Download or read book Numerical Solution of the Boltzmann Equation on the Uniform Grid written by Ilgis Ibragimov and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book NUMERICAL SOLUTION OF THE BOLTZMANN EQUATION written by ALEXANDRE JOEL. CHORIN and published by . This book was released on 2018 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Fast Numerical Method for the Boltzmann Equation on Non uniform Grids written by and published by . This book was released on 2004 with total page 28 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 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 Lecture Notes on the Discretization of the Boltzmann Equation written by Nicola Bellomo and published by World Scientific. This book was released on 2003 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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 Parallel Processing and Applied Mathematics written by Roman Wyrzykowski and published by Springer. This book was released on 2014-05-07 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume-set (LNCS 8384 and 8385) constitutes the refereed proceedings of the 10th International Conference of Parallel Processing and Applied Mathematics, PPAM 2013, held in Warsaw, Poland, in September 2013. The 143 revised full papers presented in both volumes were carefully reviewed and selected from numerous submissions. The papers cover important fields of parallel/distributed/cloud computing and applied mathematics, such as numerical algorithms and parallel scientific computing; parallel non-numerical algorithms; tools and environments for parallel/distributed/cloud computing; applications of parallel computing; applied mathematics, evolutionary computing and metaheuristics.

Download or read book Computational Methods in Transport Verification and Validation written by Frank Graziani and published by Springer Science & Business Media. This book was released on 2008-08-09 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The focus of this book deals with a cross cutting issue affecting all transport disciplines, whether it be photon, neutron, charged particle or neutrino transport. That is, verification and validation. In this book, we learn what the astrophysicist, atmospheric scientist, mathematician or nuclear engineer do to assess the accuracy of their code. What convergence studies, what error analysis, what problems do each field use to ascertain the accuracy of their transport simulations.

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 Lecture Notes on the Discretization of the Boltzmann Equation written by N. Bellomo and published by World Scientific. This book was released on 2003 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Numerical Solution of the Boltzmann Equation written by Alexandre Joel Chorin and published by . This book was released on 1971 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 Landau Equation Boltzmann type Equations Discrete Models and Numerical Methods written by Alexander V. Bobylev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-09-23 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume monograph is a comprehensive and up-to-date presentation of the theory and applications of kinetic equations. The second volume covers discrete velocity models of the Boltzmann equation, results on the Landau equation, and numerical (deterministic and stochastic) methods for the solution of kinetic equations.

Download or read book A Numerical Solution of Boltzmann s Equation written by Gary Andrew Sod and published by . This book was released on 1976 with total page 244 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 Direct Numerical Solution of the Three dimensional Generalized Boltzmann Equation for Hypersonic Non equilibrium Flows written by Christopher Daniel Wilson and published by . This book was released on 2010 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: The development and applications of a computer code for solving the three-dimensional generalized Boltzmann equation (GBE) using a direct numerical method are presented. The Boltzmann solver of Professor Felix G. Tcheremissine of the Russian Academy of Science serves as the foundation for the development effort. This jet code includes only the translational and rotational energy states of a diatomic gas and has been applied to simulate the flow field of a jet issuing into a vacuum. In this dissertation, this code is employed to accomplish three distinct developmental steps. First, the code is extended for calculating hypersonic shock waves in an inert mixture of gases. For this purpose, the GBE is formulated in an impulse space (instead of the conventional velocity space). The computational methodology is then applied to a binary mixture of gases, which requires the simultaneous solution of four GBE's. Simulations are performed using a gas mixture including both diatomic and monatomic gases in proportions similar to that in air. The solutions are validated against existing hypersonic shock wave experimental data for a single specie gas (nitrogen) in rotational-translational non-equilibrium and available computational data for a binary mixture of monatomic gases. Simulations are then performed for an inert binary mixture of monatomic and diatomic gases in translational non-equilibrium for various concentrations. The effect of mass ratio and molecular diameter ratio of the gases on the structure of the shock is also investigated. Second, boundary conditions necessary for accurately simulating the flows around immersed bodies are developed and evaluated. This research on boundary conditions constitutes a significant advancement beyond the adsorptive boundary condition used in the original Boltzmann solver of Tcheremissine. Five types of boundary conditions at the solid boundary are investigated: (a) the standard adsorptive boundary condition, (b) the specular reflection boundary condition, (c) the diffuse reflection boundary condition, (d) the Maxwellian boundary condition, and (e) the adsorptive Maxwellian boundary condition with different values for the accommodation coefficient. These boundary conditions are tested for hypersonic flow past a flat plate to evaluate their accuracy. Third, the original Boltzmann code, hard-coded for solving the flow field of a jet issuing into a vacuum, is modified to enable simulations of rarefied flows around immersed bodies. The computations are performed for three benchmark geometries, extensively used in the literature for Navier-Stokes simulations, at various hypersonic inflow conditions for flow of a diatomic gas (N2) in rotational-translational non-equilibrium. The three geometries used in the simulations are an axisymmetric blunt body, an axisymmetric bicone, and an axisymmetric hollow-flared-cylinder. Initially, a relatively coarse Cartesian grid was employed in the three-dimensional simulations because of the limitations of physical memory on the available computers. As a result, a shared memory parallel computing platform was developed and built for the sole purpose of being able to perform the fine grid solutions. Consequently, refined grid solutions were generated on the parallel computing platform. For this purpose, the code was parallelized and the parallelization issues for a Boltzmann type solver were addressed. A comparison between the coarse and refined grid solutions is presented to show the influence of grid density on solution accuracy. In light of these results, the issues of accuracy and efficiency of the three-dimensional Boltzmann solver are addressed.