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TECHNICAL PAPERS

Stabilization Parameters and Smagorinsky Turbulence Model

[+] Author and Article Information
J. E. Akin, T. Tezduyar, M. Ungor

Mechanical Engineering, Rice University, MS 321, Houston, TX 77005

S. Mittal

Aerospace Engineering, IIT Kanpur, Kanpur 208016, India

J. Appl. Mech 70(1), 2-9 (Jan 23, 2003) (8 pages) doi:10.1115/1.1526569 History: Received January 18, 2002; Revised June 11, 2002; Online January 23, 2003
Copyright © 2003 by ASME
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References

Hughes, T. J. R., and Brooks, A. N., 1979, “A Multi-dimensional Upwind Scheme With no Crosswind Diffusion,” Finite Element Methods for Convection Dominated Flows, T. J. R. Hughes, ed., ASME, New York, AMD-Vol. 34, pp. 19–35.
Tezduyar, T. E., and Hughes, T. J. R., 1983, “Finite Element Formulations for Convection Dominated Flows With Particular Emphasis on the Compressible Euler Equations,” AIAA Paper No. 83-0125.
Hughes,  T. J. R., Franca,  L. P., and Hulbert,  G. M., 1989, “A New Finite Element Formulation for Computational Fluid Dynamics: VIII. The Galerkin/Least-Squares Method for Advective-Diffusive Equations,” Comput. Methods Appl. Mech. Eng., 73, pp. 173–189.
Tezduyar,  T. E., 1991, “Stabilized Finite Element Formulations for Incompressible Flow Computations,” Adv. Appl. Mech., 28, pp. 1–44.
Tezduyar,  T., Aliabadi,  S., Behr,  M., Johnson,  A., and Mittal,  S., 1993, “Parallel Finite-Element Computation of 3D Flows,” IEEE Computer, 26, pp. 27–36.
Brooks,  A. N., and Hughes,  T. J. R., 1982, “Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier-Stokes Equations,” Comput. Methods Appl. Mech. Eng., 32, pp. 199–259.
Tezduyar,  T. E., and Park,  Y. J., 1986, “Discontinuity Capturing Finite Element Formulations for Nonlinear Convection-Diffusion-Reaction Problems,” Comput. Methods Appl. Mech. Eng., 59, pp. 307–325.
Tezduyar,  T. E., and Ganjoo,  D. K., 1986, “Petrov-Galerkin Formulations With Weighting Functions Dependent Upon Spatial and Temporal Discretization: Applications to Transient Convection-Diffusion Problems,” Comput. Methods Appl. Mech. Eng., 59, pp. 49–71.
Franca,  L. P., Frey,  S. L., and Hughes,  T. J. R., 1992, “Stabilized Finite Element Methods: I. Application to the Advective-Diffusive Model,” Comput. Methods Appl. Mech. Eng., 95, pp. 253–276.
Tezduyar,  T. E., and Osawa,  Y., 2000, “Finite Element Stabilization Parameters Computed From Element Matrices and Vectors,” Comput. Methods Appl. Mech. Eng., 190, pp. 411–430.
Tezduyar, T. E., 2001, “Adaptive Determination of the Finite Element Stabilization Parameters,” Proceedings of the ECCOMAS Computational Fluid Dynamics Conference 2001 (CD-ROM), University of Wales, Swansea, Wales.
Tezduyar, T. E., 2001, “Stabilized Finite Element Formulations and Interface-Tracking and Interface-Capturing Techniques for Incompressible Flows,” Proceedings of the Workshop on Numerical Simulations of Incompressible Flows, Half Moon Bay, CA, to appear.
Akin, J. E, 2001, Finite Element Analysis With Error Estimates, Academic Press, San Diego, CA, submitted for publication.
Smagorinsky,  J., 1963, “General Circulation Experiments With the Primitive Equations,” Mon. Weather Rev., 91, pp. 99–165.
Kato, C., and Ikegawa, M., 1991, “Large Eddy Simulation of Unsteady Turbulent Wake of a Circular Cylinder Using the Finite Element Method,” Advances in Numerical Simulation of Turbulent Flows, I. Celik, T. Kobayashi, K. N. Ghia, and J. Kurokawa, eds., ASME, New York, FED-Vol. 117, pp. 49–56.

Figures

Grahic Jump Location
For linear elements, Galerkin (broken line) and SUPG (solid line) functions, assembled for a global node A
Grahic Jump Location
For quadratic elements, Galerkin (broken line) and SUPG (solid line) functions, assembled for a global node A. For nodes at element boundaries (top) and interiors (bottom).
Grahic Jump Location
For cubic elements, Galerkin (broken line) and SUPG (solid line) functions, assembled for a global node A. For nodes at element boundaries (top), upstream interiors (middle), and downstream interiors (bottom).
Grahic Jump Location
Variation of hUGN within linear and higher-order one-dimensional elements
Grahic Jump Location
For a square Lagrangian element, the element length calculated with different definitions and as function of advection direction
Grahic Jump Location
For a square serendipity element, the element length calculated with different definitions and as function of advection direction
Grahic Jump Location
For an equilateral triangular element, the element length calculated with different definitions and as function of advection direction
Grahic Jump Location
Flow past a cylinder. A close-up view of the finite element mesh with 14,960 nodes and 14,700 elements.
Grahic Jump Location
Flow past a cylinder at Re=3,000. Vorticity (top) and νSMAGSUPG with (middle) and without (bottom) the wall function in computation of νSMAG. In displaying νSMAGSUPG, shades of gray represent the values ranging from 0.00 (white) to 0.05, with 0.05 and higher values indicated by black.
Grahic Jump Location
Flow past a cylinder at Re=50,000. Vorticity (top) and νSMAGSUPG with (middle) and without (bottom) the wall function in computation of νSMAG. In displaying νSMAGSUPG, shades of gray represent the values ranging from 0.00 (white) to 0.05, with 0.05 and higher values indicated by black.

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