A new simple h-mesh adaptation algorithm for standard Smagorinsky LES: a first step of Taylor scale as a refinement variable
DOI:
https://doi.org/10.1260/1750-9548.4.1.33Abstract
The interaction between discretization error and modeling error has led to some doubts in adopting Solution Adaptive Grid (SAG) strategies with LES. Existing SAG approaches contain undesired aspects making the use of one complicated and less convenient to apply to real engineering applications. In this work, a new refinement algorithm is proposed aiming to enhance the efficiency of SAG methodology in terms of simplicity in defining, less user’s judgment, designed especially for standard Smagorinsky LES and computational affordability. The construction of a new refinement variable as a function of the Taylor scale, corresponding to the kinetic energy balance requirement of the Smagorinsky SGS model is presented. The numerical study has been tested out with a turbulent plane jet in two dimensions. It is found that the result quality can be effectively improved as well as a significant reduction in CPU time compared to fixed grid cases.
References
Ilinca C, Zhang XD, Trepanier J-Y, Camarero R., A comparison of three error estimation techniques for finite-volume solutions of compressible flows, Comput. Methods Appl. Mech. Engrg, 2000, 189: 1277-1294. https://doi.org/10.1016/s0045-7825(99)00377-1
Zienkiewicz OC, Zhu JZ., A simple error estimator and adaptive procedure for practical engineering analysis, Int. J. Numer. Meth. Engineering, 1987, 24: 337-357. https://doi.org/10.1002/nme.1620240206
Yamaleev NK., Minimization of the truncation error by grid adaptation, Journal of Computational Physics, 2001, 170: 459-497. https://doi.org/10.1006/jcph.2001.6745
Yamaleev NK, Carpenter MH., On accuracy of adaptive grid methods for captured shocks, Journal of Computational Physics, 2002, 181: 280-316. https://doi.org/10.1006/jcph.2002.7125
Lohner R., An adaptive finite element scheme for transient problems in CFD, Comput. Methods Appl. Mech. Engrg, 1987, 61: 323-338. https://doi.org/10.1016/0045-7825(87)90098-3
Warren GP, Anderson WK, Thomas JT, Krist SL., Grid convergence for adaptive methods, AIAA JOURNAL, 1991, 91: 1592.
Baker TJ., Mesh adaptation strategies for problems in fluid dynamics, Finite Elements Anal. Design, 1997, 25: 243. https://doi.org/10.1016/s0168-874x(96)00032-7
Frey PJ, Alauzet F., Anisotropic mesh adaptation for CFD computations, Comput. Methods Appl. Mech. Engrg, 2005, 194: 5068-5082. https://doi.org/10.1016/j.cma.2004.11.025
Habashi WG, Dompierre J, Bourgault Y, Ait-Ali-Yahia D, Fortin M, Vallet M-G., Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles, Int. J. Numer. Meth. Fluids, 2000, 32: 725-744. https://doi.org/10.1002/(sici)1097-0363(20000330)32:6<725::aid-fld935>3.0.co;2-4
Ait-Ali-Yahia D, Habashi WG, Tam A, Vallet M-G., Fortin M., A directionally adaptive methodology using an edge-based error etimate on quadrilteral grids, Int. J. Numer. Meth. Fluids, 1996, 23: 673-690. https://doi.org/10.1002/(sici)1097-0363(19961015)23:7<673::aid-fld471>3.0.co;2-p
Habashi WG, Dompierre J, Bourgault Y, Fortin M, Vallet M-G., Certifiable computational fluid dynamics through mesh optimization., AIAA JOURNAL, 1998, 36 (5): 703-711. https://doi.org/10.2514/3.13883
Tam A, Robichaud MP, Tremblay P, Habashi WG, Hohmeyer M, Peeters MF, Guevremont G., Germain P. A 3-D adaptive anisotropic method for external and internal flows. in: Proceedings of the 36th aerospace sciences meeting. AIAA 98-00771 Reno, NV 1998. https://doi.org/10.2514/6.1998-771
Soni BK, Koomullil R, Thompson DS, Thornburg H., Solution adaptive grid strategies based onpoint redistribution, Comput. Methods Appl. Mech. Engrg, 2000, 189: 1183-1204. https://doi.org/10.1016/s0045-7825(99)00373-4
Scalabrin LC, Azevedo JLF., Adaptive mesh refinement and coarsening for aerodynamic flow simultations, Int. J. Numer. Meth. Fluids, 2004, 45: 1107-1122. https://doi.org/10.1002/fld.731
Dompierre J, Vallet M-G., Bourgault Y, Fortin M, Habashi WG., Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD solutions: Part III: unstructured meshes, Int. J. Numer. Meth. Fluids, 2002, 39: 675-702. https://doi.org/10.1002/fld.357
Scott McRae D., r-Refinement grid adaptation algorithms and issues, Comput. Methods Appl. Mech. Engrg, 2000, 189: 1161-1182.
Figueira da Silva LF, Azevedo JLF, Korzenowski H., Unstructured adaptive grid flow simulations of inert and reactive gas mixtures, J. Comput. Phys., 2000, 160: 522-540. https://doi.org/10.1006/jcph.2000.6470
Popiolek TL, Awruch AM., Numerical simulation of compressible flows using adaptive unstructured meshes and the pseudo-compressibility hypothesis, Advances in Engineering Software, 2006, 37: 260-274. https://doi.org/10.1016/j.advengsoft.2005.06.001
Kaennakham S, Holdo AE., The use of solution adaptive grid for low Reynolds number flows, IJAME, 2008, 13 (1): to appear.
With de G, Holdo AE, Huld TA., The use of dynamic grid adaptation algorithms for the modelling of flow around a cricular cylinder in sub-critical flow regime, Int. J. Numer. Meth. Fluids, 2003, 41: 789-808. https://doi.org/10.1002/fld.418
With de G, Holdo AE., The use of solution adaptive grid for modeling small scale turbulent structures, ASME, 2005, 127: 936-944. https://doi.org/10.1115/1.1989359
Hay A, Visonneau M., Adaptive mesh strategy applied to turbulent flows, C. R. Mecanique, 2005, 333: 103-110. https://doi.org/10.1016/j.crme.2004.09.014
Ghosal S., An analysis of numerical errors in large -eddy simulations of turbulence, Journal of Computers and Fluids, 1996, 125: 187-206.
Kravchenko AG, Moin P., On the effect of numerical errors in large eddy simulations of turbulent flows, Journal of Computers and Fluids, 1997, 131: 310-322. https://doi.org/10.1006/jcph.1996.5597
Vreman B, Geurts B, Kuerten H., Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer, Int. J. Numer. Methods Fluids, 1996, 22: 297-311. https://doi.org/10.1002/(sici)1097-0363(19960229)22:4<297::aid-fld361>3.0.co;2-x
Geurts Bernard J., Elements of direct and large-eddy simulation. Edwards. 2004.
Schumann U., Subgrid scale model for finite difference simulations of turbulent flows in plane channels annuli, Journal of Comutational Physics, 1975, 18: 376-404. https://doi.org/10.1016/0021-9991(75)90093-5
Smagorinsky J., General circulation experiment with the primitive equations I. The basic experiment, Month. Wea. Rev., 1963, 91: 91-99. https://doi.org/10.1175/1520-0493(1963)091<0099:gcewtp>2.3.co;2
Rhie CM, Chow WL., Numerical study of the turbulent flow pas an airfoil with trailing edge separation, AIAA J., 1983, 21 (11): 1525-1532. https://doi.org/10.2514/3.8284
Tennekes H, Lumley JL., A first course in turbulence, The Massachusetts Institute of Technology.1972.
Dimotakis PE., Turbulent Mixing, Ann. Rev. Fluid Mech., 2005, 37: 329-356.
Stanley SA, Sarkar S, Mellado JP., A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation, J. Fluid Mech., 2002, 450: 377-407. https://doi.org/10.1017/s0022112001006644
Klein M, Sadiki A, Janicka J., Investigation of the influence of the Reynolds number on a plane jet using direct numerical simulation, Int. J. Heat. Fluid Flow, 2003, 24: 785-794. https://doi.org/10.1016/s0142-727x(03)00089-4
Ribault C le, Sarkar S, Stanley SA., Large eddy simulation of a plane jet, Phys. Fluids, 1999 11 (10): 3069-3083. https://doi.org/10.1063/1.870165
Liu Y, Tucker PG, Kerr RM., Linear and nonlinear model large-eddy simulations of a plane jet, Journal of Computers and Fluids, 2008, 37: 439-449. https://doi.org/10.1016/j.compfluid.2007.02.005
Browne LWB, Antonia RA, Rajagopalan S, Chambers AJ. Interaction region of a two-dimensional turbulent plane jet in still air. in: Structure of complex turbulent shear flows, IUTAM Symposium Marseille, 1983. https://doi.org/10.1007/978-3-642-81991-9_40
Thomas FO, Chu HC., An experimental investigation of the transition of a plannar jet: subharmonic suppression and upstream feedback, Phys. Fluids, 1989, A(1): 1566-1587.
Gutmark E, Wygnanski I., The planar turbulent jet, J. Fluid Mech., 1976, 73 (3): 465-495. https://doi.org/10.1017/s0022112076001468
Stanley S, Sarkar S., Simulations of spatially developing two-dimensional shear layers and jets, Theoret. Comput. Fluid Dynamics, 1997, 9: 121-147. https://doi.org/10.1007/s001620050036
Stanley SA, Sarkar S, Mellado JP., A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation J. Fluid Mech., 2002, 450: 377-407. https://doi.org/10.1017/s0022112001006644
Goldschmidt VW, Bradshaw P., Effect of nozzle exit turbulence on the spreading (or widening) rate of plane free jets. in: Joint Engineering, fluid Engineering and Applied Mechanics Conference, ASME Boulder, Colorado 1981.
Klein M., An Attempt to Assess the Quality of Large Eddy Simulation in the Context of Implicit Filtering, Flow, Turbulence and Combustion, 2005, 75: 131-147. https://doi.org/10.1007/s10494-005-8581-6
Celik IB, Cehreli ZN, Yavuz I., Index of resolution quality for large eddy simulations, Journal of Fluids Engineering, 2005, 127: 949-959. https://doi.org/10.1115/1.1990201
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