The LES-method is rapidly developing in many practical applications in engineering The mathematical background is presented here for the first time in book form by one of the leaders in the field

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.

This book presents a comprehensive overview of the mathematics and physics behind the simulation of turbulent flows and discusses in detail (i) the phenomenology of turbulence in fluid dynamics, (ii) the role of direct and large-eddy simulation in predicting these dynamics, (iii) the multiple considerations underpinning subgrid modelling, and, (iv) the issue of validation and reliability resulting from interacting modelling and numerical errors.

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."

Large-Eddy Simulations of Turbulence is a reference for LES, direct numerical simulation and Reynolds-averaged Navier-Stokes simulation.

Providing a comprehensive grounding in the subject of turbulence, Statistical Theory and Modeling for Turbulent Flows develops both the physical insight and the mathematical framework needed to understand turbulent flow. Its scope enables the reader to become a knowledgeable user of turbulence models; it develops analytical tools for developers of predictive tools. Thoroughly revised and updated, this second edition includes a new fourth section covering DNS (direct numerical simulation), LES (large eddy simulation), DES (detached eddy simulation) and numerical aspects of eddy resolving simulation. In addition to its role as a guide for students, Statistical Theory and Modeling for Turbulent Flows also is a valuable reference for practicing engineers and scientists in computational and experimental fluid dynamics, who would like to broaden their understanding of fundamental issues in turbulence and how they relate to turbulence model implementation. Provides an excellent foundation to the fundamental theoretical concepts in turbulence. Features new and heavily revised material, including an entire new section on eddy resolving simulation. Includes new material on modeling laminar to turbulent transition. Written for students and practitioners in aeronautical and mechanical engineering, applied mathematics and the physical sciences. Accompanied by a website housing solutions to the problems within the book.

It is a truism that turbulence is an unsolved problem, whether in scientific, engin eering or geophysical terms. It is strange that this remains largely the case even though we now know how to solve directly, with the help of sufficiently large and powerful computers, accurate approximations to the equations that govern tur bulent flows. The problem lies not with our numerical approximations but with the size of the computational task and the complexity of the solutions we gen erate, which match the complexity of real turbulence precisely in so far as the computations mimic the real flows. The fact that we can now solve some turbu lence in this limited sense is nevertheless an enormous step towards the goal of full understanding. Direct and large-eddy simulations are these numerical solutions of turbulence. They reproduce with remarkable fidelity the statistical, structural and dynamical properties of physical turbulent and transitional flows, though since the simula tions are necessarily time-dependent and three-dimensional they demand the most advanced computer resources at our disposal. The numerical techniques vary from accurate spectral methods and high-order finite differences to simple finite-volume algorithms derived on the principle of embedding fundamental conservation prop erties in the numerical operations. Genuine direct simulations resolve all the fluid motions fully, and require the highest practical accuracy in their numerical and temporal discretisation. Such simulations have the virtue of great fidelity when carried out carefully, and repre sent a most powerful tool for investigating the processes of transition to turbulence.

With applications to climate, technology, and industry, the modeling and numerical simulation of turbulent flows are rich with history and modern relevance. The complexity of the problems that arise in the study of turbulence requires tools from various scientific disciplines, including mathematics, physics, engineering and computer science. Authored by two experts in the area with a long history of collaboration, this monograph provides a current, detailed look at several turbulence models from both the theoretical and numerical perspectives. The k-epsilon, large-eddy simulation and other models are rigorously derived and their performance is analyzed using benchmark simulations for real-world turbulent flows. Mathematical and Numerical Foundations of Turbulence Models and Applications is an ideal reference for students in applied mathematics and engineering, as well as researchers in mathematical and numerical fluid dynamics. It is also a valuable resource for advanced graduate students in fluid dynamics, engineers, physical oceanographers, meteorologists and climatologists.

Der Band enthält den Abschlußbericht des DFG-Schwerpunktprogramms "Flußsimulation mit Höchstleistungsrechnern". Es führt die Arbeiten fort, die schon als Band 38 in der Reihe "Notes on Numerical Fluid Mechanics" erschienen sind.Work is reported, which was sponsored by the Deutsche Forschungsgemeinschaft from 1993 to 1995. Scientists from numerical mathematics, fluid mechanics, aerodynamics, and turbomachinery present their work on flow simulation with massively parallel systems, on the direct and large-eddy simulation of turbulence, and on mathematical foundations, general solution techniques and applications. Results are reported from benchmark computations of laminar flow around a cylinder, in which seventeen groups participated.