Abstract
A computational formulation is proposed for second-moment closure turbulence models, especially suited to models intended to ensure physical realizability. It enables to cast the quite complicated model equations in a compact form. It is specifically applied here to a two-dimensional parabolized flow, though it lends itself to extension to more complex flows. An effective computational algorithm is proposed, based on a staggered grid and a block tridiagonal solver. The algorithm is applied to a turbulent mixing layer, and the comparison between the predictions obtained by standard modelling tools and a realizable second-moment closure clearly points out the superiority of the latter.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Jones, W.P. and Launder, B.E., 'The prediction of re–laminarization with a two-equation model of turbulence', Int. J. Heat Mass Transf. 15 (1972), 301–314.
Launder, B.E. and Spalding, D.B., 'The numerical computation of turbulent flows', Comp. Meth. Appl. Mech. Eng. 3 (1974), 269–289.
Launder, B.E., 'Turbulence modelling for the nineties: second moment closure...... and beyond?', In: Morton, K.W. (Ed), 12th Int. Conf. Num. Meth. Fluid Dynam., Springer-Verlag, Berlin, 1990, pp. 1–18.
Speziale, C.G., 'On the origin of turbulent secondary flows in non–circular ducts', ASME FED 14 (1984), 101–107.
Speziale, C.G., 'On nonlinear K–l and K–∈ models of turbulence', J. Fluid Mech. 178 (1987), 459–475.
Hanjalić, K. and Launder, B.E., 'A Reynolds stress model of turbulence and its application to thin shear flows', J. Fluid Mech. 52 (1972), 609–638.
Launder, B.E., Reece, G.J. and Rodi, W., 'Progress in the development of a Reynolds stress turbulence closure', J. Fluid Mech. 68 (1975), 537–566.
Gibson, M.M. and Launder, B.E., 'Ground effects on pressure fluctuations in the atmospheric boundary layer', J. Fluid Mech. 58 (1978), 491–511.
Lumley, J.L., 'Computational modeling of turbulent flows', Adv. Appl. Mech. 18 (1978), 123–176.
Launder, B.E., 'Second-moment closure: present... and future?', J. Heat Fluid Flow 10 (1989), 282–300.
Shih, T.–H., Chen, J.–Y. and Lumley, J.L., 'Second-order modeling of boundary-free turbulent shear flows', AIAA J. 30 (1992), 1553–1560.
Shih, T.–H. and Lumley, J.L., 'Critical comparison of second-order closures with direct numerical simulations of homogeneous turbulence', AIAA J. 31 (1993), 663–670.
Ha Minh, H.A., 'The impact of numerical modelling on the numerical prediction of flows', In: Napolitano, M. and Sabetta, F. (Eds), 13th Int. Conf. Num. Meth. Fluid Dynam., Springer–Verlag, Berlin, 1993, pp. 27–46.
Wilcox, D.C., Turbulence Modeling for CFD, DCW Ind., La Cañada, 1993.
Schiestel, R., Modélisation et Simulation des Écoulements Turbulents, Hermès, Paris, 1993.
Speziale, C.G., Abid, R. and Durbin, P.A., 'On the realizability of Reynolds stress turbulence closures', J. Sci. Comp. 9 (1994), 369–403.
Durbin, P.A. and Speziale, C.G., 'Realizability of second-moment closure via stochastic analysis', J. Fluid Mech. 280 (1994), 395–407.
Aris, R., Vectors, Tensors, and the Basic Equations of Fluid Mechanics, Prentice-Hall, Englewood Cliffs, 1962.
Daly, B.J. and Harlow, F.H., 'Transport equations in turbulence', Phys. Fluids 13 (1970), 2634–2649.
Batchelor, G.K., An Introduction to Fluid Dynamics, Cambridge Univ. Press, Cambridge, 1967.
Fletcher, C.A.J., Computational Techniques for Fluid Dynamics, Springer–Verlag, Berlin, 1991.
Spencer, B.W. and Jones, B.G, Statistical Investigation of Pressure and Velocity Fields in the Turbulent Two-Stream Mixing Layer, AIAA paper 71–613, 1971.
Tennekes, H. and Lumley, J.L., A First Course in Turbulence, MIT Press, Cambridge, 1972.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lentini, D. A Computational Algorithm for Second-Moment Closure Turbulence Modelling. Meccanica 33, 29–46 (1998). https://doi.org/10.1023/A:1004295401311
Issue Date:
DOI: https://doi.org/10.1023/A:1004295401311