Download or read book Finite Element Radiation Transport in One Dimension written by and published by . This book was released on 1997 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature 'in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog of Kershaw and Harte's two-dimensional package. This package has been installed in a two-dimensional inertial confinement fusion code, and has given excellent results for both thermal waves and highly directional radiation. In contrast, the traditional discrete ordinate and spherical harmonic methods show less accurate results in both cases.

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 Finite Element Solution of a Self adjoint Transport Equation in One Dimension written by Allan D. Goff (1LT, USAF.) and published by . This book was released on 1984 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Quadratic Finite Element Method for 1D Deterministic Transport written by J. M. Ferguson and published by . This book was released on 2004 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r}, {und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r}, {und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.

Download or read book Fundamentals of the Finite Element Method for Heat and Fluid Flow written by Roland W. Lewis and published by John Wiley and Sons. This book was released on 2008-02-07 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heat transfer is the area of engineering science which describes the energy transport between material bodies due to a difference in temperature. The three different modes of heat transport are conduction, convection and radiation. In most problems, these three modes exist simultaneously. However, the significance of these modes depends on the problems studied and often, insignificant modes are neglected. Very often books published on Computational Fluid Dynamics using the Finite Element Method give very little or no significance to thermal or heat transfer problems. From the research point of view, it is important to explain the handling of various types of heat transfer problems with different types of complex boundary conditions. Problems with slow fluid motion and heat transfer can be difficult problems to handle. Therefore, the complexity of combined fluid flow and heat transfer problems should not be underestimated and should be dealt with carefully. This book: Is ideal for teaching senior undergraduates the fundamentals of how to use the Finite Element Method to solve heat transfer and fluid dynamics problems Explains how to solve various heat transfer problems with different types of boundary conditions Uses recent computational methods and codes to handle complex fluid motion and heat transfer problems Includes a large number of examples and exercises on heat transfer problems In an era of parallel computing, computational efficiency and easy to handle codes play a major part. Bearing all these points in mind, the topics covered on combined flow and heat transfer in this book will be an asset for practising engineers and postgraduate students. Other topics of interest for the heat transfer community, such as heat exchangers and radiation heat transfer, are also included.

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 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 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 Radiative Heat Transfer written by Michael F. Modest and published by Academic Press. This book was released on 2003-03-07 with total page 850 pages. Available in PDF, EPUB and Kindle. Book excerpt: The basic physics of radiative heat - how surfaces emit, reflect, and absorb waves, and how that heat is distributed.

Download or read book MATLAB Guide to Finite Elements written by Peter I. Kattan and published by Springer Science & Business Media. This book was released on 2010-05-13 with total page 430 pages. Available in PDF, EPUB and Kindle. Book excerpt: later versions. In addition, the CD-ROM contains a complete solutions manual that includes detailed solutions to all the problems in the book. If the reader does not wish to consult these solutions, then a brief list of answers is provided in printed form at the end of the book. Iwouldliketothankmyfamilymembersfortheirhelpandcontinuedsupportwi- out which this book would not have been possible. I would also like to acknowledge the help of the editior at Springer-Verlag (Dr. Thomas Ditzinger) for his assistance in bringing this book out in its present form. Finally, I would like to thank my brother, Nicola, for preparing most of the line drawings in both editions. In this edition, I am providing two email addresses for my readers to contact me (pkattan@tedata. net. jo and pkattan@lsu. edu). The old email address that appeared in the ?rst edition was cancelled in 2004. December 2006 Peter I. Kattan PrefacetotheFirstEdition 3 This is a book for people who love ?nite elements and MATLAB . We will use the popular computer package MATLAB as a matrix calculator for doing ?nite element analysis. Problems will be solved mainly using MATLAB to carry out the tedious and lengthy matrix calculations in addition to some manual manipulations especially when applying the boundary conditions. In particular the steps of the ?nite element method are emphasized in this book. The reader will not ?nd ready-made MATLAB programsforuseasblackboxes. Insteadstep-by-stepsolutionsof?niteelementpr- lems are examined in detail using MATLAB.

Download or read book A Finite Element Solution of the Transport Equation written by F. A. Tarantino and published by . This book was released on 1985 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using a self adjoint form of the transport equation expressed as a variational integral, finite element equations for the one dimensional, one speed, homogeneous, time independent transport equation in slab geometry were derived and envoded in Fortran 77. The accuracy of C sub 0 and C sub 1 continuous fits was compared against an analytical solution for the case of noscatter. It was found that the C fits require an excessive amount of mesh refinement. The C sub 1 fit is very accurate, and does not appear to be computationally excessive. The finite element results were then compared, for the case of isotropic scatter, to a legendre polynomial solution, and the results of a recently developed code known as Ln. The methods accuracy was sufficiently verified with inexact scattering term evaluation. A technique of exact scattering integral evaluation is proposed that should reduce the amount of refinement required for convergence, and improve computational efficiency. Additional keywords: theses; numerical analysis; interpolation; computer programs. (Author).

Download or read book One Dimensional Finite Element Flux Corrected Transport written by Mehdi Vahdati and published by . This book was released on 1986 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Three dimensional Human Radiation Model with Finite Element Method written by Qing He and published by . This book was released on 1996 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Application of New Variational Principles in Finite Element Method Solutions of the Radiation Transport Equation written by Mehran Pourzand and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Multi dimensional Finite Element Transport Model Utilizing a Characteristic Galerkin Algorithm written by John Francis DeGeorge and published by . This book was released on 1996 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book ONETRAN written by and published by . This book was released on 1975 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discontinuous Galerkin Methods for Computational Radiation Transport written by Simon Richard Merton and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: This Thesis demonstrates advanced new discretisation technologies that improve the accuracy and stability of the discontinuous Galerkin finite element method applied to the Boltzmann Transport Equation, describing the advective transport of neutral particles such as photons and neutrons within a domain. The discontinuous Galerkin method in its standard form is susceptible to oscillation detrimental to the solution. The discretisation schemes presented in this Thesis enhance the basic form with linear and non-linear Petrov Galerkin methods that remove these oscillations. The new schemes are complemented by an adjoint-based error recovery technique that improves the standard solution when applied to goal-based functional and eigenvalue problems. The chapters in this Thesis have been structured to be submitted individually for journal publication, and are arranged as follows. Chapter 1 outlines the Thesis and contains a brief literature review. Chapter 2 introduces the underlying space-angle discretisation method used in the work, and discusses a series of potential modifications to the standard discontinuous Galerkin method. These differ in how the upwinding is performed on the element boundary, and comprise an upwind-average method, a Petrov-Galerkin method that removes oscillation by adding artificial diffusion internal to an element and a more sophisticated Petrov-Galerkin scheme that adds dissipation in the coupling between each element. These schemes are tested in one-dimension and Taylor analysis of their convergence rate is included. The chapter concludes with selection of one of the schemes to be developed in the next part of the Thesis. Chapter 3 develops the selected method extending it to multi-dimensions. The result is a new discontinuous Petrov-Galerkin method that is residual based and removes unwanted oscillation from the transport solution by adding numerical dissipation internal to an element. The method uses a common length scale in the upwind term for all elements. This is not always satisfactory, however, as it gives the same magnitude and type of dissipation everywhere in the domain. The chapter concludes by recommending some form of non-linearity be included to address this issue. Chapter 4 adds non-linearity to the scheme. This projects the streamline direction, in which the dissipation acts, onto the solution gradient direction. It defines locally the optimal amount of dissipation needed in the discretisation. The non-linear scheme is tested on a variety of steady-state and time-dependent transport problems. Chapters 5, 6 and 7 develop an adjoint-based error measure to complement the scheme in functional and eigenvalue problems. This is done by deriving an approximation to the error in the the bulk functional or eigenvalue, and then removing it from the calculated value in a post-process defect iteration. This is shown to dramatically accelerate mesh convergence of the goal-based functional or eigenvalue. Chapter 8 concludes the Thesis with recommendations for a further plan of work.