Abstract
In recent years adaptive stabilized finite element methods, here referred to as General Galerkin (G2) methods, have been developed as a general methodology for the computation of mean value output in turbulent flow. In earlier work, in the setting of bluff body flow, the use of no slip boundary conditions has been shown to accurately capture the separation from a laminar boundary layer, in a number of benchmark problems. In this paper we extend the G2 method to problems with turbulent boundary layers, by including a simple wall-model in the form of a friction boundary condition, to account for the skin friction of the unresolved turbulent boundary layer. In particular, we use G2 to simulate drag crisis for a circular cylinder, by adjusting the friction parameter to match experimental results. By letting the Reynolds number go to infinity and the skin friction go to zero, we get a G2 method for the Euler equations with slip boundary conditions, which we here refer to as an EG2 method. The only parameter in the EG2 method is the discretization parameter, and we present computational results indicating that EG2 may be used to model very high Reynolds numbers flow, such as geophysical flow.
Similar content being viewed by others
References
Breuer M (1998) Large eddy simulation of the subcritical flow past a circular cylinder: numerical and modeling aspects. Int J Numer Methods Fluids 28: 1281–1302
Constantinescu G, Squires K (2004) Numerical investigations of flow over a sphere in the subcritical and supercritical regimes. Phys Fluids 16(5):1449–1466
Frisch U (1995) Turbulence—the legacy of A. N. Kolmogorov. Cambridge University Press, Cambridge
Hoffman J (2005) Adaptive simulation of the turbulent flow due to a cylinder rolling along ground. Comput Methods Appl Mech Engng (under review)
Hoffman J (2005) Computation of mean drag for bluff body problems using adaptive dns/les. SIAM J Sci Comput 27(1):184–207
Hoffman J (2005) Efficient computation of mean drag for the subcritical flow past a circular cylinder using general galerkin g2. Int J Numer Methods Fluids (in press)
Hoffman J (2006) Adaptive simulation of the turbulent flow past a sphere. J Fluid Mech (in press)
Hoffman J, Johnson C (2006) Computational turbulent incompressible flow: applied mathematics body and soul, Vol 4. Springer, Berlin Heidelberg New York
Hoffman J, Johnson C (2006) A new approach to computational turbulence modeling. Comput Methods Appl Mech Engrg (in press)
Iliescu T, John V, Layton WJ (2002) Convergence of finite element approximations of large eddy motion. Numer Method Part Diff Equ 18:689–710
John V (2002) Slip with friction and penetration with resistance boundary conditions for the navier–stokes equations—numerical tests and aspects of the implementation. J Comp Appl Math 147:287–300
John V, Layton WJ, Sahin N (2003) Derivation and analysis of near wall models for channel and recirculating flows. Comput Math Appl (in press)
John V, Liakos A (2005) Time dependent flow across a step: the slip with friction boundary condition. Int J Numer Methods Fluids (in press)
Krajnović S, Davidson L (2002) Large-eddy simulation of the flow around a bluff body. AIAA 40:927–936
Kravchenko AG, Moin P (2000) Numerical studies of flow over a circular cylinder at re d =3900. Phys Fluids 12(2):403–417
Maxwell JC (1879) Phil. Trans. Royal Society
Mittal R (1996) Progress on les of flow past a circular cylinder. Center for Turbulence Research Annual Research Briefs
NASA (2005) Various views of von karman vortices. http://www.disc.gsfc.nasa.gov/oceancolor/scifocus/oceanColor/vonKarman_vortices.shtml
Navier CLMH (1823) Mémoire sur les lois du mouvement des fluiales. Mém Acad R Soc 6:389–440
Rodi W, Ferziger JH, Breuer M, Pourquié M (1997) Status of large eddy simulation: results of a workshop. ASME J Fluids Eng 119:248–262
Sagaut P (2001) Large Eddy simulation for incompressible flows. Springer, Berlin Heidelberg New York
Schlichting H (1955) Boundary layer theory. McGraw-Hill, New York
Zdravkovich MM (1997) Flow around circular cylinders: a comprehensive guide through flow phenomena, experiments, applications, mathematical models, and simulations, vol 1 [Fundamentals]. Oxford University Press, Oxford
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hoffman, J. Simulation of Turbulent Flow Past Bluff Bodies on Coarse Meshes Using General Galerkin Methods: Drag Crisis and Turbulent Euler Solutions. Comput Mech 38, 390–402 (2006). https://doi.org/10.1007/s00466-006-0053-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00466-006-0053-x