zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Truncation of scales by time relaxation. (English) Zbl 1167.76338
Summary: We study a time relaxation regularization of flow problems proposed and tested extensively by Stolz and Adams. The aim of the relaxation term is to drive the unresolved fluctuations in a computational simulation to zero exponentially fast by an appropriate and often problem dependent choice of its coefficient; this relaxation term is thus intermediate between a tunable numerical stabilization and a continuum modeling term. Our aim herein is to understand how this term, by itself, acts to truncate solution scales and to use this understanding to give insight into parameter selection.

76F65Direct numerical and large eddy simulation of turbulence
35Q35PDEs in connection with fluid mechanics
76D05Navier-Stokes equations (fluid dynamics)
Full Text: DOI
[1] Adams, N. A.; Stolz, S.: Deconvolution methods for subgrid-scale approximation in large eddy simulation. Modern simulation strategies for turbulent flow (2001)
[2] Adams, N. A.; Stolz, S.: A subgrid-scale deconvolution approach for shock capturing. J. comput. Phys. 178, 391-426 (2002) · Zbl 1139.76319
[3] J. Bardina, Improved turbulence models based on large eddy simulation of homogeneous, incompressible turbulent flows, PhD thesis, Stanford University, Stanford, 1983
[4] Bertero, M.; Boccacci, B.: Introduction to inverse problems in imaging. (1998) · Zbl 0914.65060
[5] Berselli, L. C.; Iliescu, T.; Layton, W.: Mathematics of large eddy simulation of turbulent flows. (2005) · Zbl 1089.76002
[6] Childress, S.; Kerswell, R. R.; Gilbert, A. D.: Bounds on dissipation for Navier -- Stokes flows with Kolmogorov forcing. Phys. D 158, 1-4 (2001) · Zbl 1098.76525
[7] Constantin, P.; Doering, C.: Energy dissipation in shear driven turbulence. Phys. rev. Lett. 69, 1648-1651 (1992)
[8] Doering, C.; Foias, C.: Energy dissipation in body-forced turbulence. J. fluid mech. 467, 289-306 (2002) · Zbl 1029.76025
[9] A. Dunca, Y. Epshteyn, On the Stolz -- Adams de-convolution LES mode, SIAM J. Math. Anal., 2006, in press · Zbl 1128.76029
[10] Foias, C.: What do the Navier -- Stokes equations tell us about turbulence?. Contemp. math. 208, 151-180 (1997) · Zbl 0890.76030
[11] Foias, C.; Holm, D. D.; Titi, E.: The Navier -- Stokes-alpha model of fluid turbulence. Phys. D 152 -- 153, 505-519 (2001) · Zbl 1037.76022
[12] Frisch, U.: Turbulence. (1995) · Zbl 0832.76001
[13] Galdi, G. P.: Lectures in mathematical fluid dynamics. (2000)
[14] Galdi, G. P.: An introduction to the mathematical theory of the Navier -- Stokes equations, volume I. (1994) · Zbl 0949.35004
[15] Galdi, G. P.; Layton, W. J.: Approximation of the large eddies in fluid motion II: A model for space-filtered flow. Math. models methods appl. Sci. 10, 343-350 (2000) · Zbl 1077.76522
[16] Germano, M.: Differential filters of elliptic type. Phys. fluids 29, 1757-1758 (1986) · Zbl 0647.76042
[17] Geurts, B. J.: Inverse modeling for large eddy simulation. Phys. fluids 9, 3585 (1997)
[18] R. Guenanff, Non-stationary coupling of Navier -- Stokes/Euler for the generation and radiation of aerodynamic noises, PhD thesis, Dept. of Mathematics, Universite Rennes 1, Rennes, France, 2004
[19] Hirt, C. W.: Phys. fluids, suppl. II. 219-227 (1969)
[20] John, V.: Large eddy simulation of turbulent incompressible flows. (2004) · Zbl 1035.76001
[21] Ladyzhenskaya, O.: The mathematical theory of viscous incompressible flow. (1969) · Zbl 0184.52603
[22] Layton, W.; Lewandowski, R.: A simple and stable scale similarity model for large eddy simulation: energy balance and existence of weak solutions. Appl. math. Lett. 16, 1205-1209 (2003) · Zbl 1039.76027
[23] Layton, W.; Lewandowski, R.: On a well posed turbulence model. Dcds-b 6, 111-178 (2006) · Zbl 1089.76028
[24] Lesieur, M.: Turbulence in fluids. (1997) · Zbl 0876.76002
[25] Layton, W.; Lewandowski, R.: Consistency and feasibility of approximate de-convolution models of turbulence · Zbl 1273.76206
[26] D.K. Lilly, The representation of small-scale turbulence in numerical simulation experiments, in: Proc. IBM Scientific Computing Symposium on Environmental Sciences, Yorktown Heights, 1967
[27] C. Manica, S. Kaya, Convergence analysis of the finite element method for a fundamental model in turbulence, Tech. Report, Dept. of Mathematics, Univ. of Pittsburgh, 2005 · Zbl 1252.76043
[28] Muschinsky, A.: A similarity theory of locally homogeneous and isotropic turbulence generated by a smagorinsky-type LES. J. fluid mech. 325, 239-260 (1996) · Zbl 0891.76045
[29] Pope, S.: Turbulent flows. (2000) · Zbl 0966.76002
[30] Reynolds, O.: On the dynamic theory of incompressible viscous fluids and the determination of the criterion. Phil. trans. R. soc. London A 186, 123-164 (1895) · Zbl 26.0872.02
[31] Rosenau, Ph.: Extending hydrodynamics via the regularization of the Chapman -- Enskog expansion. Phys. rev. A 40, 7193 (1989)
[32] Saddoughi, S. G.; Veeravalli, S. V.: Local isotropy in turbulent boundary layers at high Reynolds number. J. fluid mech. 268, 333-372 (1994)
[33] Sagaut, P.: Large eddy simulation for incompressible flows. (2001) · Zbl 0964.76002
[34] Schochet, S.; Tadmor, E.: The regularized Chapman -- Enskog expansion for scalar conservation laws. Arch. ration. Mech. anal. 119, 95 (1992) · Zbl 0793.76005
[35] Sreenivasan, K. R.: On the scaling of the turbulent energy dissipation rate. Phys. fluids 27, No. 5, 1048-1051 (1984)
[36] Sreenivasan, K. R.: An update on the energy dissipation rate in isotropic turbulence. Phys. fluids 10, No. 2, 528-529 (1998) · Zbl 1185.76674
[37] Stolz, S.; Adams, N. A.: An approximate deconvolution procedure for large eddy simulation. Phys. fluids II, 1699-1701 (1999) · Zbl 1147.76506
[38] Stolz, S.; Adams, N. A.; Kleiser, L.: The approximate deconvolution model for LES of compressible flows and its application to shock-turbulent-boundary-layer interaction. Phys. fluids 13, 2985 (2001) · Zbl 1184.76531
[39] Stolz, S.; Adams, N. A.; Kleiser, L.: An approximate deconvolution model for large eddy simulation with application to wall-bounded flows. Phys. fluids 13, 997 (2001) · Zbl 1184.76530
[40] Stolz, S.; Adams, N. A.; Kleiser, L.: The approximate deconvolution model for compressible flows: isotropic turbulence and shock-boundary-layer interaction. Advances in LES of complex flows (2002) · Zbl 1088.76022
[41] Wang, X.: The time averaged energy dissipation rates for shear flows. Phys. D 99, 555-563 (1997) · Zbl 0897.76019
[42] Wyngaard, J. C.; Pao, Y. H.: Some measurements of fine structure of large Reynolds number turbulence. Lecture notes in phys. 12, 384-401 (1972)