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Large-Eddy Simulations of Turbulence is a reference for LES, direct numerical simulation and Reynolds-averaged Navier-Stokes simulation.
This volume focuses on the mathematical foundations of LES and its models and provides a connection between the tools of applied mathematics, partial differential equations and LES. A useful entry point into the field for PhD students in applied mathematics, computational mathematics and partial differential equations is offered.
The numerical simulation of turbulent flows is a subject of great practical importance to scientists and engineers. The difficulty in achieving predictive simulations is perhaps best illustrated by the wide range of approaches that have been developed and are still being used by the turbulence modeling community. In this book the authors describe one of these approaches, Implicit Large Eddy Simulation (ILES). ILES is a relatively new approach that combines generality and computational efficiency with documented success in many areas of complex fluid flow. This book synthesizes the theoretical basis of the ILES methodology and reviews its accomplishments. ILES pioneers and lead researchers combine here their experience to present a comprehensive description of the methodology. This book should be of fundamental interest to graduate students, basic research scientists, as well as professionals involved in the design and analysis of complex turbulent flows.
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.
Computational resources have developed to the level that, for the first time, it is becoming possible to apply large-eddy simulation (LES) to turbulent flow problems of realistic complexity. Many examples can be found in technology and in a variety of natural flows. This puts issues related to assessing, assuring, and predicting the quality of LES into the spotlight. Several LES studies have been published in the past, demonstrating a high level of accuracy with which turbulent flow predictions can be attained, without having to resort to the excessive requirements on computational resources imposed by direct numerical simulations. However, the setup and use of turbulent flow simulations requires a profound knowledge of fluid mechanics, numerical techniques, and the application under consideration. The susceptibility of large-eddy simulations to errors in modelling, in numerics, and in the treatment of boundary conditions, can be quite large due to nonlinear accumulation of different contributions over time, leading to an intricate and unpredictable situation. A full understanding of the interacting error dynamics in large-eddy simulations is still lacking. To ensure the reliability of large-eddy simulations for a wide range of industrial users, the development of clear standards for the evaluation, prediction, and control of simulation errors in LES is summoned. The workshop on Quality and Reliability of Large-Eddy Simulations, held October 22-24, 2007 in Leuven, Belgium (QLES2007), provided one of the first platforms specifically addressing these aspects of LES.
Optimal LES modeling is a new approach to the development of subgrid models of turbulence. It has been found to produce accurate LES simulations when based on reliable statistical information. Now, the primary effort in optimal model development is the determination of this statistical information from theoretical considerations, with minimal empirical input. The validity of the theoretically determined statistics is being tested against experimental and DNS data. When small-scales are isotropic, Kolmogorov theory, the quasi-normal approximation and a dynamic procedure allow optimal models to be constructed with no empirical input. Such models have been found to perform well, though the dynamic procedure has not yet been tested in this context. Tests using channel flow DNS show that, except for a region very near the wall, the quasi-normal approximation is valid. Further, for the log-region, a representation for the anisotropy and inhomogeneity of the statistics is being developed. Thus, the above modeling approach can be adapted to near-wall turbulence, except for the thin viscous region. To handle this wall layer, a filtered boundary optimal LES model is being developed and tested.
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