Author | John, Volker. author |
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Title | Large Eddy Simulation of Turbulent Incompressible Flows [electronic resource] : Analytical and Numerical Results for a Class of LES Models / by Volker John |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004 |
Connect to | http://dx.doi.org/10.1007/978-3-642-18682-0 |
Descript | XII, 261 p. 24 illus. online resource |
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 โ ? 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 -- 7 Discretisation of the LES Models -- 7.1 Discretisation in Time by the Crank-Nicolson or the Fractional-Step ?-Scheme -- 7.2 The Variational Formulation and the Linearisation of the Time-Discrete Problem -- 7.3 The Discretisation in Space -- 7.4 Inf-Sup Stable Pairs of Finite Element Spaces -- 7.5 The Upwind Stabilisation for Lowest Order Non-Conforming Finite Elements -- 7.6 The Implementation of the Slip With Friction and Penetration With Resistance Boundary Condition -- 7.7 The Discretisation of the Auxiliary Problem in the Rational LES Model -- 7.8 The Computation of the Convolution in the Rational LES Model -- 7.9 The Evaluation of Integrals, Numerical Quadrature -- 8 Error Analysis of Finite Element Discretisations of the LES Models -- 8.1 The Smagorinsky Model -- 8.2 The Taylor LES Model -- 9 The Solution of the Linear Systems -- 9.1 The Fixed Point Iteration for the Solution of Linear Systems -- 9.2 Flexible GMRES (FGMRES) With Restart -- 9.3 The Coupled Multigrid Method -- 9.4 The Solution of the Auxiliary Problem in the Rational LES Model -- 10 A Numerical Study of a Necessary Condition for the Acceptability of LES Models -- 10.1 The Flow Through a Channel -- 10.2 The Failure of the Taylor LES Model -- 10.3 The Rational LES Model -- 10.4 Summary -- 11 A Numerical Study of the Approximation of Space Averaged Flow Fields by the Considered LES Models -- 11.1 A Mixing Layer Problem in Two Dimensions -- 11.2 A Mixing Layer Problem in Three Dimensions -- 12 Problems for Further Investigations -- 13 Notations -- References