On the Large Eddy Simulation of the Taylor–Green vortex

Abstract.In this paper we analyze the role of the Taylor–Green vortex in the study of some Large Eddy Simulation models. More precisely, we consider such a particular flow in connection with the Gradient model and the Rational model. In particular, we study: 1) the mechanism of small scale generation; 2) the symmetries of the flow and their role in the Spectral Galerkin approximation; 3) the connection between pressure fluctuations and quadratic mean velocity.

[1]  J. Ferziger,et al.  Evaluation of subgrid-scale turbulence models using a fully simulated turbulent flow , 1977 .

[2]  Steven A. Orszag,et al.  The Taylor-Green vortex and fully developed turbulence , 1984 .

[3]  T. Iliescu,et al.  A Numerical Study of a Class of LES Models , 2003 .

[4]  M. Brachet Direct simulation of three-dimensional turbulence in the Taylor–Green vortex , 1991 .

[5]  Steven A. Orszag,et al.  Numerical Simulation of the Taylor-Green Vortex , 1973, Computing Methods in Applied Sciences and Engineering.

[6]  Andrew J. Majda,et al.  Vorticity and Incompressible Flow: Index , 2001 .

[7]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[8]  Á. Aldama Filtering Techniques for Turbulent Flow Simulation , 1990 .

[9]  Volker John,et al.  Large Eddy Simulation of Turbulent Incompressible Flows - Analytical and Numerical Results for a Class of LES Models , 2003, Lecture Notes in Computational Science and Engineering.

[10]  Robert McDougall Kerr Evidence for a Singularity of the Three Dimensional, Incompressible Euler Equations , 1993 .

[11]  C. Ross Ethier,et al.  Exact fully 3D Navier–Stokes solutions for benchmarking , 1994 .

[12]  A. Leonard Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows , 1975 .

[13]  L. Berselli,et al.  Mathematics of Large Eddy Simulation of Turbulent Flows , 2005 .

[14]  S. A. Orsag,et al.  Small-scale structure of the Taylor-Green vortex , 1984 .

[15]  William Layton,et al.  APPROXIMATION OF THE LARGER EDDIES IN FLUID MOTIONS II: A MODEL FOR SPACE-FILTERED FLOW , 2000 .

[16]  Steven A. Orszag,et al.  Numerical simulation of incompressible flows within simple boundaries: accuracy , 1971, Journal of Fluid Mechanics.

[17]  Osborne Reynolds On the dynamical theory of incompressible viscous fluids and the determination of the criterion , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[18]  O. Reynolds On the dynamical theory of incompressible viscous fluids and the determination of the criterion , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[19]  Luigi C. Berselli,et al.  Regularity criteria involving the pressure for the weak solutions to the Navier-Stokes equations , 2002 .

[20]  Luigi C. Berselli,et al.  Analytical and Numerical Results for the Rational Large Eddy Simulation Model , 2007 .

[21]  P. Sagaut Large Eddy Simulation for Incompressible Flows , 2001 .

[22]  T. N. Stevenson,et al.  Fluid Mechanics , 2021, Nature.

[23]  Traian Iliescu,et al.  MATHEMATICAL ANALYSIS FOR THE RATIONAL LARGE EDDY SIMULATION MODEL , 2002 .

[24]  G. Taylor,et al.  Mechanism of the production of small eddies from large ones , 1937 .

[25]  V. Arnold,et al.  Sur la topologie des écoulements stationnaires des fluides parfaits , 1965 .

[26]  P. Fischer,et al.  Large eddy simulation of turbulent channel flows by the rational large eddy simulation model , 2002 .

[27]  T. von Karman,et al.  On the Statistical Theory of Turbulence. , 1937, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Akira Ogawa,et al.  Vorticity and Incompressible Flow. Cambridge Texts in Applied Mathematics , 2002 .

[29]  L. Berselli,et al.  On the consistency of the Rational Large Eddy Simulation model , 2004 .

[30]  Stephen Childress,et al.  New Solutions of the Kinematic Dynamo Problem , 1970 .