Practices and Advances on Rational Subgrid-Scale Modeling

doi:10.19596/j.cnki.1001-246x.7800

Abstract

Abstract: Subgrid-scale modeling is spirit of large-eddy simulation. Original intention of rational subgrid-scale modeling is to remove empirical and phenomenological components of modeling process, so that every step in modeling process is physically and mathematically traceable. According to theory of rational subgrid modeling, we developed a series of subgrid models that do not depend on empirical constants and phenomenological models, but their effect in practical problems is still insufficient, which leads to, in recent years, reflection on proper idea of subgrid modeling. This paper reviews existing research and new progress, whose goal is to give a rational and self-consistent theoretical guidance of future large eddy simulation.

Key words: subgrid-scale modeling, large-eddy simulation, rational modeling, Kolmogorov equation, mathematical criterions on compatibility

CLC Number:

O357.5

FANG Le, WANG Chuhan. Practices and Advances on Rational Subgrid-Scale Modeling[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 35(3): 253-261.

References

[1] 张兆顺. 湍流理论与模拟[M]. 北京:清华大学出版社,2005:80.
[2] SPALART P R, Detached-eddy simulation[J]. Annu Rev Fluid Mech, 2009,41:181-202.
[3] SMAGORINSKY J. General circulation experiments with primitive equation[J]. Mon Weather Rev, 1963,91:99.
[4] GERMANO M, PIOMELLI U, MOIN P P, CABOT W H. A dynamic subgrid-scale eddy viscosity model[J]. Phys Fluids A, 1991,3(7):1760-1765.
[5] BARDINA J, FERZIGER J, REYNOLDS W C. Improved subgrid-scale models for large-eddy simulation[J]. AIAA Paper, 1980,AIAA-80-1357.
[6] METAIS O, LESIEUR M. Spectral large-eddy simulation of isotropic and stably stratified turbulence[J]. J Fluid Mech, 1992,239:157-194.
[7] SAGAUT P. Large eddy simulation for incompressible flows:An introduction[M]. Springer, 2006.
[8] FANG L, SHAO L, BERTOGLIO J P. Recent understanding on the subgrid-scale modeling of large-eddy simulation in physical space[J]. Sci China Phys Mech Astro,2014,57(12):2188-2193.
[9] LU H, RUTLAND C J. Structural subgrid-scale modeling for large-eddy simulation:A review[J]. Acta Mechanica Sinica, 2016,32(4):567-578.
[10] VERMA A, PARK N, MAHESH K. A hybrid subgrid-scale model constrained by Reynolds stress[J]. Phys Fluids, 2013,25(11):110805.
[11] GHORBANIASL G, AGNIHOTRI V, LACOR C. A self-adjusting flow dependent formulation for the classical Smagorinsky model coefficient[J]. Phys Fluids, 2013,25(5):055102.
[12] TRIAS F X, FOLCH D, GOROBETS A, OLIVA A. Building proper invariants for eddy viscosity subgrid-scale models[J]. Phys Fluids, 2015,27:065103.
[13] ROZEMA W, BAE H J, MOIN P, VERSTAPPEN R. Minimum-dissipation models for large eddy simulation[J]. Phys Fluids, 2015,27:085107.
[14] THIRY O, WINCKELMANS G. A mixed multiscale model better accounting for the cross term of the subgrid-scale stress and for backscatter[J]. Phys Fluids, 2016,28:025111.
[15] RASTHOFER U, BURTON G C, WALL W A, et al. Multifractal subgrid-scale modeling within a variational multiscale method for large-eddy simulation of passive-scalar mixing in turbulent flow at low and high Schmidt numbers[J]. Phys Fluids, 2014,26(5):055108.
[16] BALARAC G, LE SOMMER J, MEUNIER X, et al. A dynamic reglarized gradient model of the subgrid-scale scalar flux for large-eddy simulations[J]. Phys Fluids, 2014,25(7):075107.
[17] VOLLANT A, BALARAC G, CORRE C. A dynamic regularized gradient model of the subgrid scale stress tensor for large-eddy simulation[J]. Phys Fluids, 2016,28:025114.
[18] MAZZITELLI I M, TOSCHI F, LANOTTE A S. An accurate and efficient Lagrangian subgrid model[J]. Phys Fluids, 2014,26(9):095101.
[19] JIN G D, HE G W. A nonlinear model for the subgrid timescale experienced by heavy particles in large eddy simulation of isotropic turbulence with a stochastic differential equation[J]. New J Phys, 2013,15:035011.
[20] SHI Y P, XIAO Z L, CHEN S Y. Constrained subgrid-scale stress model for large eddy simulation[J]. Phys Fluids, 2008,20(1):011701.
[21] CHEN S Y, XIA Z H, PEI S Y, et al. Reynolds-stress constrained large-eddy simulation of wall-bounded turbulent flows[J]. J Fluid Mech, 2012,703:1-28.
[22] XIA Z H, SHI Y P, HONG R, et al. Constrained large-eddy simulation of separated flow in a channel with streamwise-periodic constrictions[J]. J Turbulence, 2013,14(1):1-21.
[23] JIANG Z, XIAO Z L, SHI Y P, et al. Constrained large-eddy simulation of wall bounded compressible turbulent flows[J]. Phys Fluids, 2013,25(10):106102.
[24] ZHAO Y M, XIA Z H, SHI Y P, et al. Constrained large-eddy simulation of laminar-turbulent transition in channel flow[J]. Phys Fluids, 2014,26(9):095103.
[25] YU C P, HONG R K, XIAO Z L, et al. Subgrid-scale eddy viscosity model for helical turbulence[J]. Phys Fluids, 2013,25(9):095101.
[26] YU C P, XIAO Z L. Refined subgrid-scale model for large-eddy simulation of helical turbulence[J]. Phys Rev E, 2013,87(1):013006.
[27] YU C P, XIAO Z L, SHI Y P, et al. Joint-constraint model for large-eddy simulation of helical turbulence[J]. Phys Rev E, 2014,89(4):043021.
[28] YU C P, XIAO Z L, Li X. Dynamic optimization methodology based on subgrid-scale dissipation for large eddy simulation[J]. Phys Fluids, 2016,28(1):015113.
[29] HORIUTI K, TAMAKI T. Non equilibrium energy spectrum in the subgrid scale one equation model in large-eddy simulation[J]. Phys Fluids, 2013, 25(12):125104.
[30] PARK G I, MOIN P. An improved dynamic non-equilibrium wall-model for large eddy simulation[J]. Phys Fluids, 2014, 26(1):015108.
[31] FANG L, ZHU Y, LIU Y W, et al. Spectral non-equilibrium property in homogeneous isotropic turbulence and its implication in subgrid-scale modeling[J]. Phys Lett A, 2015, 379(38):2331-2336.
[32] HINZ D F, KIM T Y, RILEY J J, et al. A priori testing of alpha regularization models as subgrid-scale closures for large-eddy simulations[J]. J Turbulence, 2013, 14(6):1-20.
[33] PARK N, YOO J Y, CHOI H. Toward improved consistency of a priori tests with a posteriori tests in large eddy simulation[J]. Phys Fluids, 2005, 17:015103.
[34] VREMAN B, GEURTS B, KUERTEN H. Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer[J]. Int J Numer Methods Fluids, 1996, 22(4):297-311.
[35] RODI W, FERZIGER J H, BREUER M, et al. Status of large eddy simulation:Results of a workshop[J]. J Fluids Eng, 1997,119(2):248-262.
[36] VOKE R R. Flow past a square cylinder:Test case LES2[C]//Proceedings of the Second ERCOFTAC Workshop on Direct and Large-Eddy Simulation, 1997:355-373.
[37] BREUER M. A challenging test case for large eddy simulation:High Reynolds number circular cylinder flow[J]. Int J Heat Fluid Flow, 2000,21:648-654.
[38] SCHMIDT S, THIELE F. Investigation of subgrid-scale models in LES of turbulent flows with separation[C]//New Results in Numerical and Experimental Fluid Mechanics Ⅲ, 2002:199-206.
[39] CADIEUX F, DOMARADZKI J A. Performance of subgrid-scale models in coarse large eddy simulations of a laminar separation bubble[J]. Phys Fluids, 2015, 27:045112.
[40] SILVIS M H, REMMERSWAAL R A, VERSTAPPEN R. Physical consistency of subgrid-scale models for large-eddy simulation of incompressible turbulent flows[J]. Phys Fluids, 2017, 29:015105.
[41] SPALART P R. Strategies for turbulence modelling and simulations[J]. Int J Heat Fluid Flow, 2000, 21:252-263.
[42] FANG L, GE M W, WU J Z. Comment on "A self-adjusting flow dependent formulation for the classical Smagorinsky model coefficient"[J]. Phys Fluids, 2013, 25(9):099101.
[43] MENEVEAU C. Statistics of turbulence subgrid-scale stresses:Necessary conditions and experimental tests[J]. Phys Fluids, 1994, 6(2):815-833.
[44] FANG L. Applying the Kolmogorov equation to the problem of subgrid modeling for large-eddy simulation of turbulence[D]. Ecole Centrale de Lyon, 2009.
[45] SHAO L, ZHANG Z S, CUI G X, et al. Subgrid modeling of anisotropic rotating homogeneous turbulence[J]. Phys Fluids, 2005, 17(11).
[46] CUI G X, XU C X, FANG L, et al. A new subgrid eddy-viscosity model for large-eddy simulation of anisotropic turbulence[J]. J Fluid Mech, 2007, 582:377-397.
[47] FANG L, BOS W J Y, SHAO L, et al. A dynamic multiscale subgrid model for MHD turbulence based on Kolmogorov's equation[C]. ETC12, Marburg, 2009.
[48] 马威, 方乐, 邵亮, 陆利蓬. 可解尺度各向同性湍流的标度律[J]. 力学学报, 2011, 43(2):267-276.
[49] FANG L, SHAO L, BERTOGLIO J P, et al. An improved velocity increment model based on Kolmogorov equation of filtered velocity[J]. Physics of Fluids, 2009, 21(6):065108.
[50] FANG L, LI B, LU L P. Scaling law of resolved-scale isotropic turbulence and its application in large-eddy simulation[J]. Acta Mechanica Sinica, 2014, 30(3):339-350.
[51] YAO S Y, FANG L, LV J M, et al. Multiscale three-point velocity increment correlation in turbulent flows[J]. Physics Letters A, 2014, 378(11-12):886-891.
[52] FANG L, SUN X Y, LIU Y W. A criterion of orthogonality on the assumption and restrictions in subgrid-scale modelling of turbulence[J]. Physics Letters A, 2016, 380(47):3988-3992.
[53] FANG F, GE M W. Mathematical constraints in multiscale subgrid-scale modeling of nonlinear systems[J]. Chinese Physics Letters, 2017, 34(3):030501.
[54] CUI G X, ZHOU H B, ZHANG Z S, et al. A new dynamic subgrid eddy viscosity model with application to turbulent channel flow[J]. Phys Fluids, 2004, 16(8):2835-2842.
[55] FANG L, SHAO L, BERTOGLIO J P, et al. The rapid-slow decomposition of the subgrid flux in inhomogeneous scalar turbulence[J]. Journal of Turbulence, 2011, 12(8):1-23.
[56] BRUN C, FRIEDIRICH R, DA SILVA C B. A non-linear SGS model based on the spatial velocity increment[J]. Theoretical and Computational Fluid Dynamics, 2006,20(1).
[57] FANG L. A new dynamic formula for determining the coefficient of Smagorinsky model[J]. Theoretical & Applied Mechanics Letters, 2011, 1(3):032002.
[58] SCHUMANN U. Stochastic backscatter of turbulence energy and scalar variance by random subgrid-scale fluxes[J]. Proc R Soc Lond A, 1995, 451(293).
[59] CARATI D, WINCKELMANS G S, JEANMART H. On the modelling of subgrid-scale and filtered-scale stress tensors in large-eddy simulation[J]. J Fluid Mech, 2001, 441:119-138.
[60] PUMIR A, SHRAIMAN B I. Lagrangian particle approach to large eddy simulations of hydrodynamic turbulence[J]. Journal of Statistical Physics, 2003, 113:693-700.
[61] FANG L, BOS W J T, SHAO L, et al. Time-reversibility of Navier-Stokes turbulence and its implication for subgrid scale models[J]. Journal of Turbulence, 2012, 13(3):1-14.