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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.
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.
The global community requires increasing supplies of cheap, clean, and transportable energy. Combustion devices currently provide for the bulk of these energy needs, but their operation also produces a variety of undesirable consequences such as instabilities, noise, and pollution. Accordingly, new energy strategies emphasize the importance of improving combustion device designs. The design process itself remains a particular challenge, however, and not even the newest designs can be said to optimally control for the products of combustion. The technique of large eddy simulation (LES) provides a framework for improving this device design process. But while a variety of LES combustion models have been proposed, no champion model yet exists that could be considered truly predictive and regime independent. This work seeks to improve the accuracy and the predictive capabilities of reactive LES. The flamelet approach is accepted here as a working baseline model because of its ability to represent asymptotic combustion physics. Several deficiencies exist in current flamelet implementations, however. First, premixed flamelet LES models are underdeveloped, and cannot yet accurately describe the full range of burning behavior seen in many devices. Second, because the flamelet approach is asymptotic in nature, it only accounts for a single combustion regime of a time. Flamelet methods therefore fail when applied to arbitrarily complex or partially premixed flows. In the first part of this work, a generalized flamelet transformation is derived. This transformation describes how chemical source terms are balanced in the asymptotic limit of either the non-premixed, the premixed, or the auto-ignition regime. The transformation is then used to formulate a method of determining which combustion regime exists locally in a simulation. The indicator is validated using fully resolved triple flame simulations, and is applied in a flamelet based LES of a low swirl burner. The simulations show that the indicator describes combustion regimes more accurately than the traditional flame index. Next, a level set equation is formalized for use in premixed combustion LES. Level set methods are employed in the proposed generalized model because premixed flame fronts tend to be significantly underresolved in LES. Typical transport equation approaches are consequently subject to significant numerical error. Level set methods have historically been problematic, however, when applied in the context of a filtering procedure. Once it has been derived, the appropriate front tracking equation is used to formulate a dynamic model for the turbulent burning velocity of a flame. This dynamic burning velocity model is validated in a direct numerical simulation of a propagating turbulent front, and applied in an LES of a premixed turbulent jet flame. Finally, premixed flamelet models are considered with respect to the issue of flame structure. A new variation of a coupled level set and progress variable approach is proposed in an effort to improve descriptions of turbulence and front interactions. This method is tested using a direct numerical simulation of a premixed turbulent flame propagating in the thin reaction zones regime. The new coupling approach is then applied in an LES of a spray fueled lean direct injection combustor. This simulation makes use of both the new coupled premixed approach, and a traditional non-premixed approach. These approaches are integrated using the proposed combustion regime indicator.
First concise textbook on Large-Eddy Simulation, a very important method in scientific computing and engineering From the foreword to the third edition written by Charles Meneveau: "... this meticulously assembled and significantly enlarged description of the many aspects of LES will be a most welcome addition to the bookshelves of scientists and engineers in fluid mechanics, LES practitioners, and students of turbulence in general."

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