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Numerical Studies Of The Diffusion Transport Approximation
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Book Synopsis Numerical Studies of the Diffusion-transport Approximation by : Arnold J. Sisk
Download or read book Numerical Studies of the Diffusion-transport Approximation written by Arnold J. Sisk and published by . This book was released on 1968 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Detailed reactor design calculations are routinely performed using group diffusion theory as the computational method for obtaining the neutron flux distribution. Diffusion theory, however, yields an adequate approximation to the correct neutron distribution only for limited situations which are not common in modern high performance reactors. The difficulty can be circumvented, in principle, by using neutron transport theory, but this alternative is not practical because of the complexity of the Boltzmann transport equation for neutrons. The Diffusion-Transport Approximation is a technique which uses two diffusion-type equations: a standard asymptotic equation and a correction equation which introduces the space transients of transport theory into the solution. The approximation yields excellent results in simple situations. The equations and the boundary conditions associated with them have been numerically analyzed and made amenable to computer solution by the line inversion technique, in the hope of developing a useful reactor design tool. This technique involves what is known as a forward elimination-bac kward substitution process. A program which is applicable to plane, cylindrical or spherical geometry has been written and has given excellent results for plane geometry situations. It was then tested on two problems in cylindrical geometry; these situations are considered much more representative of actual reactor design problems. It appears that the approximation gives results which are somewhat better than F-1 diffusion theory for regions which are not too small. However, the approximation failed for small regions. It is concluded that the parameters used in the theory need to be recalculated for cases involving cylindrical geometry. The numerical analysis and programming could then be tested on more complex multiregion problems in this geometry with the hope that a good approximation to the actual neutron flux will result.
Book Synopsis Reactive Flows, Diffusion and Transport by : Willi Jäger
Download or read book Reactive Flows, Diffusion and Transport written by Willi Jäger and published by Springer Science & Business Media. This book was released on 2007-05-31 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume summarize the research results obtained in the former SFB 359 "Reactive Flow, Diffusion and Transport" which has been supported by the DFG over the period 1993-2004. The main subjects are physical-chemical processes sharing the difficulty of interacting diffusion, transport and reaction which cannot be considered separately. The modeling and simulation within this book is accompanied by experiments.
Book Synopsis A Numerical Investigation of Extending Diffusion Theory Codes to Solve the Generalized Diffusion Equation in the Edge Pedestal by : John-Patrick Floyd (II.)
Download or read book A Numerical Investigation of Extending Diffusion Theory Codes to Solve the Generalized Diffusion Equation in the Edge Pedestal written by John-Patrick Floyd (II.) and published by . This book was released on 2011 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The presence of a large pinch velocity in the edge pedestal of high confinement (H-mode) tokamak plasmas implies that particle transport in the plasma edge ust be treated by a pinch-diffusion theory, rather than a pure diffusion theory. Momentum balance also requires the inclusion of a pinch term in descriptions of edge article transport. A numerical investigation of solving generalized pinch-diffusion theory using methods extended from the numerical solution methodology of pure iffusion theory has been carried out. The generalized diffusion equation has been numerically integrated using the central finite-difference approximation for the diffusion erm and three finite difference approximations of the pinch term, and then solved using Gauss reduction. The pinch-diffusion relation for the radial particle flux was solved directly and used as a benchmark for the finite-difference algorithm solutions to the generalized diffusion equation. Both equations are solved using several esh pacings, and it is found that a finer mesh spacing will be required in the edge pedestal, where the inward pinch velocity is large in H-mode plasmas, than is necessary or similar accuracy further inward where the pinch velocity diminishes. An expression for the numerical error of various finite-differencing algorithms is presented.
Book Synopsis Convection-diffusion Problems by : Martin Stynes
Download or read book Convection-diffusion Problems written by Martin Stynes and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Many physical problems involve diffusive and convective (transport) processes. When diffusion dominates convection, standard numerical methods work satisfactorily. But when convection dominates diffusion, the standard methods become unstable, and special techniques are needed to compute accurate numerical approximations of the unknown solution. This convection-dominated regime is the focus of the book. After discussing at length the nature of solutions to convection-dominated convection-diffusion problems, the authors motivate and design numerical methods that are particularly suited to this c.
Book Synopsis Diffusion in Random Fields by : Nicolae Suciu
Download or read book Diffusion in Random Fields written by Nicolae Suciu and published by Springer. This book was released on 2019-05-31 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents, in an accessible and self-consistent way, the theory of diffusion in random velocity fields, together with robust numerical simulation approaches. The focus is on transport processes in natural porous media, with applications to contaminant transport in groundwater. Starting from basic information on stochastic processes, more challenging issues are subsequently addressed, such as the correlation structure of the diffusion process in random fields, the relation between memory effects and ergodic properties, derivation and parameterizations of evolution equations for probability densities, and the relation between measurements and spatio-temporal upscaling. Written for readers with a background in applied mathematics, engineering, physics or geophysics, the book offers an essential basis for further research in the stochastic modeling of groundwater systems.
Book Synopsis Spectral Elements for Transport-Dominated Equations by : Daniele Funaro
Download or read book Spectral Elements for Transport-Dominated Equations written by Daniele Funaro and published by Springer Science & Business Media. This book was released on 1997-04-17 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with the numerical approximation of various PDEs using the spectral element method, with particular emphasis for elliptic equations dominated by first-order terms. It provides a simple introduction to spectral elements with additional new tools (upwind grids and preconditioners). Applications to fluid dynamics and semiconductor devices are considered, as well as in other models were transport-diffusion equations arise. The aim is to provide the reader with both introductive and more advanced material on spectral Legendre collocation methods. The book however does not cover all the aspects of spectral methods. Engineers, physicists and applied mathematicians may study how to implement the collocation method and use the results to improve their computational codes.
Book Synopsis Catalogue by : United States Naval Academy
Download or read book Catalogue written by United States Naval Academy and published by . This book was released on 1968 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1991 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Diffusion Phenomena in Building Physics by : Nathan Mendes
Download or read book Numerical Methods for Diffusion Phenomena in Building Physics written by Nathan Mendes and published by Springer Nature. This book was released on 2019-11-29 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the second edition of Numerical methods for diffusion phenomena in building physics: a practical introduction originally published by PUCPRESS (2016). It intends to stimulate research in simulation of diffusion problems in building physics, by providing an overview of mathematical models and numerical techniques such as the finite difference and finite-element methods traditionally used in building simulation tools. Nonconventional methods such as reduced order models, boundary integral approaches and spectral methods are presented, which might be considered in the next generation of building-energy-simulation tools. In this reviewed edition, an innovative way to simulate energy and hydrothermal performance are presented, bringing some light on innovative approaches in the field.
Book Synopsis Nonlinear Cosmic Ray Diffusion Theories by : Andreas Shalchi
Download or read book Nonlinear Cosmic Ray Diffusion Theories written by Andreas Shalchi and published by Springer Science & Business Media. This book was released on 2009-06-04 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: If charged particles move through the interplanetary or interstellar medium, they interact with a large-scale magnetic ?eld such as the magnetic ?eld of the Sun or the Galactic magnetic ?eld. As these background ?elds are usually nearly constant in time and space, they can be approximated by a homogeneous ?eld. If there are no additional ?elds, the particle trajectory is a perfect helix along which the par- cle moves at a constant speed. In reality, however, there are turbulent electric and magnetic?elds dueto the interstellaror solar wind plasma. These ?elds lead to sc- tering of the cosmic rays parallel and perpendicular to the background ?eld. These scattering effects, which usually are of diffusive nature, can be described by s- tial diffusion coef?cients or, alternatively, by mean free paths. The knowledge of these parameters is essential for describing cosmic ray propagation as well as d- fusive shock acceleration. The latter process is responsible for the high cosmic ray energies that have been observed. The layout of this book is as follows. In Chap. 1, the general physical scenario is presented. We discuss fundamental processes such as cosmic ray propagation and acceleration in different systems such as the solar system or the interst- lar space. These processes are a consequence of the interaction between charged cosmic particles and an astrophysical plasma (turbulence). The properties of such plasmas are therefore the subject of Chap. 2.
Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1975 with total page 1146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Methods for Diffusive Relaxation in the $P_N$ Equations by :
Download or read book Methods for Diffusive Relaxation in the $P_N$ Equations written by and published by . This book was released on 2009 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Mathematics of Diffusion by : John Crank
Download or read book The Mathematics of Diffusion written by John Crank and published by Oxford University Press. This book was released on 1979 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Though it incorporates much new material, this new edition preserves the general character of the book in providing a collection of solutions of the equations of diffusion and describing how these solutions may be obtained.
Book Synopsis Fractional Dynamics In Comb-like Structures by : Alexander Iomin
Download or read book Fractional Dynamics In Comb-like Structures written by Alexander Iomin and published by World Scientific. This book was released on 2018-08-28 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random walks often provide the underlying mesoscopic mechanism for transport phenomena in physics, chemistry and biology. In particular, anomalous transport in branched structures has attracted considerable attention. Combs are simple caricatures of various types of natural branched structures that belong to the category of loopless graphs. The comb model was introduced to understand anomalous transport in percolation clusters. Comb-like models have been widely adopted to describe kinetic processes in various experimental applications in medical physics and biophysics, chemistry of polymers, semiconductors, and many other interdisciplinary applications.The authors present a random walk description of the transport in specific comb geometries, ranging from simple random walks on comb structures, which provide a geometrical explanation of anomalous diffusion, to more complex types of random walks, such as non-Markovian continuous-time random walks. The simplicity of comb models allows to perform a rigorous analysis and to obtain exact analytical results for various types of random walks and reaction-transport processes.
Book Synopsis Numerical Methods for Fluid Dynamics by : Dale R. Durran
Download or read book Numerical Methods for Fluid Dynamics written by Dale R. Durran and published by Springer Science & Business Media. This book was released on 2010-09-14 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: This scholarly text provides an introduction to the numerical methods used to model partial differential equations, with focus on atmospheric and oceanic flows. The book covers both the essentials of building a numerical model and the more sophisticated techniques that are now available. Finite difference methods, spectral methods, finite element method, flux-corrected methods and TVC schemes are all discussed. Throughout, the author keeps to a middle ground between the theorem-proof formalism of a mathematical text and the highly empirical approach found in some engineering publications. The book establishes a concrete link between theory and practice using an extensive range of test problems to illustrate the theoretically derived properties of various methods. From the reviews: "...the books unquestionable advantage is the clarity and simplicity in presenting virtually all basic ideas and methods of numerical analysis currently actively used in geophysical fluid dynamics." Physics of Atmosphere and Ocean
Book Synopsis Improved Finite Analytic Methods for Solving Advection-dominated Transport Equation in Highly Variable Velocity Field by : Cuifeng Wei
Download or read book Improved Finite Analytic Methods for Solving Advection-dominated Transport Equation in Highly Variable Velocity Field written by Cuifeng Wei and published by . This book was released on 1995 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Equations of Radiation Hydrodynamics by : Gerald C. Pomraning
Download or read book The Equations of Radiation Hydrodynamics written by Gerald C. Pomraning and published by Courier Corporation. This book was released on 2005-01-01 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level text examines propagation of thermal radiation through a fluid and its effects on the hydrodynamics of fluid motion. Topics include approximate formulations of radiative transfer and relativistic effects of fluid motion; microscopic physics associated with the equation of transfer; inverse Compton scattering; and hydrodynamic description of fluid. 1973 edition.
