Download or read book A Kinetic Approach to Collision Processes in Gases written by P. L. Bhatnagar and published by . This book was released on 1953 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A KINETIC APPROACH TO COLLISION PROCESSES IN GASES I SMALL AMPLITUDE PROCESSES IN CHARGES AND NEUTRAL ONE COMPONENT SYSTEMS written by and published by . This book was released on 1953 with total page 43 pages. Available in PDF, EPUB and Kindle. Book excerpt: This approach appears adequate for the unified treatment of the dynamic properties of gases over a continuous range pressures from the Knudsen limit to the high-pressure limit where the aerodynamic equations are valid. Alterations are made in the collision terms of the Boltzmann equation; each collision conserves particle number, momentum, and energy; persistence of velocities angular dependence may be included. The approach illustrates a technique for a simple model involving the assumption of a collision time independent of velocity; this model is applied to the study of small amplitude oscillations of 1-component ionized and neutral gases. The initial value problem for unbounded space is solved by performing a Fourier transformation of the space variable and Laplace transformation on the time variable. For uncharged gases there results the correct adiabatic limiting law for sound-wave propagation at high pressures. For ionized gases the difference in the nature of the organization in the low-pressure plasma oscillations and in high-pressure sound type oscillations is studied. Two important cases are distinguished. If the wave length of the oscillations is long compared to either the Debye length or the mean free path, a small change in frequency is obtained as the collision frequency varies from zero to infinity. The accompanying absorption is small and reaches its maximum value when the collion frequency equals the plasma frequency. the other case refers to waves shorter than both the Debye length and the mean free path; these waves are characterized by a very heavy absorption.
Download or read book Lattice Boltzmann Modeling of Complex Flows for Engineering Applications written by Andrea Montessori and published by Morgan & Claypool Publishers. This book was released on 2018-02-20 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nature continuously presents a huge number of complex and multi-scale phenomena, which in many cases, involve the presence of one or more fluids flowing, merging and evolving around us. Since its appearance on the surface of Earth, Mankind has tried to exploit and tame fluids for their purposes, probably starting with Hero's machinery to open the doors of the Temple of Serapis in Alexandria to arrive to modern propulsion systems and actuators. Today we know that fluid mechanics lies at the basis of countless scientific and technical applications from the smallest physical scales (nanofluidics, bacterial motility, and diffusive flows in porous media), to the largest (from energy production in power plants to oceanography and meteorology). It is essential to deepen the understanding of fluid behaviour across scales for the progress of Mankind and for a more sustainable and efficient future. Since the very first years of the Third Millennium, the Lattice Boltzmann Method (LBM) has seen an exponential growth of applications, especially in the fields connected with the simulation of complex and soft matter flows. LBM, in fact, has shown a remarkable versatility in different fields of applications from nanoactive materials, free surface flows, and multiphase and reactive flows to the simulation of the processes inside engines and fluid machinery. LBM is based on an optimized formulation of Boltzmann's Kinetic Equation, which allows for the simulation of fluid particles, or rather quasi-particles, from a mesoscopic point of view thus allowing the inclusion of more fundamental physical interactions in respect to the standard schemes adopted with Navier-Stokes solvers, based on the continuum assumption. In this book, the authors present the most recent advances of the application of the LBM to complex flow phenomena of scientific and technical interest with particular focus on the multi-scale modeling of heterogeneous catalysis within nano-porous media and multiphase, multicomponent flows.
Download or read book Computational Bioengineering written by M. Cerrolaza and published by Imperial College Press. This book was released on 2004 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a significant contribution to the state of the art in the field of computational bioengineering from the need for a living human database to meshless methods in biomechanics, from computational mechanobiology to the evaluation of stresses in hip prosthesis replacement, from lattice Boltzmann methods for analyzing blood flow to the analysis of fluid movement in long bones, among other interesting topics treated herein. Well-known international experts in bioengineering have contributed to the book, giving it a unique style and cutting-edge material for graduate students, academic researchers and design bioengineers, as well as those interested in getting a better understanding of such complex and fascinating human and living processes.
Download or read book Advances in Spacecraft Technologies written by Jason Hall and published by BoD – Books on Demand. This book was released on 2011-02-14 with total page 612 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development and launch of the first artificial satellite Sputnik more than five decades ago propelled both the scientific and engineering communities to new heights as they worked together to develop novel solutions to the challenges of spacecraft system design. This symbiotic relationship has brought significant technological advances that have enabled the design of systems that can withstand the rigors of space while providing valuable space-based services. With its 26 chapters divided into three sections, this book brings together critical contributions from renowned international researchers to provide an outstanding survey of recent advances in spacecraft technologies. The first section includes nine chapters that focus on innovative hardware technologies while the next section is comprised of seven chapters that center on cutting-edge state estimation techniques. The final section contains eleven chapters that present a series of novel control methods for spacecraft orbit and attitude control.
Download or read book Multiscale and Multiphysics Flow Simulations of Using the Boltzmann Equation written by Jun Li and published by Springer Nature. This book was released on 2019-08-28 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the kinetic theory for describing flow problems from molecular scale, hydrodynamic scale, to Darcy scale. The author presents various numerical algorithms to solve the same Boltzmann-like equation for different applications of different scales, in which the dominant transport mechanisms may differ. This book presents a concise introduction to the Boltzmann equation of the kinetic theory, based on which different simulation methods that were independently developed for solving problems of different fields can be naturally related to each other. Then, the advantages and disadvantages of different methods will be discussed with reference to each other. It mainly covers four advanced simulation methods based on the Boltzmann equation (i.e., direct simulation Monte Carlo method, direct simulation BGK method, discrete velocity method, and lattice Boltzmann method) and their applications with detailed results. In particular, many simulations are included to demonstrate the applications for both conventional and unconventional reservoirs. With the development of high-resolution CT and high-performance computing facilities, the study of digital rock physics is becoming increasingly important for understanding the mechanisms of enhanced oil and gas recovery. The advanced methods presented here have broad applications in petroleum engineering as well as mechanical engineering , making them of interest to researchers, professionals, and graduate students alike. At the same time, instructors can use the codes at the end of the book to help their students implement the advanced technology in solving real industrial problems.
Download or read book Coping with Complexity Model Reduction and Data Analysis written by Alexander N. Gorban and published by Springer Science & Business Media. This book was released on 2010-10-21 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the extended version of selected talks given at the international research workshop "Coping with Complexity: Model Reduction and Data Analysis", Ambleside, UK, August 31 – September 4, 2009. The book is deliberately broad in scope and aims at promoting new ideas and methodological perspectives. The topics of the chapters range from theoretical analysis of complex and multiscale mathematical models to applications in e.g., fluid dynamics and chemical kinetics.
Download or read book Progress in Vehicle Aerodynamics and Thermal Management written by Jochen Wiedemann and published by Springer. This book was released on 2017-12-04 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: The books presents latest information about new car developments, new or improved testing techniques and new or improved calculation procedures. Presenters are from industry and academia.
Download or read book Study of a Directional mean free path Method for Gas Flow in Translational Nonequilibrium written by E. Dale Martin and published by . This book was released on 1970 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Molecular Gas Dynamics written by Yoshio Sone and published by Springer Science & Business Media. This book was released on 2007-10-16 with total page 667 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained book is an up-to-date description of the basic theory of molecular gas dynamics and its various applications. The book, unique in the literature, presents working knowledge, theory, techniques, and typical phenomena in rarefied gases for theoretical development and application. Basic theory is developed in a systematic way and presented in a form easily applied for practical use. In this work, the ghost effect and non-Navier–Stokes effects are demonstrated for typical examples—Bénard and Taylor–Couette problems—in the context of a new framework. A new type of ghost effect is also discussed.
Download or read book Analysis and Numerics for Conservation Laws written by Gerald Warnecke and published by Springer Science & Business Media. This book was released on 2005-12-05 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Whatdoasupernovaexplosioninouterspace,?owaroundanairfoil and knocking in combustion engines have in common? The physical and chemical mechanisms as well as the sizes of these processes are quite di?erent. So are the motivations for studying them scienti?cally. The super- 8 nova is a thermo-nuclear explosion on a scale of 10 cm. Astrophysicists try to understand them in order to get insight into fundamental properties of the universe. In ?ows around airfoils of commercial airliners at the scale of 3 10 cm shock waves occur that in?uence the stability of the wings as well as fuel consumption in ?ight. This requires appropriate design of the shape and structure of airfoils by engineers. Knocking occurs in combustion, a chemical 1 process, and must be avoided since it damages motors. The scale is 10 cm and these processes must be optimized for e?ciency and environmental conside- tions. The common thread is that the underlying ?uid ?ows may at a certain scale of observation be described by basically the same type of hyperbolic s- tems of partial di?erential equations in divergence form, called conservation laws. Astrophysicists, engineers and mathematicians share a common interest in scienti?c progress on theory for these equations and the development of computational methods for solutions of the equations. Due to their wide applicability in modeling of continua, partial di?erential equationsareamajor?eldofresearchinmathematics. Asubstantialportionof mathematical research is related to the analysis and numerical approximation of solutions to such equations. Hyperbolic conservation laws in two or more spacedimensionsstillposeoneofthemainchallengestomodernmathematics.
Download or read book A Unified Computational Fluid Dynamics Framework from Rarefied to Continuum Regimes written by Kun Xu and published by Cambridge University Press. This book was released on 2021-06-10 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Element presents a unified computational fluid dynamics framework from rarefied to continuum regimes. The framework is based on the direct modelling of flow physics in a discretized space. The mesh size and time step are used as modelling scales in the construction of discretized governing equations. With the variation-of-cell Knudsen number, continuous modelling equations in different regimes have been obtained, and the Boltzmann and Navier-Stokes equations become two limiting equations in the kinetic and hydrodynamic scales. The unified algorithms include the discrete velocity method (DVM)–based unified gas-kinetic scheme (UGKS), the particlebased unified gas-kinetic particle method (UGKP), and the wave and particle–based unified gas-kinetic wave-particle method (UGKWP). The UGKWP is a multi-scale method with the particle for non-equilibrium transport and wave for equilibrium evolution. The particle dynamics in the rarefied regime and the hydrodynamic flow solver in the continuum regime have been unified according to the cell's Knudsen number.
Download or read book Lattice Boltzmann Methods for Shallow Water Flows written by Jian Guo Zhou and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lattice Boltzmann method (LBM) is a modern numerical technique, very efficient, flexible to simulate different flows within complex/varying geome tries. It is evolved from the lattice gas automata (LGA) in order to overcome the difficulties with the LGA. The core equation in the LBM turns out to be a special discrete form of the continuum Boltzmann equation, leading it to be self-explanatory in statistical physics. The method describes the micro scopic picture of particles movement in an extremely simplified way, and on the macroscopic level it gives a correct average description of a fluid. The av eraged particle velocities behave in time and space just as the flow velocities in a physical fluid, showing a direct link between discrete microscopic and continuum macroscopic phenomena. In contrast to the traditional computational fluid dynamics (CFD) based on a direct solution of flow equations, the lattice Boltzmann method provides an indirect way for solution of the flow equations. The method is characterized by simple calculation, parallel process and easy implementation of boundary conditions. It is these features that make the lattice Boltzmann method a very promising computational method in different areas. In recent years, it receives extensive attentions and becomes a very potential research area in computational fluid dynamics. However, most published books are limited to the lattice Boltzmann methods for the Navier-Stokes equations. On the other hand, shallow water flows exist in many practical situations such as tidal flows, waves, open channel flows and dam-break flows.
Download or read book Continuum Thermodynamics written by Wilmanski and published by World Scientific. This book was released on 2008 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a unique presentation of thermodynamic methods of construction of continuous models. It is based on a uniform approach following from the entropy inequality and using Lagrange multipliers as auxiliary quantities in its evaluation. It covers a wide range of models — ideal gases, thermoviscoelastic fluids, thermoelastic and thermoviscoelastic solids, plastic polycrystals, miscible and immiscible mixtures, and many others. The structure of phenomenological thermodynamics is justified by a systematic derivation from the Liouville equation, through the BBGKY-hierarchy-derived Boltzmann equation, to an extended thermodynamics. In order to simplify the reading, an extensive introduction to classical continuum mechanics and thermostatics is included. As a complementary volume to Part II, which will contain applications and examples, and to Part III, which will cover numerical methods, only a few simple examples are presented in this first Part. One exception is an extensive example of a linear poroelastic material because it will not appear in future Parts.The book is the first presentation of continuum thermodynamics in which foundations of continuum mechanics, microscopic foundations and transition to extended thermodynamics, applications of extended thermodynamics beyond ideal gases, and thermodynamic foundations of various material theories are exposed in a uniform and rational way. The book may serve both as a support for advanced courses as well as a desk reference.
Download or read book Spectral Methods in Chemistry and Physics written by Bernard Shizgal and published by Springer. This book was released on 2015-01-07 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of this book is to provide the basic concepts to enable the use of spectral and pseudospectral methods to solve problems in diverse fields of interest and to a wide audience. While spectral methods are generally based on Fourier Series or Chebychev polynomials, non-classical polynomials and associated quadratures are used for many of the applications presented in the book. Fourier series methods are summarized with a discussion of the resolution of the Gibbs phenomenon. Classical and non-classical quadratures are used for the evaluation of integrals in reaction dynamics including nuclear fusion, radial integrals in density functional theory, in elastic scattering theory and other applications. The subject matter includes the calculation of transport coefficients in gases and other gas dynamical problems based on spectral and pseudospectral solutions of the Boltzmann equation. Radiative transfer in astrophysics and atmospheric science, and applications to space physics are discussed. The relaxation of initial non-equilibrium distributions to equilibrium for several different systems is studied with the Boltzmann and Fokker-Planck equations. The eigenvalue spectra of the linear operators in the Boltzmann, Fokker-Planck and Schrödinger equations are studied with spectral and pseudospectral methods based on non-classical orthogonal polynomials. The numerical methods referred to as the Discrete Ordinate Method, Differential Quadrature, the Quadrature Discretization Method, the Discrete Variable Representation, the Lagrange Mesh Method, and others are discussed and compared. MATLAB codes are provided for most of the numerical results reported in the book - see Link under 'Additional Information' on the the right-hand column.
Download or read book Lattice Boltzmann Modeling for Chemical Engineering written by and published by Academic Press. This book was released on 2020-06-19 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lattice Boltzmann Modeling for Chemical Engineering, Volume 56 in the Advances in Chemical Engineering series, highlights new advances in the field, with this new volume presenting interesting chapters on Simulations of homogeneous and heterogeneous chemical reactions, LBM for 3D Chemical Reactors, LBM Simulations of PEM fuel cells, LBM for separation processes, LBM for two-phase flow (bio)reactors, and more. Provides the authority and expertise of leading contributors from an international board of authors Presents the latest release in the Advances in Chemical Engineering series Includes the latest information on Lattice Boltzmann Modeling for Chemical Engineering
Download or read book Exergy for A Better Environment and Improved Sustainability 1 written by Fethi Aloui and published by Springer. This book was released on 2018-08-04 with total page 1443 pages. Available in PDF, EPUB and Kindle. Book excerpt: This multi-disciplinary book presents the most recent advances in exergy, energy, and environmental issues. Volume 1 focuses on fundamentals in the field and covers current problems, future needs, and prospects in the area of energy and environment from researchers worldwide. Based on selected lectures from the Seventh International Exergy, Energy and Environmental Symposium (IEEES7-2015) and complemented by further invited contributions, this comprehensive set of contributions promote the exchange of new ideas and techniques in energy conversion and conservation in order to exchange best practices in "energetic efficiency". Included are fundamental and historical coverage of the green transportation and sustainable mobility sectors, especially regarding the development of sustainable technologies for thermal comforts and green transportation vehicles. Furthermore, contributions on renewable and sustainable energy sources, strategies for energy production, and the carbon-free society constitute an important part of this book. Exergy for Better Environment and Sustainability, Volume 1 will appeal to researchers, students, and professionals within engineering and the renewable energy fields.
