A heuristic argument for the sole use of numerical stabilization with no physical LES modeling in the simulation of incompressible turbulent flows

We aim at giving support to the idea that no physical Large Eddy Simulation (LES) model should be used in the simulation of turbulent flows. It is heuristically shown that the rate of transfer of subgrid kinetic energy provided by the stabilization terms of the Orthogonal Subgrid Scale (OSS) finite element method is already proportional to the molecular physical dissipation rate (for an appropriate choice of the stabilization parameter). This precludes the necessity of including an extra LES physical model to achieve this behavior and somehow justifies the purely numerical approach to solve turbulent flows. The argumentation is valid for a fine enough mesh with characteristic element size, $h$, so that $h$ lies in the inertial subrange of a turbulent flow.

[1]  Jean-Luc Guermond,et al.  Mathematical Perspectives on Large Eddy Simulation Models for Turbulent Flows , 2004 .

[2]  Johan Hoffman,et al.  A new approach to computational turbulence modeling , 2006 .

[3]  T. Hughes,et al.  Variational and Multiscale Methods in Turbulence , 2005 .

[4]  R. Codina,et al.  Time dependent subscales in the stabilized finite element approximation of incompressible flow problems , 2007 .

[5]  Nikolaus A. Adams,et al.  An adaptive local deconvolution method for implicit LES , 2005, J. Comput. Phys..

[6]  Roger Temam,et al.  Navier-Stokes Equations and Turbulence. Encyclopedia of Math and its Applications, Vol. 83 , 2002 .

[7]  P. Moin,et al.  A General Class of Commutative Filters for LES in Complex Geometries , 1998 .

[8]  R. Codina.  On stabilized finite element methods for linear systems of convection-diffusion-reaction equations , 2000 .

[9]  Assad A. Oberai,et al.  Generalized Smagorinsky model in physical space , 2008 .

[10]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[11]  Volker John,et al.  The Commutation Error of the Space Averaged Navier{Stokes Equations on a Bounded Domain , 2004 .

[12]  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.

[13]  T. Hughes,et al.  Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows , 2007 .

[14]  R. Codina.  A stabilized finite element method for generalized stationary incompressible flows , 2001 .

[15]  Meinhard E. Mayer,et al.  Navier-Stokes Equations and Turbulence , 2008 .

[16]  S Ghosal.  AN ANALYSIS OF NUMERICAL ERROR IN LARGE EDDY SIMULATION OF TURBULENCE , 1996 .

[17]  M. Germano.  Differential filters of elliptic type , 1986 .

[18]  Ramon Codina,et al.  A nodal-based implementation of a stabilized finite element method for incompressible flow problems , 2000 .

[19]  J. Domaradzki,et al.  Large eddy simulations using the subgrid scale estimation model and truncated Navier-Stokes dynamics. , 2001 .

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

[21]  J. P. Boris,et al.  New insights into large eddy simulation , 1992 .

[22]  J. Guermond,et al.  On the construction of suitable solutions to the Navier-Stokes equations and questions regarding the definition of large eddy simulation , 2005 .

[23]  Victor M. Calo,et al.  Residual-based multiscale turbulence modeling: Finite volume simulations of bypass transition , 2005 .

[24]  R. Codina.  Stabilization of incompressibility and convection through orthogonal sub-scales in finite element methods , 2000 .

[25]  R. Codina.  Stabilized finite element approximation of transient incompressible flows using orthogonal subscales , 2002 .

[26]  P. Moin,et al.  The basic equations for the large eddy simulation of turbulent flows in complex geometry , 1995 .

[27]  Jean-Luc Guermond,et al.  Finite-element-based Faedo–Galerkin weak solutions to the Navier–Stokes equations in the three-dimensional torus are suitable , 2006 .

[28]  Thomas J. R. Hughes,et al.  Large eddy simulation of turbulent channel flows by the variational multiscale method , 2001 .

[29]  A. Kolmogorov.  The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers , 1991, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[30]  T. Hughes,et al.  The variational multiscale method—a paradigm for computational mechanics , 1998 .

[31]  Alvaro L. G. A. Coutinho,et al.  A stabilized finite element procedure for turbulent fluid–structure interaction using adaptive time–space refinement , 2004 .

[32]  T. Hughes,et al.  Large Eddy Simulation and the variational multiscale method , 2000 .

[33]  Thomas J. R. Hughes,et al.  The multiscale formulation of large eddy simulation: Decay of homogeneous isotropic turbulence , 2001 .

[34]  Daniele Carati,et al.  Large-eddy simulation without filter , 2005 .

[35]  K. Lilly.  The representation of small-scale turbulence in numerical simulation experiments , 1966 .

[36]  Giancarlo Sangalli,et al.  Variational Multiscale Analysis: the Fine-scale Green's Function, Projection, Optimization, Localization, and Stabilized Methods , 2007, SIAM J. Numer. Anal..

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

[38]  Kenneth E. Jansen,et al.  Spatial test filters for dynamic model large‐eddy simulation with finite elements , 2002 .

[39]  Caskey,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS I . THE BASIC EXPERIMENT , 1962 .

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

[41]  M. Germano.  Differential filters for the large eddy numerical simulation of turbulent flows , 1986 .

[42]  T. Hughes.  Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[43]  R. Codina.  Analysis of a stabilized finite element approximation of the Oseen equations using orthogonal subscales , 2008 .

[44]  P. Moin,et al.  A further study of numerical errors in large-eddy simulations , 2003 .