Download or read book Discontinuous Finite Element Methods for Particle Transport Problems written by Hiromi Stone and published by . This book was released on 2002 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Methods for Particle Transport written by Ron Tunstall Ackroyd and published by Taylor & Francis Group. This book was released on 1997 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on the transport of neutral particles, neutrons and photons, using the finite element method to address practical problems in nuclear power and mineral prospecting. Includes discussions of how the method began and has matured to become a practical tool complementing the stochastic Monte Carlo method, spatial finite elements, examples of calculations, equivalent forms of the Boltzmann equation, neutron streaming in voids, some aspects of discontinuous variational solutions, complementary principles and benchmarking, time-dependent transport, and modelling three-dimensional systems. Double spaced. Annotation copyright by Book News, Inc., Portland, OR
Download or read book The Piecewise Linear Discontinuous Finite Element Method Applied to the RZ and XYZ Transport Equations written by Teresa S Bailey and published by . This book was released on 2008 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In this dissertation we discuss the development, implementation, analysis and testing of the Piecewise Linear Discontinuous Finite Element Method (PWLD) applied to the particle transport equation in two-dimensional cylindrical (RZ) and three-dimensional Cartesian (XYZ) geometries. We have designed this method to be applicable to radiative-transfer problems in radiation-hydrodynamics systems for arbitrary polygonal and polyhedral meshes. For RZ geometry, we have implemented this method in the Capsaicin radiative-transfer code being developed at Los Alamos National Laboratory. In XYZ geometry, we have implemented the method in the Parallel Deterministic Transport code being developed at Texas A & M University. We discuss the importance of the thick diffusion limit for radiative-transfer problems, and perform a thick diffusion-limit analysis on our discretized system for both geometries. This analysis predicts that the PWLD method will perform well in this limit for many problems of physical interest with arbitrary polygonal and polyhedral cells. Finally, we run a series of test problems to determine some useful properties of the method and verify the results of our thick diffusion limit analysis. Finally, we test our method on a variety of test problems and show that it compares favorably to existing methods. With these test problems, we also show that our method performs well in the thick diffusion limit as predicted by our analysis. Based on PWLD's solid finite-element foundation, the desirable properties it shows under analysis, and the excellent performance it demonstrates on test problems even with highly distorted spatial grids, we conclude that it is an excellent candidate for radiativetransfer problems that need a robust method that performs well in thick diffusive problems or on distorted grids.
Download or read book Asymptotic Diffusion Accelerated Discontinuous Finite Element Methods for Transport Problems written by Todd Arlin Wareing and published by . This book was released on 1993 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations written by Xiaobing Feng and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.
Download or read book Discontinuous Finite Elements in Fluid Dynamics and Heat Transfer written by Ben Q. Li and published by Springer Science & Business Media. This book was released on 2006-06-29 with total page 587 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past several years, significant advances have been made in developing the discontinuous Galerkin finite element method for applications in fluid flow and heat transfer. Certain unique features of the method have made it attractive as an alternative for other popular methods such as finite volume and finite elements in thermal fluids engineering analyses. This book is written as an introductory textbook on the discontinuous finite element method for senior undergraduate and graduate students in the area of thermal science and fluid dynamics. It also can be used as a reference book for researchers and engineers who intend to use the method for research in computational fluid dynamics and heat transfer. A good portion of this book has been used in a course for computational fluid dynamics and heat transfer for senior undergraduate and first year graduate students. It also has been used by some graduate students for self-study of the basics of discontinuous finite elements. This monograph assumes that readers have a basic understanding of thermodynamics, fluid mechanics and heat transfer and some background in numerical analysis. Knowledge of continuous finite elements is not necessary but will be helpful. The book covers the application of the method for the simulation of both macroscopic and micro/nanoscale fluid flow and heat transfer phenomena.
Download or read book An adaptive discontinuous finite element method for the transport equation written by Jens Lang and published by . This book was released on 1991 with total page 14 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Element Methods and Their Applications written by Zhangxin Chen and published by Springer Science & Business Media. This book was released on 2005-06-23 with total page 415 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduce every concept in the simplest setting and to maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Contains unique recent developments of various finite elements such as nonconforming, mixed, discontinuous, characteristic, and adaptive finite elements, along with their applications. Describes unique recent applications of finite element methods to important fields such as multiphase flows in porous media and semiconductor modelling. Treats the three major types of partial differential equations, i.e., elliptic, parabolic, and hyperbolic equations.
Download or read book Exponential Discontinuous Finite Element Scheme for Coupled Charged uncharged Particle Transport written by Alejandro Gonzalez-Aller and published by . This book was released on 2000 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discontinuous Galerkin Methods written by Bernardo Cockburn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: A class of finite element methods, the Discontinuous Galerkin Methods (DGM), has been under rapid development recently and has found its use very quickly in such diverse applications as aeroacoustics, semi-conductor device simula tion, turbomachinery, turbulent flows, materials processing, MHD and plasma simulations, and image processing. While there has been a lot of interest from mathematicians, physicists and engineers in DGM, only scattered information is available and there has been no prior effort in organizing and publishing the existing volume of knowledge on this subject. In May 24-26, 1999 we organized in Newport (Rhode Island, USA), the first international symposium on DGM with equal emphasis on the theory, numerical implementation, and applications. Eighteen invited speakers, lead ers in the field, and thirty-two contributors presented various aspects and addressed open issues on DGM. In this volume we include forty-nine papers presented in the Symposium as well as a survey paper written by the organiz ers. All papers were peer-reviewed. A summary of these papers is included in the survey paper, which also provides a historical perspective of the evolution of DGM and its relation to other numerical methods. We hope this volume will become a major reference in this topic. It is intended for students and researchers who work in theory and application of numerical solution of convection dominated partial differential equations. The papers were written with the assumption that the reader has some knowledge of classical finite elements and finite volume methods.
Download or read book Methods for Solving Discontinuous Galerkin Finite Element Equations with Application to Neutron Transport written by Steven Murphy and published by . This book was released on 2015 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Finite Element Projection Method for the Solution of Particle Transport Problems with Anisotropic Scattering written by Eze Ewart Wills and published by . This book was released on 1984 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: A solution method for solving particle transport problems has been developed. This solution approach embodies a finite element projection technique and a related equivalent variational Raleigh-Ritz formalism. Particle flux in the transport equation is expressed as a linear and separable sum of odd and even components in the direction variables. Then a classical variational principle is obtained and shown to be equivalent to a Bubnov-Galerkin projected solution. A dual finite element basis of polynomial splines in space and spherical harmonics in angle is used in the Bubnov-Galerkin equations. The general theoretical and numerical problem formalism is carried out in a 3-dimensional geometry with anisotropic scattering and with a piecewise constant energy dependence. This is a seven-dimensional problem with time dependence, three spatial and two angular or directional variables and with a multigroup treatment of the energy dependence. The boundary conditions for most physical problems of interest are dealt with explicitly and rigorously by a classical minimization (variational) principle. The computational validation of the method was obtained by a computer solution to the air-over-ground problem. This problem is of significant interest in the areas of nuclear weapons effects and radiation physics.
Download or read book Higher Order Discontinuous Finite Element Methods for Discrete Ordinates Thermal Radiative Transfer written by Peter Gregory Maginot and published by . This book was released on 2015 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The linear discontinuous finite element method (LDFEM) is the current work horse of the radiation transport community. The popularity of LDFEM is a result of LDFEM (and its Q1 multi-dimensional extensions) being both accurate and preserving the thick diffusion limit. In practice, the LDFEM equations must be "lumped" to mitigate negative radiation transport solutions. Negative solutions are non-physical, but are inherent to the mathematics of LDFEM and other spatial discretizations. Ongoing changes in high performance computing (HPC) are dictating a preference for increased numbers of floating point operations (FLOPS) per unknown. Higher order discontinuous finite element methods (DFEM), those with polynomial trial spaces greater than linear, have been found to offer more accuracy per unknown than LDFEM. However, DFEM with higher degree trial spaces have received only limited attention due to their increased computational time per unknown, LDFEM's preservation of the thick diffusion limit, and the relative accuracy of LDFEM compared to other historical spatial discretizations. As solution methods evolve to make the most efficient use of HPC, it is possible that the increased computational work of higher order DFEM may become a strength rather than a hindrance. For higher order DFEM to be useful in practice, lumping techniques must be developed to inhibit negative radiation transport solutions. We will show that traditional mass matrix lumping does not guarantee positive solutions and limits the overall accuracy of the DFEM scheme. To solve this problem, we propose a new, quadrature based, self-lumping technique. Our self-lumping technique does not limit solution order of convergence, improves solution positivity, and can be easily adapted to account for the within cell variation of interaction cross section. To test and demonstrate the characteristics of our self-lumping methodology, we apply our schemes to several test problems: a homogeneous, source-free pure absorber; a pure absorber with spatially varying cross section; a model fuel depletion problem; and finally, we solve the grey thermal radiative transfer equations. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/155489
Download or read book Nuclear Computational Science written by Yousry Azmy and published by Springer Science & Business Media. This book was released on 2010-04-15 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nuclear engineering has undergone extensive progress over the years. In the past century, colossal developments have been made and with specific reference to the mathematical theory and computational science underlying this discipline, advances in areas such as high-order discretization methods, Krylov Methods and Iteration Acceleration have steadily grown. Nuclear Computational Science: A Century in Review addresses these topics and many more; topics which hold special ties to the first half of the century, and topics focused around the unique combination of nuclear engineering, computational science and mathematical theory. Comprising eight chapters, Nuclear Computational Science: A Century in Review incorporates a number of carefully selected issues representing a variety of problems, providing the reader with a wealth of information in both a clear and concise manner. The comprehensive nature of the coverage and the stature of the contributing authors combine to make this a unique landmark publication. Targeting the medium to advanced level academic, this book will appeal to researchers and students with an interest in the progression of mathematical theory and its application to nuclear computational science.
Download or read book Numerical Methods in Multidimensional Radiative Transfer written by Guido Kanschat and published by Springer Science & Business Media. This book was released on 2008-12-24 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, radiative transfer has been the domain of astrophysicists and climatologists. In nuclear technology one has been dealing with the ana- gous equations of neutron transport. In recent years, applications of radiative transferincombustionmachinedesignandinmedicinebecamemoreandmore important. In all these disciplines one uses the radiative transfer equation to model the formation of the radiation ?eld and its propagation. For slabs and spheres e?ective algorithms for the solution of the transfer equation have been ava- able for quite some time. In addition, the analysis of the equation is quite well developed. Unfortunately, in many modern applications the approximation of a 1D geometry is no longer adequate and one has to consider the full 3D dependencies. This makes the modeling immensely more intricate. The main reasons for the di?culties result from the fact that not only the dimension of the geometric space has to be increased but one also has to employ two angle variables (instead of one) and very often one has to consider frequency coupling (due to motion or redistribution in spectral lines). In actual cal- lations this leads to extremely large matrices which, in addition, are usually badly conditioned and therefore require special care. Analytical solutions are not available except for very special cases. Although radiative transfer problems are interesting also from a ma- ematical point of view, mathematicians have largely neglected the transfer equation for a long time.
Download or read book A Quadratic Discontinuous Finite Element Solution for the Fokker Planck Transport Equation for Charged Particles written by Joel Robert Turinetti and published by . This book was released on 1999 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Galerkin Finite Element Methods for Parabolic Problems written by V. Thomee and published by Springer. This book was released on 2006-11-14 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:
