Kinetic Equations: Volume 1: Boltzmann Equation, Maxwell Models, and Hydrodynamics beyond Navier–Stokes, Alexander V. Bobylev
Автор: Sauro Succi Название: The Lattice Boltzmann Equation ISBN: 0199592357 ISBN-13(EAN): 9780199592357 Издательство: Oxford Academ Рейтинг: Цена: 70230.00 T Наличие на складе: Есть Описание: An introductory textbook to Lattice Boltzmann methods in computational fluid dynamics, aimed at a broad audience of scientists working with flowing matter. LB has known a burgeoning growth of applications, especially in connection with the simulation of complex flows, and also on the methodological side.
Автор: Valery I. Klyatskin Название: Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1 ISBN: 3319075861 ISBN-13(EAN): 9783319075860 Издательство: Springer Рейтинг: Цена: 148020.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings.
Автор: Igor V Lebed Название: The Foundations of Multimoment Hydrodynamics: Part 1: Ideas, Methods and Equations ISBN: 1536133647 ISBN-13(EAN): 9781536133646 Издательство: Nova Science Рейтинг: Цена: 232310.00 T Наличие на складе: Невозможна поставка. Описание: The Boltzmann hypothesis of molecular chaos (Stosszahlansatz) closes the classic kinetic equation. Equations of classic hydrodynamics that directly follow from the Boltzmann equation inevitably contain the error involved in the derivation of classic kinetic equation. The physical meaning of the error introduced by the Boltzmann hypothesis in the equations of hydrodynamics is as follows. Only the Boltzmann hypothesis makes it possible to build hydrodynamics for only three lower principal hydrodynamic values, say, density, velocity, and temperature. The Boltzmann hypothesis also excludes objectively existing higher principal hydrodynamic values from participation in the formation of hydrodynamics equations. Thus, the possibility of the improvement of classic hydrodynamics equations should be sought toward an increase in the number of principal hydrodynamic values. The idea of separating gas particles into pairs allows using the higher principal hydrodynamic values when constructing equations of hydrodynamics. Two particles are called a pair if they either move towards the collision with each other or fly apart after the collision with each other. Created formalism allows hydrodynamics equations to be built with an arbitrary number of principal hydrodynamic values specified beforehand. As expected, classic hydrodynamics experience difficulties when interpreting states of medium, which are far removed from the state of statistical equilibrium. A detailed evaluation of the results of direct numerical integration of the Navier-Stokes equations against experimental data in an unstable regime of flow around a sphere reveals a number of obvious discrepancies. Most importantly, observed transition from a stable regime of flow to turbulence is invariably accompanied by the appearance of regular vortex shedding. There are no such experiments in which chaotic regime replaces regular stable flow bypassing vortex shedding modes. On the contrary, calculated transition from a regular stable mode to the chaotic deterministic one occurs directly, bypassing the vortex shedding. Thus, the solutions to the Navier-Stokes equations lead the development of instability along the direction of incompatibility with the experiment. The movement in the wrong direction doesnt allow these solutions to interpret the turbulence correctly. Equations of multimoment hydrodynamics are created to solve these problems. The solutions to the Navier-Stokes equations suggest a single scenario for the development of instability; this is the Landau-Hopf scenario. The Landau-Hopf scenario is simple and uncomplicated. It interprets the process of development of instability as a sequence of transitions from one stable solution to another. On the contrary, the appearance of a vortex street is a complex multistage physical phenomenon. An increase in the number of principal hydrodynamic values in the equations of multimoment hydrodynamics essentially enriches the scenario of development of instability by new actions. These actions are not available for solutions to the equations of three-moment classic hydrodynamics. It follows that the Landau-Hopf scenario does not have the slightest prospect of reproducing the phenomenon of vortex shedding. An analysis of the experimental data shows that the transition to turbulence occurs as a result of chaotic distortion of the regular vortex shedding in any shear flow (wakes and jets, pipes and channels, shear layers, etc.). It is likely that this is the only mechanism for the development of turbulence. In this case, the turbulence of the shear flow is nothing else but a regular regime of vortex shedding distorted by excessively overgrown stochastic fluctuations.
Автор: Alessandro Manacorda Название: Lattice Models for Fluctuating Hydrodynamics in Granular and Active Matter ISBN: 3030069710 ISBN-13(EAN): 9783030069711 Издательство: Springer Рейтинг: Цена: 93160.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book investigates the common nature of granular and active systems, which is rooted in their intrinsic out-of-equilibrium behavior, with the aim of finding minimal models able to reproduce and predict the complex collective behavior observed in experiments and simulations. Granular and active matter are among the most studied systems in out-of-equilibrium statistical physics. The book guides readers through the derivation of a fluctuating hydrodynamic description of granular and active matter by means of controlled and transparent mathematical assumptions made on a lattice model. It also shows how a macroscopic description can be provided from microscopic requirements, leading to the prediction of collective states such as cooling, swarming, clustering and the transitions among them. The analytical and numerical results shed new light on the physical connection between the local, microscopic properties of few particles and the macroscopic collective motion of the whole system.
The series is devoted to the publication of high-level monographs and specialized graduate texts which cover the whole spectrum of applied mathematics, including its numerical aspects. The focus of the series is on the interplay between mathematical and numerical analysis, and also on its applications to mathematical models in the physical and life sciences.
The aim of the series is to be an active forum for the dissemination of up-to-date information in the form of authoritative works that will serve the applied mathematics community as the basis for further research.
Editorial Board
Remi Abgrall, Universitat Zurich, Switzerland Jose Antonio Carrillo de la Plata, University of Oxford, UK Jean-Michel Coron, Universite Pierre et Marie Curie, Paris, France Athanassios S. Fokas, Cambridge University, UK Irene Fonseca, Carnegie Mellon University, Pittsburgh, USA
Автор: Valery I. Klyatskin Название: Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, Volume 1 ISBN: 3319357751 ISBN-13(EAN): 9783319357751 Издательство: Springer Рейтинг: Цена: 121890.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings.
Автор: Liming Yang; Yan Wang; Zhen Chen Название: Lattice Boltzmann and Gas Kinetic Flux Solvers ISBN: 9811224684 ISBN-13(EAN): 9789811224683 Издательство: World Scientific Publishing Рейтинг: Цена: 132000.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Computational fluid dynamics (CFD) has been widely applied in a wide variety of industrial applications, including aeronautics, astronautics, energy, chemical, pharmaceuticals, power and petroleum.This unique compendium documents the recent developments in CFD based on kinetic theories, introducing flux reconstruction strategies of kinetic methods for the simulation of complex incompressible and compressible flows, namely the lattice Boltzmann and the gas kinetic flux solvers (LBFS or GKFS). LBFS and GKFS combine advantages of both Navier-Stokes (N-S) solvers and kinetic solvers.Detailed derivations, evaluations and applications of LBFS and GKFS, and their advantages over conventional flux reconstruction strategies are analyzed and discussed in the volume.The must-have reference text is useful for scholars, researchers, professionals and students who are keen in CFD methods and numerical simulations.
Автор: Matteo Colangeli Название: From Kinetic Models to Hydrodynamics ISBN: 146146305X ISBN-13(EAN): 9781461463054 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: From Kinetic Models to Hydrodynamics serves as an introduction to the asymptotic methods necessary to obtain hydrodynamic equations from a fundamental description using kinetic theory models and the Boltzmann equation. The work is a survey of an active research area, which aims to bridge time and length scales from the particle-like description inherent in Boltzmann equation theory to a fully established "continuum" approach typical of macroscopic laws of physics.The author sheds light on a new method-using invariant manifolds-which addresses a functional equation for the nonequilibrium single-particle distribution function. This method allows one to find exact and thermodynamically consistent expressions for: hydrodynamic modes; transport coefficient expressions for hydrodynamic modes; and transport coefficients of a fluid beyond the traditional hydrodynamic limit. The invariant manifold method paves the way to establish a needed bridge between Boltzmann equation theory and a particle-based theory of hydrodynamics. Finally, the author explores the ambitious and longstanding task of obtaining hydrodynamic constitutive equations from their kinetic counterparts. The work is intended for specialists in kinetic theory-or more generally statistical mechanics-and will provide a bridge between a physical and mathematical approach to solve real-world problems.
Автор: Eu Название: Kinetic Theory of Nonequilibrium Ensembles, Irreversible Thermodynamics, and Generalized Hydrodynamics ISBN: 3319411527 ISBN-13(EAN): 9783319411521 Издательство: Springer Рейтинг: Цена: 104480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick.
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