Sagaut Large Eddy Simulation for Incompressible Flows

An Introduction
Erscheinungsjahr 2013
ISBN: 978-3-662-04416-2
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 319 Seiten, eBook

Reihe: Scientific Computation

Still today, turbulence in fluids is considered as one of the most difficult problems of modern physics. Yet we are quite far from the complexity of microscopic molecular physics, since we only deal with Newtonian mechanics laws applied to a continuum, in which the effect of molecular fluctuations has been smoothed out and is represented by molecular-viscosity coefficients. Such a system has a dual behaviour of determinism in the Laplacian sense, and extreme sensitivity to initial conditions because of its very strong non linear character. One does not know, for instance, how to predict the critical Reynolds number of transition to turbulence in a pipe, nor how to compute precisely the drag of a car or an aircraft, even with today's largest computers. 1 We know, since the meteorologist Richardson, numerical schemes allow ing us to solve in a deterministic manner the equations of motion, starting with a given initial state and with prescribed boundary conditions. They are based on moment um and energy balances. However, such aresolution requires formidable computing power, and is only possible for low Reynolds numbers. These Direct-Numerical Simulations may involve calculating the interaction of several million interacting sites. Generally, industrial, natural, or experimental configurations involve Reynolds numbers that are far too large to allow direct simulations,2 and the only possibility then is Large Eddy Simulation, where the small-scale turbulent fluctuations are themselves smoothed out and modelled via eddy-viscosity and diffusivity assumptions.

Zielgruppe

Research

Autoren/Hrsg.

Sagaut, Pierre

Inhaltsverzeichnis

1. Introduction.- 2. Formal Introduction to Scale Separation: Band-Pass Filtering.- 3. Application to Navier—Stokes Equations.- 4. Functional Modeling (Isotropic Case).- 5. Functional Modeling: Extension to Anisotropic Cases.- 6. Structural Modeling.- 7. Numerical Solution: Interpretation and Problems.- 8. Analysis and Validation of Large-Eddy Simulation Data.- 9. Boundary Conditions.- 10. Implementation.- 11. Examples of Applications.- A. Statistical and Spectral Analysis of Turbulence.- A.1 Turbulence Properties.- A.2 Foundations of the Statistical Analysis of Turbulence.- A.2.1 Motivations.- A.2.2 Statistical Average: Definition and Properties.- A.2.3 Ergodicity Principle.- A.2.4 Decomposition of a Turbulent Field.- A.2.5 Isotropic Homogeneous Turbulence.- A.3 Introduction to Spectral Analysis of the Isotropic Turbulent Fields.- A.3.1 Definitions.- A.3.2 Modal Interactions.- A.3.3 Spectral Equations.- A.4 Characteristic Scales of Turbulence.- A.5 Spectral Dynamics of Isotropic Homogeneous Turbulence.- A.5.1 Energy Cascade and Local Isotropy.- A.5.2 Equilibrium Spectrum.- B. EDQNM Modeling.- B.1 Isotropic EDQNM Model.- B.2 Cambon’s Anisotropic EDQNM Model.