[PDF] A Discrete Ordinate Technique For The Non Linear Boltzmann Equation With Application To Pseudo Shock Relaxation eBook

Author : Murray Wachman
Publisher :
Page : 36 pages
File Size : 50,36 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 : V.V. Aristov
Publisher : Springer Science & Business Media
Page : 305 pages
File Size : 36,14 MB
Release : 2012-12-06
Category : Science
ISBN : 9401008663

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This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.

Author :
Publisher :
Page : 1262 pages
File Size : 41,51 MB
Release : 1967
Category : Aeronautics
ISBN :

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Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.

Author : Alexandre Joel Chorin
Publisher : Academic Press
Page : 240 pages
File Size : 46,58 MB
Release : 2014-06-28
Category : Technology & Engineering
ISBN : 1483271552

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Computational Fluid Mechanics: Selected Papers compiles papers on computational fluid dynamics written between 1967 and 1982. This book emphasizes the numerical solution of the equations of fluid mechanics in circumstances where the viscosity is small. The vortex and projection methods, numerical solution of problems in kinetic theory, combustion theory, and gas dynamics are also discussed. This publication elaborates that turbulence in fluids is dominated by the mechanics of vorticity, and many of the methods are based on vortex representations of the flow. The convergence of vortex calculations in three space dimensions and motion of vortex filaments are likewise deliberated. This compilation is a good source for physicists and students researching on computational fluid mechanics.