Download or read book Truncation Errors in Numerical Solutions of the Transport Equation written by John Henry Bennett and published by . This book was released on 1962 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: The numerical solution is given of the transport equation for monoenergetic neutrons in a medium with isotropic scattering. The object is to determine the accuracy of the numerial methods generally used to solve the transport equation. The analyss is largely confined to the solution of the criticality problem for homogeneos slabs. A ritcality problem in X-Y geometry is also considered. The criterion of accurcy used is the difference between c, the number of secondary neutrons per collision required for criticality, and an approximation to c given by an N-parameter approximate method. (Author).

Download or read book Numerical Methods for Radiative Transport Equations written by Vincent Edmund Heningburg and published by . This book was released on 2019 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation, we present and analyze a discrete ordinates (SN̳) discretization of a filtered radiative transport equation (RTE). Under certain conditions, SN̳ discretizations of the standard RTE create numeric artifacts, known as ``ray-effects"; the goal of using a filter is to remove such artifacts. We analyze convergence of the filtered discrete ordinates solution to the solution of the non-filtered RTE, taking into account the effect of the filter as well as the usual quadrature and truncation errors that arise in discrete ordinates methods. We also present a hybrid spatial discretization for the radiative transport equation that combines a second-order discontinuous Galerkin (DG) method and a second-order finite volume (FV) method. The strategy relies on a simple operator splitting that has been used previously to combine different angular discretizations. Unlike standard FV methods with upwind fluxes, the hybrid approach is able to accurately simulate problems in scattering dominated regimes. However, it requires less memory and yields a faster time to solution than a standard DG approach. In addition, the underlying splitting allows naturally for hybridization in both space and angle. We demonstrate, via the simulation of two benchmark problems, the effectiveness of the filtering approach in reducing ray effects. In addition, we also examine efficiency of both methods, in particular the balance between improved accuracy and additional cost of including the filter, and the ability of the spatial hybrid to leverage its efficiency to produce more accurate results.

Download or read book The Numerical Solution of the Time dependent Transport Equation in Finite Cylindrical Geometry written by Joseph Fleck and published by . This book was released on 1957 with total page 30 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Development of a Numerical Solution to the Transport Equation Report 2 Computational Procedures written by R. A Schmalz (Jr) and published by . This book was released on 1983 with total page 113 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report, Report 2 in a three-report series, develops the computational procedures for implementing the numerical approximations to the transport equation. The stability and truncation error characteristics are presented for the schemes selected in Report 1 for the linearized form of the transport equation. Computational procedures are next developed for the nonlinear equation in transformed coordinates. Numerical approximations near boundaries, the hydrodynamic interface, and the determination of dispersion coefficients are developed for simulating conditions in Mississippi Sound and adjacent areas. (Author).

Download or read book Verification and Validation in Scientific Computing written by William L. Oberkampf and published by Cambridge University Press. This book was released on 2010-10-14 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advances in scientific computing have made modelling and simulation an important part of the decision-making process in engineering, science, and public policy. This book provides a comprehensive and systematic development of the basic concepts, principles, and procedures for verification and validation of models and simulations. The emphasis is placed on models that are described by partial differential and integral equations and the simulations that result from their numerical solution. The methods described can be applied to a wide range of technical fields, from the physical sciences, engineering and technology and industry, through to environmental regulations and safety, product and plant safety, financial investing, and governmental regulations. This book will be genuinely welcomed by researchers, practitioners, and decision makers in a broad range of fields, who seek to improve the credibility and reliability of simulation results. It will also be appropriate either for university courses or for independent study.

Download or read book The Development of a Numerical Solution to Transport Equation written by R. A. Schmalz and published by . This book was released on 1983 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book On the Formulation and Analysis of Numerical Methods for Time Dependent Transport Equations written by Herbert Bishop Keller and published by . This book was released on 1956 with total page 46 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Global Error Bounds for the Petrov Galerkin Discretization of the Neutron Transport Equation written by P. Brown and published by . This book was released on 2005 with total page 23 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we prove that the numerical solution of the mono-directional neutron transport equation by the Petrov-Galerkin method converges to the true solution in the L{sup 2} norm at the rate of h{sup 2}. Since consistency has been shown elsewhere, the focus here is on stability. We prove that the system of Petrov-Galerkin equations is stable by showing that the 2-norm of the inverse of the matrix for the system of equations is bounded by a number that is independent of the order of the matrix. This bound is equal to the length of the longest path that it takes a neutron to cross the domain in a straight line. A consequence of this bound is that the global error of the Petrov-Galerkin approximation is of the same order of h as the local truncation error. We use this result to explain the widely held observation that the solution of the Petrov-Galerkin method is second accurate for one class of problems, but is only first order accurate for another class of problems.

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

Download or read book Computational Techniques for Differential Equations written by J. Noye and published by Elsevier. This book was released on 2000-04-01 with total page 689 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Techniques for Differential Equations

Download or read book Numerical Solutions of Partial Differential Equations written by John Noye and published by North Holland. This book was released on 1982 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solving Hyperbolic Equations with Finite Volume Methods written by M. Elena Vázquez-Cendón and published by Springer. This book was released on 2015-04-16 with total page 195 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite volume methods are used in numerous applications and by a broad multidisciplinary scientific community. The book communicates this important tool to students, researchers in training and academics involved in the training of students in different science and technology fields. The selection of content is based on the author’s experience giving PhD and master courses in different universities. In the book the introduction of new concepts and numerical methods go together with simple exercises, examples and applications that contribute to reinforce them. In addition, some of them involve the execution of MATLAB codes. The author promotes an understanding of common terminology with a balance between mathematical rigor and physical intuition that characterizes the origin of the methods. This book aims to be a first contact with finite volume methods. Once readers have studied it, they will be able to follow more specific bibliographical references and use commercial programs or open source software within the framework of Computational Fluid Dynamics (CFD).

Download or read book Numerical Methods for Partial Differential Equations written by Vitoriano Ruas and published by John Wiley & Sons. This book was released on 2016-08-22 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Methods for Partial Differential Equations: An Introduction Vitoriano Ruas, Sorbonne Universités, UPMC - Université Paris 6, France A comprehensive overview of techniques for the computational solution of PDE's Numerical Methods for Partial Differential Equations: An Introduction covers the three most popular methods for solving partial differential equations: the finite difference method, the finite element method and the finite volume method. The book combines clear descriptions of the three methods, their reliability, and practical implementation aspects. Justifications for why numerical methods for the main classes of PDE's work or not, or how well they work, are supplied and exemplified. Aimed primarily at students of Engineering, Mathematics, Computer Science, Physics and Chemistry among others this book offers a substantial insight into the principles numerical methods in this class of problems are based upon. The book can also be used as a reference for research work on numerical methods for PDE’s. Key features: A balanced emphasis is given to both practical considerations and a rigorous mathematical treatment The reliability analyses for the three methods are carried out in a unified framework and in a structured and visible manner, for the basic types of PDE's Special attention is given to low order methods, as practitioner's overwhelming default options for everyday use New techniques are employed to derive known results, thereby simplifying their proof Supplementary material is available from a companion website.

Download or read book U S Government Research Reports written by and published by . This book was released on 1962 with total page 1170 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Hydraulics of Groundwater written by Jacob Bear and published by Courier Corporation. This book was released on 2012-03-15 with total page 594 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text explores the laws governing the flow and storage of groundwater in aquifers and provides all the necessary tools to forecast the behavior of a regional aquifer system. 1979 edition.

Download or read book Environmental Processes and Management written by Raj Mohan Singh and published by Springer Nature. This book was released on 2020-02-17 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an in-depth, science-based approach to applying key project-management and spatial tools and practices in environmental projects. Providing important data for those considering projects that balance social-economic growth against minimizing its ill-effects on planet Earth, the book discusses various aspects of environmental engineering, as well as formula and analytical approaches required for more informed decision-making. Beginning with a broad overview of the factors and features of environmental processes and management, the book then clearly details the general application of fundamental processes, the characteristics of the different systems in which they occur, and the way in which these factors influence process dynamics, environmental systems, and their possible remedies. While primarily intended for professionals responsible for the management of environmental projects or interested in improving the overall efficiency of such projects, it is also useful for managers in the private, public, and not-for-profit sectors. Further, it is a valuable resource for students at both undergraduate and postgraduate levels, and an indispensable guide for anyone wanting to develop their skills in modern environmental management and related techniques.

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1990 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: