Large Eddy Simulation of Turbulent Incompressible Flows: Analytical and Numerical Results for a Class of LES Models [Paperback]

Large eddy simulation (LES) seeks to simulate the large structures of a turbulent flow. This is the first monograph which considers LES from a mathematical point of view. It concentrates on LES models for which mathematical and numerical analysis is already available and on related LES models. Most of the available analysis is given in detail, the implementation of the LES models into a finite element code is described, the efficient solution of the discrete systems is discussed and numerical studies with the considered LES models are presented.

1 Introduction.- 1.1 Short Remarks on the Nature and Importance of Turbulent Flows.- 1.2 Remarks on the Direct Numerical Simulation (DNS) and the k  ? Model.- 1.3 Large Eddy Simulation (LES).- 1.4 Contents of this Monograph.- 2 Mathematical Tools and Basic Notations.- 2.1 Function Spaces.- 2.2 Some Tools from Analysis and Functional Analysis.- 2.3 Convolution and Fourier Transform.- 2.4 Notations for Matrix-Vector Operations.- 3 The Space Averaged Navier-Stokes Equations and the Commutation Error.- 3.1 The Incompressible Navier-Stokes Equations.- 3.2 The Space Averaged Navier-Stokes Equations in the Case ? = ?d.- 3.3 The Space Averaged Navier-Stokes Equations in a Bounded Domain.- 3.4 The Gaussian Filter.- 3.5 Error Estimate of the Commutation Error Term in the Lp (?d) Norm.- 3.6 Error Estimate of the Commutation Error Term in the H-1 (?) Norm.- 3.7 Error Estimate for a Weak Form of the Commutation Error.- 4 LES Models Which are Based on Approximations in Wave Number Space.- 4.1 Eddy Viscosity Models.- 4.2 Modelling of the Large Scale and Cross Terms.- 4.3 Models for the Subgrid Scale Term.- 5 The Variational Formulation of the LES Models.- 5.1 The Weak Formulation of the Equations.- 5.2 Boundary Conditions for the LES Models.- 5.3 Function Spaces for the LES Models.- 6 Existence and Uniqueness of Solutions of the LES Models.- 6.1 The Smagorinsky Model.- 6.2 The Taylor LES Model.- 6.3 The Rational LES Model“=