Download or read book Numerical Solutions to the Two Dimensional Boltzmann Equation written by Christopher G. Smithtro and published by . This book was released on 1999-03-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: A strict kinetic, two-dimensional model of the electron kinetics within a glow discharge positive column is developed. The problem is solved in cylindrical geometry using the standard two-term Legendre expansion of the electron velocity distribution function. The model establishes a steady state solution, such that the net ionization rate is exactly balanced by the wall loss. In addition to a thorough analytic development, we present the numerical techniques used to solve the resulting elliptic partial differential equation, including an efficient method to treat sparse banded matrices. The model is validated against published results, local and nonlocal kinetic approximations, and a previous Monte Carlo treatment. Having created a working model, we conduct an investigation into current flow within the solution area of a neon column, made possible by this 2-D treatment. Furthermore, we investigate the range of applicability of the earlier local and nonlocal kinetic approximations and finally present a short discussion on the effect different forms of wall loss have on the overall distribution function.

Download or read book A Numerical Solution of the Boltzmann Equation for a Two dimensional Gas written by Frank Robben and published by . This book was released on 1967 with total page 42 pages. Available in PDF, EPUB and Kindle. Book excerpt: An attempt to solve the Boltzmann equation numerically was carried out by means of a more direct method than the Monte-Carlo technique. The initial value problem of the energy relaxation of a two-dimensional gas of hard spheres was studied, using direct numerical integration techniques. A finite difference approximation to the Boltzmann equation was used. While the results are qualitatively correct, conservation of energy and number were violated to the extent of about 4% per collision. On comparing the detailed results to that predicted by a Krook model, quantitative differences are noted. It is believed that the inaccuracies of the solutions obtained are due to a singularity in the collision integrals. (Author).

Download or read book Numerical Solutions of the Two Dimensional Confined Non linear Poisson Boltzmann Equation written by Mark Ospeck and published by . This book was released on 1996 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solutions of the Boltzmann Equation in Two Space Dimensions written by E. L. Secrest and published by . This book was released on 1959 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows written by V.V. Aristov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Analysis of Lattice Boltzmann Methods written by Martin Rheinländer and published by GRIN Verlag. This book was released on 2007 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2007 in the subject Mathematics - Analysis, University of Constance (Fachbereich Mathematik & Statistik), 69 entries in the bibliography, language: English, abstract: Lattice-Boltzmann algorithms represent a quite novel class of numerical schemes, which are used to solve evolutionary partial differential equations (PDEs). In contrast to other methods (FEM, FVM), lattice-Boltzmann methods rely on a mesoscopic approach. The idea consists in setting up an artificial, grid-based particle dynamics, which is chosen such that appropriate averages provide approximate solutions of a certain PDE, typically in the area of fluid dynamics. As lattice-Boltzmann schemes are closely related to finite velocity Boltzmann equations being singularly perturbed by special scalings, their consistency is not obvious. This work is concerned with the analysis of lattice-Boltzmann methods also focusing certain numeric phenomena like initial layers, multiple time scales and boundary layers. As major analytic tool, regular (Hilbert) expansions are employed to establish consistency. Exemplarily, two and three population algorithms are studied in one space dimension, mostly discretizing the advection-diffusion equation. It is shown how these model schemes can be derived from two-dimensional schemes in the case of special symmetries. The analysis of the schemes is preceded by an examination of the singular limit being characteristic of the corresponding scaled finite velocity Boltzmann equations. Convergence proofs are obtained using a Fourier series approach and alternatively a general regular expansion combined with an energy estimate. The appearance of initial layers is investigated by multiscale and irregular expansions. Among others, a hierarchy of equations is found which gives insight into the internal coupling of the initial layer and the regular part of the solution. Next, the consistency of the model algorithms is considered followed by

Download or read book Molecular Gas Dynamics and the Direct Simulation of Gas Flows written by G. A. Bird and published by Oxford University Press on Demand. This book was released on 1994 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of a highly regarded text covers all the recent research developments in gas dynamics including the direct simulation Monte Carlo method (DSMC).

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1988 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Lattice Boltzmann Equation on a 2D Rectangular Grid written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-20 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean invariance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions; (b) Poiseuille flow with an arbitrasy inclined angle with respect to the lattice orientation: and (c) a cylinder &symmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations. Bouzidi, MHamed and DHumieres, Dominique and Lallemand, Pierre and Luo, Li-Shi and Bushnell, Dennis M. (Technical Monitor) Langley Research Center NASA/CR-2002-211658, NAS 1.26:211658, ICASE-2002-18

Download or read book Multigrid Solution of the Poisson Boltzmann Equation written by Michael Holst and published by . This book was released on 1992 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abstract: "A multigrid method is presented for the numerical solution of the linearized Poisson-Boltzmann equation arising in molecular biophysics. The equation is discretized with the finite volume method, and the numerical solution of the discrete equations is accomplished with multiple grid techniques originally developed for two-dimensional interface problems occurring in reactor physics. A detailed analysis of the resulting method is presented for several computer architectures, including comparisons to diagonally scaled CG, ICCG, vectorized ICCG and MICCG, and to SOR provided with an optimal relaxation parameter. Our results indicate that the multigrid method is superior to the preconditioned CG methods and SOR, and that the advantage of multigrid grows with the problem size."

Download or read book Numerical Methods in Fluid Dynamics written by Nikolaĭ Nikolaevich I︠A︡nenko and published by . This book was released on 1984 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lattice Boltzmann Equation On a 2D Rectangular Grid written by M'Hamed Bouzidi and published by . This book was released on 2002 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: We construct a multi-relaxation lattice Boltzmann model on a two-dimensional rectangular grid. The model is partly inspired by a previous work of Koelman to construct a lattice BGK model on a two-dimensional rectangular grid. The linearized disperson equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and Galilean in variance for various wave propagations in the model. The linear stability of the model is also studied. The model is numerically tested for three cases: (a) a vortex moving with a constant velocity on a mesh periodic boundary conditions: (b) Poiseuille flow with an arbitrary inclined angle with respect to the lattice orientation; and (c) a cylinder asymmetrically placed in a channel. The numerical results of these tests are compared with either analytic solutions or the results obtained by other methods. Satisfactory results are obtained for the numerical simulations.

Download or read book Microelectronics Technology and Devices SBMICRO 2002 written by Electrochemical Society. Electronics Division and published by The Electrochemical Society. This book was released on 2002 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Numerical Solution to the Angle integrated Boltzmann Equation written by J. H. Bennett and published by . This book was released on 1958 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Solution of Boltzmann s Equation written by and published by . This book was released on 1976 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical solution of Boltzmann's equation is considered for a gas model consisting of rigid spheres by means of Hilbert's expansion. If only the first two terms of the expansion are retained, Boltzmann's equation reduces to the Boltzmann-Hilbert integral equation. Successive terms in the Hilbert expansion are obtained by solving the same integral equation with a different source term. The Boltzmann-Hilbert integral equation is solved by a new very fast numerical method. The success of the method rests upon the simultaneous use of four judiciously chosen expansions; Hilbert's expansion for the distribution function, another expansion of the distribution function in terms of Hermite polynomials, the expansion of the kernel in terms of the eigenvalues and eigenfunctions of the Hilbert operator, and an expansion involved in solving a system of linear equations through a singular value decomposition. The numerical method is applied to the study of the shock structure in one space dimension. Numerical results are presented for Mach numbers of 1.1 and 1.6. 94 refs, 7 tables, 1 fig.

Download or read book A Student s Guide to Numerical Methods written by Ian H. Hutchinson and published by Cambridge University Press. This book was released on 2015-04-30 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: The plain language style, worked examples and exercises in this book help students to understand the foundations of computational physics and engineering.

Download or read book NASA Technical Translation written by and published by . This book was released on 1971 with total page 1292 pages. Available in PDF, EPUB and Kindle. Book excerpt: