiuti, "Higher-order terms in the anisotropic representation of Reynolds stresses," Phys. Fluids APFADEB0899-821310.1063/ 1.857697 2, 1708 (1990).
20. G. Mompean, "Numerical simulation of a turbulent flow near a right-angled corner using the Speziale non-linear model with RNG K-ε equations," Comput. FluidsCPFLBI0045-793010.1016/ S0045-7930(98)00004-8 27, 847 (1998).
21. C. G. Speziale and X.-H. Xu, "Towards the development of second-order closure models for nonequilibrium turbulent flows," Int. J. Heat Fluid FlowIJHFD20142-727X10.1016/0142-727X(96)00028-8 17, 238 (1996).
22. R. Rubinstein and J. M. Barton, "Nonlinear Reynolds stress models and the renormalization group," Phys. Fluids APFADEB0899-821310.1063/1.857595 2, 1472 (1990).
23. T. J. Craft, B. E. Launder, and K. Suga, "Development and application of a cubic eddy-viscosity model of turbulence," Int. J. Heat Fluid FlowIJHFD20142-727X10.1016/0142-727X(95)00079-6 17, 108 (1996).
24. K. M. Wall and D. B. Taulbee, "Application of a nonlinear stress-strain model to axisymmtric turbulent swirling flows," Int. J. Heat Fluid FlowIJHFD20142-727X10.1016/0142-727X(95)00084-4 17, 116 (1996).
25. A. Leonard, "Energy cascade in large-eddy simulations of turbulent fluid flows," Adv. Geophys.ADGOAR0065-2687 18A, 237 (1974).
26. R. A. Clark, J. H. Ferziger, and W. C. Reynolds, "Evaluation of subgrid-scale models using an accurately simulated turbulent flow," J. Fluid Mech.JFLSA70022-1120 91, 1 (1979).
27. J. Bardina, "Improved turbulent models based on large eddy simulation of homogeneous, incompressible, turbulent flows," Ph.D. thesis, Stanford University, 1983.
28. C. Meneveau and J. Katz, "Scale-invariance and turbulence models for large-eddy simulation," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/annurev.fluid.32.1.1 32, 1 (2000).
29. T. S. Lund and E. A. Novikov, "Parameterization of subgrid-scale stress by the velocity gradient tensor," Annual Research Briefs (CTR, Stanford University, Stanford, 1992), p. 27.
30. C. Meneveau, T. S. Lund, and P. Moin, "Search for subgrid scale parameterization by projection pursuit regression," in Proceedings of Summer Program (CTR, Stanford University, Stanford, 1992), p. 61.
31. V. C. Wong, "A proposed statistical-dynamic closure method for the linear and non-linear subgrid-scale stresses," Phys. Fluids APFADEB0899-821310.1063/1.858261 4, 1080 (1992).
32. B. Tao, J. Katz, and C. Meneveau, "Geometry and scale relationships in high Reynolds number turbulence determined from three-dimensional holographic velocimetry," Phys. FluidsPHFLE61070-663110.1063/ 1.870348 12, 941 (2000).
33. B. Tao, J. Katz, and C. Meneveau, "Statistical geometry of subgrid-scale stresses determined from holographic particle image velocimetry measurements," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112001007443 457, 35 (2002).
34. K. Horiuti, "Alignment of eigenvectors for strain rate and subgrid-scale stress tensors," in Direct and Large-Eddy Simulation IV, ERCOFTAC Series, Vol. 8, edited by B. J. Geurts (Kluwer Academic, Dordrecht, 2001), p. 67.
35. V. M. Canuto and Y. Cheng, "Determination of the Smagorinsky-Lilly constant CS," Phys. FluidsPHFLE61070-663110.1063/1.869251 9, 1368 (1997).
36. B. Kosović, "Subgrid-scale modelling for the large-eddy simulation of high-Reynolds-number boundary layers," J. Fluid Mech.JFLSA70022-112010.1017/S0022112096004697 336, 151 (1997).
37. Y. Zang, R. L. Street, and J. R. Koseff, "A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows," Phys. Fluids APFADEB0899-821310.1063/1.858675 5, 3186 (1993).
38. S. Liu, C. Meneveau, and J. Katz, "On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet," J. Fluid Mech.JFLSA70022-1120 275, 83 (1994).
39. B. Vreman, B. Geurts, and H. Kuerten, "Large-eddy simulation of the turbulent mixing layer," J. Fluid Mech.JFLSA70022-112010.1017/ S0022112097005429 339, 357 (1997).
40. G. S. Winckelmans, A. A. Wray, O. V. Vasilyev, and H. Jeanmart, "Explicit-filtering large-eddy simulation using the tensor-diffusivity model supplemented by a dynamic Smagorinsky term," Phys. FluidsPHFLE61070-663110.1063/1.1360192 13, 1385 (2001).
41. J. M. Robertson and H. F. Johnson, "Turbulence structure in plane Couette flow," J. Eng. Mech. Div.JMCEA30044-7951 96, 1171 (1970).
42. H. J. Leutheusser and V. H. Chu, "Experiments on plane Couette flow," J. Hydraul. Div., Am. Soc. Civ. Eng.JYCEAJ0044-796X 97, 1269 (1971).
43. M. Aydin and H. J. Leutheusser, "Novel experimental facility for the study of plane Couette flow," Rev. Sci. Instrum.RSINAK0034-674810.1063/1.1135726 50, 1362 (1979).
44. E. M. Aydin and H. J. Leutheusser, "Plane-Couette flow between smooth and rough walls," Exp. FluidsEXFLDU0723-4864 11, 302 (1991).
45. N. Tillmark and P. H. Alfredsson, "Experiments on transition in plane Couette flow," J. Fluid Mech.JFLSA70022-1120 235, 89 (1992).
46. N. Tillmark and P. H. Alfredsson, "Turbulence in plane Couette flow," Appl. Sci. Res.ASRHAU0003-699410.1007/BF01082543 51, 237 (1993).
47. K. Bech, N. Tillmark, P. H. Alfredsson, and H. I. Andersson, "An investigation of turbulent plane Couette flow at low Reynolds numbers," J. Fluid Mech.JFLSA70022-1120 286, 291 (1995).
48. A. Lundbladh and A. V. Johansson, "Direct simulation of turbulent spots in plane Couette flow," J. Fluid Mech.JFLSA70022-1120 229, 499 (1991).
49. J. Komminaho, A. Lundbladh, and A. V. Johansson, "Very large structures in plane Couette flow," J. Fluid Mech.JFLSA70022-1120 320, 259 (1996).
50. J. M. Hamilton, J. Kim, and F. Waleffe, "Regeneration mechanisms of near-wall turbulence structures," J. Fluid Mech.JFLSA70022-1120 287, 317 (1995).
51. D. V. Papavassiliou and T. J. Hanratty, "Interpretation of large-scale structures observed in a turbulent plane Couette flow," Int. J. Heat Fluid FlowIJHFD20142-727X10.1016/S0142-727X(96)00138-5 18, 55 (1997).
52. G. Kawahara and S. Kinda, "Periodic motion embedded in plane Couette turbulence: Regeneration cycle and burst," J. Fluid Mech.JFLSA70022-1120 449, 291 (2001).
53. J. Komminaho and M. Skote, "Reynolds stress budgets in Couette and boundary layer flows," Flow, Turbul. Combust.FTCOF91386-6184 68, 167 (2002).
54. W.-W. Kim and S. Menon, "Application of the localized dynamic subgrid-scale model to turbulent wall-bounded flows," in Proceedings of the 35th Aerospace Sciences Meeting & Exhibit, Reno, Nevada [AIAA Pap. AAPRAQ0146-370597-0210 (1997)].
55. W.-W. Kim and S. Menon, "An unsteady incompressible Navier-Stokes solver for large eddy simulation of turbulent flows," Int. J. Numer. Methods FluidsIJNFDW0271-209110.1002/ (SICI)1097-0363(1130):6<::AID-FLD908>3.0.CO;2-Q 31, 983 (1999).
56. J. Kim and P. Moin, "Application of a fractional-step method to incompressible Navier-Stokes equations," J. Comput. Phys.JCTPAH0021-999110.1016/0021-9991(85)90148-2 59, 308 (1985).
57. P. Sagaut and R. Grohens, "Discrete filters for large eddy simulation," Int. J. Numer. Methods FluidsIJNFDW0271-209110.1002/ (SICI)1097-0363(1230):83.3.CO;2-8 31, 1195 (1999).
58. D. Carati, S. Ghosal, and P. Moin, "On the representation of backscatter in dynamic localization models," Phys. FluidsPHFLE61070-663110.1063/1.868585 7, 606 (1995).
59. Th. von Kármán, "The analogy between fluid friction and heat transfer," Trans. ASMETASMAV0097-6822 61, 705 (1939).
60. A. G. Kravchenko, P. Moin, and R. Moser, "Zonal embedded grids for numerical simulations of wall-bounded turbulent flows," J. Comput. Phys.JCTPAH0021-999110.1006/jcph.1996.0184 127, 412 (1996).
61. F. Sarghini, U. Piomelli, and E. Balaras, "Scale-similar models for large-eddy simulations," Phys. FluidsPHFLE61070-663110.1063/ 1.870021 11, 1596 (1999).
62. P. Moin and J. Kim, "Numerical investigation of turbulence channel flow," J. Fluid Mech.JFLSA70022-1120 118, 341 (1982).
63. K. Horiuti, "A new dynamic two-parameter mixed model for large-eddy simulation," Phys. FluidsPHFLE61070-663110.1063/1.869454 9, 3443 (1997).
64. K. Horiuti, "A proper velocity scale for modelling subgrid-scale eddy viscosities in large eddy simulation," Phys. Fluids APFADEB0899-821310.1063/1.858800 5, 146 (1993).
65. A. Scotti and U. Piomelli, "Numerical simulation of pulsating turbulent channel flow," Phys. FluidsPHFLE61070-663110.1063/ 1.1359766 13, 1367 (2001).
66. V. C. Wong and D. K. Lilly, "A comparison of two dynamic subgrid closure methods for turbulent thermal convection," Phys. FluidsPHFLE61070-663110.1063/1.868335 6, 1016 (1994).
67. A. S. Monin and A. M. Yaglom, Statistical Fluid Mechanics: Mechanics of Turbulence (MIT, Cambridge, MA, 1971), Vol. 1.
68. J. Kim, P. Moin, and R. Moser, "Turbulence statistics in fully developed channel flow at low Reynolds number," J. Fluid Mech.JFLSA70022-1120 177, 133 (1987).
69. U. Piomelli, "Large-eddy and direct simulation of turbulent flows," Lecture Notes for the 9th Annual Conference of the CFD Society of Canada, Kitchener, Ontario, 2001.
70. R. M. Kerr, "Histograms of helicity and strain in numerical turbulence," Phys. Rev. Lett.PRLTAO0031-900710.1103/ PhysRevLett.59.783 59, 783 (1987).
71. Wm. T. Ashurst, A. R. Kerstein, R. M. Kerr, and C. H. Gibson, "Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence," Phys. FluidsPFLDAS0031-917110.1063/1.866513 30, 2343 (1987).
72. A. Tsinober, E. Kit, and T. Dracos, "Experimental investigation of the field of velocity gradients in turbulent flows," J. Fluid Mech.JFLSA70022-1120 242, 169 (1992).
73. T. S. Lund and M. M. Rogers, "An improved measure of strain state probability in turbulent flows," Phys. FluidsPHFLE61070-663110.1063/ 1.868440 6, 1838 (1994).
74. A. Vincent and M. Meneguzzi, "The dynamics of vorticity tubes in homogeneous turbulence," J. Fluid Mech.JFLSA70022-1120 258, 245 (1994).
75. V. Borue and S. A. Orszag, "Local energy flux and subgrid-scale statistics in three-dimensional turbulence," J. Fluid Mech.JFLSA70022-112010.1017/S0022112097008306 366, 1 (1998).
76. D. I. Pullin and P. G. Saffman, "Reynolds stresses and one-dimensional spectra for a vortex model of homogeneous anisotropic turbulence," Phys. FluidsPHFLE61070-663110.1063/1.868240 6, 1787 (1994).
77. A. Misra and D. I. Pullin, "A vortex-based subgrid stress model for large-eddy simulation," Phys. FluidsPHFLE61070-663110.1063/1.869361 9, 2443 (1997).
78. T. Voelkl, D. I. Pullin, and D. C. Chan, "A physical-space version of the stretched-vortex subgrid-stress model for large-eddy simulation," Phys. FluidsPHFLE61070-663110.1063/1.870429 12, 1810 (2000).
79. S. Ghosal, T. S. Lund, P. Moin, and K. Akselvoll, "A dynamic localization model for large-eddy simulation of turbulent flows," J. Fluid Mech.JFLSA70022-1120 286, 229 (1995).
80. P. Moin, "Advances in large eddy simulation methodology for complex flows," Int. J. Heat Fluid FlowIJHFD20142-727X10.1016/ S0142-727X(02)00167-4 23, 710 (2002).
81. U. Piomelli and E. Balaras, "Wall-layer models for large-eddy simulations," Annu. Rev. Fluid Mech.ARVFA30066-418910.1146/ annurev.fluid.34.082901.144919 34, 349 (2002).
82. O. J. McMillan and J. H. Ferziger, "Direct testing of subgrid-scale models," AIAA J.AIAJAH0001-1452 17, 1340 (1979).
83. U. Piomelli, P. Moin, and J. H. Ferziger, "Model consistency in large eddy simulation of turbulent channel flows," Phys. FluidsPFLDAS0031-917110.1063/1.866635 31, 1884 (1988).