Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics,' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely.

obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each· chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C~apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied (§1-3). A first detailed study of homogeneous turbulent flows follows (§4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in §5 with the l"Csulting ~alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms (§ 1), their general dynamics (§2) with the particular case of homogeneous, isotropie turbulence (§3) whel"C the so-called Kolmogorov's assumptions are discussed at length.

Turbulence modeling both addresses a fundamental problem in physics, 'the last great unsolved problem of classical physics,' and has far-reaching importance in the solution of difficult practical problems from aeronautical engineering to dynamic meteorology. However, the growth of supercom puter facilities has recently caused an apparent shift in the focus of tur bulence research from modeling to direct numerical simulation (DNS) and large eddy simulation (LES). This shift in emphasis comes at a time when claims are being made in the world around us that scientific analysis itself will shortly be transformed or replaced by a more powerful 'paradigm' based on massive computations and sophisticated visualization. Although this viewpoint has not lacked ar ticulate and influential advocates, these claims can at best only be judged premature. After all, as one computational researcher lamented, 'the com puter only does what I tell it to do, and not what I want it to do. ' In turbulence research, the initial speculation that computational meth ods would replace not only model-based computations but even experimen tal measurements, have not come close to fulfillment. It is becoming clear that computational methods and model development are equal partners in turbulence research: DNS and LES remain valuable tools for suggesting and validating models, while turbulence models continue to be the preferred tool for practical computations. We believed that a symposium which would reaffirm the practical and scientific importance of turbulence modeling was both necessary and timely.

This title provides the fundamental bases for developing turbulence models on rational grounds. The main different methods of approach are considered, ranging from statistical modelling at various degrees of complexity to numerical simulations of turbulence. Each of these various methods has its own specific performances and limitations, which appear to be complementary rather than competitive. After a discussion of the basic concepts, mathematical tools and methods for closure, the book considers second order closure models. Emphasis is placed upon this approach because it embodies potentials for clarifying numerous problems in turbulent shear flows. Simpler, generally older models are then presented as simplified versions of the more general second order models. The influence of extra physical parameters is also considered. Finally, the book concludes by examining large Eddy numerical simulations methods. Given the book’s comprehensive coverage, those involved in the theoretical or practical study of turbulence problems in fluids will find this a useful and informative read.

Advanced Approaches in Turbulence: Theory, Modeling, Simulation and Data Analysis for Turbulent Flows focuses on the updated theory, simulation and data analysis of turbulence dealing mainly with turbulence modeling instead of the physics of turbulence. Beginning with the basics of turbulence, the book discusses closure modeling, direct simulation, large eddy simulation and hybrid simulation. The book also covers the entire spectrum of turbulence models for both single-phase and multi-phase flows, as well as turbulence in compressible flow. Turbulence modeling is very extensive and continuously updated with new achievements and improvements of the models. Modern advances in computer speed offer the potential for elaborate numerical analysis of turbulent fluid flow while advances in instrumentation are creating large amounts of data. This book covers these topics in great detail. - Covers the fundamentals of turbulence updated with recent developments - Focuses on hybrid methods such as DES and wall-modeled LES - Gives an updated treatment of numerical simulation and data analysis

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.

1. 1 Scope of the Study The detailed and reasonably accurate computation of large scale turbulent flows has become increasingly important in geophysical and engi neering applications in recent years. The definition of water quality management policies for reservoirs, lakes, estuaries, and coastal waters, as well as the design of cooling ponds and solar ponds, requires an ade quate quantitative description of turbulent flows. When the diffusion of some tracer (be it active, such as temperature or salinity, or passive, such as dissolved oxygen) is of relevance to a specific application, the proper determination of the effects of turbulent transport processes has paramount importance. Thus, for instance, the proper understanding of lake and reservoir dynamics requires, as a first step, the ability to simulate turbulent flows. Applications in other areas of geophysical research, such as meteorology and oceanography are easily identified and large in number. It should be stressed that, in this context, the analyst seeks predictive ability to a certain extent. Accordingly, the need for simulation models that closely resemble the natural processes to be repre sented has recently become more evident. Since the late 1960s considerable effort has been devoted to the development of models for the simulation of complex turbulent flows. This has resulted in the establishment of two approaches which have been, or 2 have the potential for being, applied to problems of engineering and geophysical interest.

After a brief review of the more popular turbulence models, the author presents and discusses accurate and efficient numerical methods for solving the boundary-layer equations with turbulence models based on algebraic formulas (mixing length, eddy viscosity) or partial-differential transport equations. A computer program employing the Cebeci-Smith model and the k-e model for obtaining the solution of two-dimensional incompressible turbulent flows without separation is discussed in detail and is presented in the accompanying CD.

A comprehensive account of advanced RANS turbulence models including numerous applications to complex flows in engineering and the environment.

The present book contains contributions presented at the Fourth Symposium on Hybrid RANS-LES Methods, held in Beijing, China, 28-30 September 2011, being a continuation of symposia taking place in Stockholm (Sweden, 2005), in Corfu (Greece, 2007), and Gdansk (Poland, 2009). The contributions to the last two symposia were published as NNFM, Vol. 97 and Vol. 111. At the Beijing symposium, along with seven invited keynotes, another 46 papers (plus 5 posters) were presented addressing topics on Novel turbulence-resolving simulation and modelling, Improved hybrid RANS-LES methods, Comparative studies of difference modelling methods, Modelling-related numerical issues and Industrial applications.. The present book reflects recent activities and new progress made in the development and applications of hybrid RANS-LES methods in general.