[PDF] Energy Conserving Discrete Boltzmann Equation For Nonideal Systems eBook

Author : S. Succi
Publisher : Oxford University Press
Page : 308 pages
File Size : 26,82 MB
Release : 2001-06-28
Category : Mathematics
ISBN : 9780198503989

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Certain forms of the Boltzmann equation, have emerged, which relinquish most mathematical complexities of the true Boltzmann equation. This text provides a detailed survey of Lattice Boltzmann equation theory and its major applications.

Author : Nicola Bellomo
Publisher : World Scientific
Page : 320 pages
File Size : 50,8 MB
Release : 2003
Category : Science
ISBN : 9789812796905

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This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community. Contents: From the Boltzmann Equation to Discretized Kinetic Models (N Bellomo & R Gatignol); Discrete Velocity Models for Gas Mixtures (C Cercignani); Discrete Velocity Models with Multiple Collisions (R Gatignol); Discretization of the Boltzmann Equation and the Semicontinuous Model (L Preziosi & L Rondoni); Semi-continuous Extended Kinetic Theory (W Koller); Steady Kinetic Boundary Value Problems (H Babovsky et al.); Computational Methods and Fast Algorithms for the Boltzmann Equation (L Pareschi); Discrete Velocity Models and Dynamical Systems (A Bobylev & N Bernhoff); Numerical Method for the Compton Scattering Operator (C Buet & S Cordier); Discrete Models of the Boltzmann Equation in Quantum Optics and Arbitrary Partition of the Velocity Space (F Schrrer). Readership: Higher level postgraduates in applied mathematics.

Author : Laure Saint-Raymond
Publisher : Springer
Page : 203 pages
File Size : 11,43 MB
Release : 2009-04-20
Category : Science
ISBN : 3540928472

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The aim of this book is to present some mathematical results describing the transition from kinetic theory, and, more precisely, from the Boltzmann equation for perfect gases to hydrodynamics. Different fluid asymptotics will be investigated, starting always from solutions of the Boltzmann equation which are only assumed to satisfy the estimates coming from physics, namely some bounds on mass, energy and entropy.

Author : Murray Wachman
Publisher :
Page : 36 pages
File Size : 25,77 MB
Release : 1966
Category : Kinetic theory of gases
ISBN :

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A numerical method for the solution of the non-linear Boltzmann equation for hard sphere molecules is developed, in which approximations are made only in the sense of numerical truncations. This is an extension of the work on the linearized Boltzmann equation previously reported in AD-604 749. The distribution function is evaluated at a three-dimensional grid of distinct velocity points. A five fold Gaussian quadrature is performed to evaluate the derivatives at these points. The distribution function is then evaluated at t sub o + delta t by solving a system of first order ordinary differential equations. In the non-linear case the grid is no longer closed, and the procedure to circumvent the difficulty is described. In the present paper, this technique is applied to the problem of non-linear, homogeneous, pseudo-shock relaxation. (Author).

Author : David Packwood
Publisher :
Page : pages
File Size : 19,41 MB
Release : 2012
Category :
ISBN :

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Lattice Boltzmann methods are a fully discrete model and numerical method for simulating fluid dynamics, historically they have been developed as a continuation of lattice gas systems. Another route to a lattice Boltzmann system is a discrete approximation to the Boltzmann equation. An analysis of lattice Boltzmann systems is usually performed from one of these directions. In this thesis the lattice Boltzmann method is presented ab initio as a fully discrete system in its own right. Using the Invariant Manifold hypothesis the microscopic and macroscopic fluid dynamics arising from such a model are found. In particular this analysis represents a validation for lattice Boltzmann methods far from equilibrium. Far from equilibrium, at high Reynolds or Mach numbers, lattice Boltzmann methods can exhibit stability problems. In this work a conditional stability theorem for lattice Boltzmann methods is established. Furthermore several practical numerical techniques for stabilizing lattice Boltzmann schemes are tested.

Author : Sauro Succi
Publisher : Oxford University Press
Page : 784 pages
File Size : 49,12 MB
Release : 2018-04-13
Category : Technology & Engineering
ISBN : 0192538853

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Flowing matter is all around us, from daily-life vital processes (breathing, blood circulation), to industrial, environmental, biological, and medical sciences. Complex states of flowing matter are equally present in fundamental physical processes, far remote from our direct senses, such as quantum-relativistic matter under ultra-high temperature conditions (quark-gluon plasmas). Capturing the complexities of such states of matter stands as one of the most prominent challenges of modern science, with multiple ramifications to physics, biology, mathematics, and computer science. As a result, mathematical and computational techniques capable of providing a quantitative account of the way that such complex states of flowing matter behave in space and time are becoming increasingly important. This book provides a unique description of a major technique, the Lattice Boltzmann method to accomplish this task. The Lattice Boltzmann method has gained a prominent role as an efficient computational tool for the numerical simulation of a wide variety of complex states of flowing matter across a broad range of scales; from fully-developed turbulence, to multiphase micro-flows, all the way down to nano-biofluidics and lately, even quantum-relativistic sub-nuclear fluids. After providing a self-contained introduction to the kinetic theory of fluids and a thorough account of its transcription to the lattice framework, this text provides a survey of the major developments which have led to the impressive growth of the Lattice Boltzmann across most walks of fluid dynamics and its interfaces with allied disciplines. Included are recent developments of Lattice Boltzmann methods for non-ideal fluids, micro- and nanofluidic flows with suspended bodies of assorted nature and extensions to strong non-equilibrium flows beyond the realm of continuum fluid mechanics. In the final part, it presents the extension of the Lattice Boltzmann method to quantum and relativistic matter, in an attempt to match the major surge of interest spurred by recent developments in the area of strongly interacting holographic fluids, such as electron flows in graphene.