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Über dieses Buch

Since their first introduction in natural sciences through the work of Einstein on Brownian motion in 1905 and further works, in particular by Langevin, Smoluchowski and others, stochastic processes have been used in several areas of science and technology. For example, they have been applied in chemical studies, or in fluid turbulence and for combustion and reactive flows. The articles in this book provide a general and unified framework in which stochastic processes are presented as modeling tools for various issues in engineering, physics and chemistry, with particular focus on fluid mechanics and notably dispersed two-phase flows. The aim is to develop what can referred to as stochastic modeling for a whole range of applications.



Mathematical background on stochastic processes

As mentioned in the introduction to this volume, the purpose of the formation was mainly to provide an in-depth presentation of stochastic processes as modelling tools. The chosen standpoint is thus a physical point of view. However, it has also been emphasised that, in order to be able to follow the details of specific models and build bridges between different subjects where new ideas related to stochastic modelling can appear, researchers must have a sound knowledge of the mathematical properties of stochastic processes. This represents a middle-of-the-road approach. Indeed, even though the subject is still relatively young, a vast mathematical literature exists on stochastic processes (Arnold, 1974; Klebaner, 1998; Oksendal, 1995; Karatzas and Shreve, 1991) but these works may not be easily accessible to physically-oriented readers. On the other hand, stochastic processes have been used in separated fields of Applied Physics but not always with a clear presentation or resorting to some ‘recipes’. Yet, in recent decades, attempts have been made to come up with improved introductions to stochastic processes in the Physics community.
Jean-Pierre Minier, Sergio Chibbaro

Stochastic modelling of polydisperse turbulent two-phase flows

In this chapter we focus on the Lagrangian stochastic approach to turbulent polydispersed two-phase flows. This chapter has several objectives. The first important objective is to use this interesting and relevant physical subject to apply the mathematical techniques presented in the first chapter. It is important to understand how the stochastic approach actually works and what are the main issues related to it. The second objective is to offer the reader the possibility to become more familiar with particle-laden flows, a sub-field of fluid mechanics which is quite fascinating and important in many industrial and environmental applications. Third, this chapter offers a comprehensive but concise description of the whole formalism needed to develop the stochastic approach to turbulent polydispersed flows. While Lagrangian stochastic models have been put forward since the sixties for single-phase flows (Lundgren, 1967) and applied with success to reactive flows since the seventies (Pope, 1985, 1994), their development and diffusion for polydispersed flows is much more recent (Minier and Pozorski, 1999; Minier and Peirano, 2001). In this sense, the formalism generalises the reactive flow one. Finally, the study of a typical industrial application is shown. This test-case helps to clarify that stochastic models can be used to investigate realistic phenomena (they are computationally performing), and, at the same time, give satisfactory answers in complex problems, for which less refined approaches like two-fluid models are not able to give acceptable results.
Sergio Chibbaro, Jean-Pierre Minier

Quadrature-Based Moment Methods for Polydisperse Multiphase Flows

We provide a brief introduction to quadrature-based moment methods that can be used to model polydisperse multiphase flows. A more detailed description can be found in Marchisio and Fox (2013). Our focus here is to introduce the reader to the principal topics and to provide insight into the numerial algorithms. An example application of gas-particle flow is used to illustrate the methods.
Rodney O. Fox

Mesoscopic particle models of fluid flows

We review the general ideas behind coarse-grained representations of fluid dynamics, with special focus on two mesoscopic techniques which have proven particularly successful over the last two decades for the simulation of complex fluid flows, namely Dissipative Particle Dynamics and the Lattice Boltzmann method.
Sauro Succi
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