Large eddy simulation of turbulent flows in external flow field using three-step FEM-BEM model. (English) Zbl 1195.76211

Summary: An innovative computational model is presented for the large eddy simulation (LES) modeling of multi-dimensional unsteady turbulent flow problems in external flow field. Based on the LES principles, the model uses a pressure projection method to solve the Navier-Stokes equations in transient condition. The turbulent motion is simulated by Smagorinsky sub-grid scale (SGS) eddy viscosity model. The momentum equation of the flow motion is solved using a three-step finite element method (FEM). The external flow field is simulated using a boundary element method (BEM) by solving a pressure Poisson equation that assumes the pressure as zero at the infinity. Through extracting the boundary effects on a specified finite computational domain, the model is able to solve the infinite boundary value problems. The present model is used to simulate the flows past a two-dimensional square rib and a three-dimensional cube at high Reynolds number. The simulation results are found to be reasonable and comparable with other models available in the literature even for coarse meshes.


76F65 Direct numerical and large eddy simulation of turbulence
76M10 Finite element methods applied to problems in fluid mechanics
76M15 Boundary element methods applied to problems in fluid mechanics
Full Text: DOI


[1] Blevins, R. D., Flow-induced vibration (1990), Van Nostrand Reinhold: Van Nostrand Reinhold New York
[2] Baetke, F.; Werner, H., Numerical simulation of turbulence flow over surface-mounted obstacles with sharp edges and corners, J Wind Eng Ind Aerod, 35, 129-147 (1990)
[3] Smagorinsky, J. S., General circulation experiments with the primitive equations. Part 1. Basic experiments, Mon Weather Rev, 91, 99-164 (1963)
[4] Deardorff, J. W., A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers, J Fluid Mech, 41, 2, 453-480 (1970) · Zbl 0191.25503
[5] Schumann, U., Sub-grid scale model for finite difference simulation of turbulent flows in plane channels and annuli, J Comput Phys, 18, 376-404 (1975) · Zbl 0403.76049
[6] Moin, P.; Kim, J., Numerical investigation of turbulent channel flow, J Fluid Mech, 118, 341-377 (1982) · Zbl 0491.76058
[7] Murakami, S.; Mochida, A.; Hibi, K., Three-dimensional simulation of air flow around a cubic model by means of large eddy simulation, J Wind Eng Ind Aerod, 25, 291-305 (1987)
[8] Kobayashi, T.; Ishiara, T.; Kano, M., Prediction of turbulent flow in two-dimensional channel with turbulence promoters, III— improvement of large eddy simulation and formation of streaklines, JSME Bull, 28, 246, 2948-2953 (1985)
[9] Song, C. C.S.; He, J., Computation of wind flow around a tall building and the large-scale vortex structure, J Wind Eng Ind Aerod, 46-47, 219-228 (1993)
[10] Rail, M. M.; Moin, P., Direct simulations of turbulent flow using finite difference schemes, J Comput Phys, 96, 15-53 (1991) · Zbl 0726.76072
[11] Reddy, J. N.; Gartling, D. K., The finite element method in heat transfer and fluid dynamics (1992), CRC Press: CRC Press London · Zbl 0855.76002
[12] Power, H.; Wrobel, L. C., Boundary integral methods in fluid mechanics (1995), Computational Mechanics Publications: Computational Mechanics Publications Southampton · Zbl 0815.76001
[13] Brookes, A. N.; Hughes, T. J.R., Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations, Comput Meth Appl Mech Eng, 32, 199-259 (1982) · Zbl 0497.76041
[14] Lohner, R.; Morgan, K.; Zienkiewics, O. C., The solution of nonlinear hyperbolic equations systems by the finite element method, Int J Numer Methods Fluids, 4, 1043-1063 (1984) · Zbl 0551.76002
[15] Jiang, C. B.; Kawahara, M., The analysis of unsteady incompressible flows by a three-step finite element method, Int J Numer Methods Fluids, 16, 793-811 (1993) · Zbl 0772.76036
[16] Young, D. L.; Chang, J. T.; Eldho, T. I., A coupled BEM and arbitrary Lagrangian-Eulerian FEM model for the solution of two-dimensional laminar flows in external flow fields, Int J Numer Meth Eng, 9, 1053-1077 (2001) · Zbl 1051.76042
[17] Young, D. L.; Huang, J. L.; Eldho, T. I., Simulation of laminar vortex shedding flow past cylinders using a coupled BEM and FEM model, Comput Meth Appl Mech Eng, 190, 5975-5998 (2001) · Zbl 1043.76041
[18] Young, D. L.; Huang, J. L.; Eldho, T. I., Numerical simulation of high-Reynolds number flow around circular cylinders by a three-step FEM-BEM model, Int J Numer Methods Fluids, 37, 657-689 (2001) · Zbl 1009.76060
[19] Young, D. L.; Chang, J. T.; Eldho, T. I., Solution of three-dimensional unsteady external flow using a coupled arbitrary Lagrangian FEM-BEM model, Eng Anal Bound Elem, 28, 711-723 (2004) · Zbl 1130.76370
[20] Yoshizawa, A., Eddy-viscosity-type subgrid-scale model with a variable Smagorinsky coefficient and its relationship with the one-equation model in large eddy simulation, J Phys Fluids, A3, 2007-2009 (1991) · Zbl 0746.76060
[21] Debler, W. A., Fluid mechanics fundamentals. Englewood Cliffs (1990), Prentice Hall: Prentice Hall NJ
[22] Reddy, J. N. (1993), McGraw-Hill: McGraw-Hill New York
[23] Young, D. L.; Liao, C. B.; Sheen, H. J., Computations of recirculation zones of a confined annular swirling flow, Int J Numer Methods Fluids, 29, 791-810 (1999) · Zbl 0951.76067
[24] Brebbia, C. A.; Telles, J. C.F.; Wrobel, L. C., Boundary element techniques—theory and applications in engineering (1984), Springer: Springer Berlin · Zbl 0556.73086
[25] Crabb, D.; Durao, D. F.G.; Whitelaw, J. H., Velocity characteristics in the vicinity of a two dimensional rib, Proceedings of fourth Brazilian congress on mechanical engineering, Florianopolis, Brazil, December (1977), p. 415-29
[26] Benodekar, R. W.; Goddard, A. J.H.; Gosman, A. D.; Issac, R. I., Numerical prediction of turbulent flow over surface-mounted ribs, AIAA J, 23, 3, 359-366 (1985) · Zbl 0589.76074
[27] Castro, I. P.; Robins, A. G., The flow around a surface mounted cube in uniform and turbulent streams, J Fluid Mech, 79, 2, 307-335 (1977)
[28] He, J.; Song, C. C.S., Computation of turbulent shear flow over surface-mounted obstacle, J Eng Mech ASCE, 118, 11, 2282-2297 (1992)
[29] Yu, D.; Kareem, A., Parametric study of flow around rectangular prisms using LES, J Wind Eng Ind Aerod, 77/78, 653-662 (1998)
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.