A Numerical Study of a Class of LES Models

This paper tests if two related types of LES models satisfy some simple necessary conditions for acceptability: replication of laminar flows and boundedness of total kinetic energy. The considered LES models are based on the approximation of the Fourier transform of the Gaussian filter by a simpler function. One uses a Taylor polynomial approximation (Taylor LES model), whereas the other model is obtained by a rational approximation (rational LES model). The numerical experiments at high Reynolds number 2D and 3D driven cavity flows show a blow up of the total kinetic energy of the solutions computed with the Taylor LES model. The details of the calculations and the review of this model's derivation point to this blow up being clearly a shortcoming of the model. In contrast, the rational LES model gives solutions with bounded total kinetic energy. In addition, the large eddies are well captured on a coarse grid.

[1]  Gunar Matthies,et al.  The Inf-Sup Condition for the Mapped Qk−Pk−1disc Element in Arbitrary Space Dimensions , 2002, Computing.

[2]  Stefan Turek,et al.  Efficient Solvers for Incompressible Flow Problems - An Algorithmic and Computational Approach , 1999, Lecture Notes in Computational Science and Engineering.

[3]  P. Kloucek,et al.  Stability of the fractional step T-scheme for the nonstationary Navier-Stokes equations , 1994 .

[4]  S. Pope.  Turbulent Flows: FUNDAMENTALS , 2000 .

[5]  J. Ferziger,et al.  Evaluation of subgrid-scale models using an accurately simulated turbulent flow , 1979, Journal of Fluid Mechanics.

[6]  J. Szmelter.  Incompressible flow and the finite element method , 2001 .

[7]  R. Glowinski,et al.  Numerical methods for the navier-stokes equations. Applications to the simulation of compressible and incompressible viscous flows , 1987 .

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

[9]  Problems and solutions (generalized and FEM) related to rapid and impulsive changes for incompressible flows , 1997 .

[10]  R. Luettich,et al.  Low and Moderate Reynolds Number Transient Flow Simulations Using Space Filtered Navier-Stokes Equations , 1994 .

[11]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[12]  U. Ghia,et al.  High-Re solutions for incompressible flow using the Navier-Stokes equations and a multigrid method , 1982 .

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

[14]  Volker John,et al.  International Journal for Numerical Methods in Fluids Numerical Performance of Smoothers in Coupled Multigrid Methods for the Parallel Solution of the Incompressible Navier – Stokes Equations , 2022 .

[15]  Michel Fortin.  Finite element solution of the Navier—Stokes equations , 1993, Acta Numerica.

[16]  P. Saugat.  Large eddy simulation for incompressible flows , 2001 .

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

[18]  Joel H. Ferziger,et al.  Status of Large Eddy Simulation: Results of a Workshop , 1997 .

[19]  J. Koseff,et al.  A dynamic mixed subgrid‐scale model and its application to turbulent recirculating flows , 1993 .

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

[21]  Gunar Matthies,et al.  International Journal for Numerical Methods in Fluids Higher-order Finite Element Discretizations in a Benchmark Problem for Incompressible Flows , 2022 .

[22]  M. Germano.  A proposal for a redefinition of the turbulent stresses in the filtered Navier–Stokes equations , 1986 .

[23]  Rolf Rannacher,et al.  Finite Element Methods for the Incompressible Navier-Stokes Equations , 2000 .