Stochastic Methods In Fluid Mechanics
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Stochastic Methods in Fluid Mechanics
Author: Sergio Chibbaro
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-09-05
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.
Stochastic Processes in Polymeric Fluids
Author: Hans C. Öttinger
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
A SPECTER is haunting the scientific world-the specter of com puters. All the powers of traditional science have entered into a holy alliance to exorcise this specter: puristic theoreticians and tradition alistic experimentalists, editors and referees of prestigious journals, philosophers of science and mathematicians. Where is a pioneering computer simulation that has not been decried as unreliable by its opponents in power? The Computer Manifesto As a result of the enormous progress in computer technology made during the last few decades, computer simulations have become a very powerful and widely applicable tool in science and engineering. The main purpose of this . book is a comprehensive description of the background and possibilities for the application of computer simulation techniques in polymer fluid dynamics. Mod eling and understanding the flow behavior of polymeric liquids on the kinetic theory level is not merely a great intellectual challenge but rather a matter of immense practical importance, for example, in connection with plastics manu facture, processing of foods, and movement of biological fluids. The classical computer simulation technique for static problems in statis tical mechanics is the Monte Carlo method developed in the early 1950s. The name of this method underlines how unusual and strange the idea of using ran dom numbers in the exact sciences is at first glance. However, the Monte Carlo method is a rigorous and efficient means for evaluating moments and static spa tial correlation functions for given probability distributions.
Spectral Methods for Uncertainty Quantification
Author: Olivier Le Maitre
language: en
Publisher: Springer Science & Business Media
Release Date: 2010-03-11
This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic features of these methods which are most useful in dealing with models based on partial differential equations, with special att- tion to models arising in simulations of ?uid ?ows. Implementations are illustrated through applications to elementary problems, as well as more elaborate examples selected from the authors’ interests in incompressible vortex-dominated ?ows and compressible ?ows at low Mach numbers. Spectral stochastic methods are probabilistic in nature, and are consequently rooted in the rich mathematical foundation associated with probability and measure spaces. Despite the authors’ fascination with this foundation, the discussion only - ludes to those theoretical aspects needed to set the stage for subsequent applications. The book is authored by practitioners, and is primarily intended for researchers or graduate students in computational mathematics, physics, or ?uid dynamics. The book assumes familiarity with elementary methods for the numerical solution of time-dependent, partial differential equations; prior experience with spectral me- ods is naturally helpful though not essential. Full appreciation of elaborate examples in computational ?uid dynamics (CFD) would require familiarity with key, and in some cases delicate, features of the associated numerical methods. Besides these shortcomings, our aim is to treat algorithmic and computational aspects of spectral stochastic methods with details suf?cient to address and reconstruct all but those highly elaborate examples.