Numerical Methods In Multidimensional Radiative Transfer
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Numerical Methods In Multidimensional Radiative Transfer
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Author : Guido Kanschat
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-24
Numerical Methods In Multidimensional Radiative Transfer written by Guido Kanschat and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-24 with Mathematics categories.
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.
The Influence Of Numerical Diffusion On The Solution Of The Radiative Transfer Equations
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Author : Jürgen Steinacker
language : de
Publisher:
Release Date : 2002
The Influence Of Numerical Diffusion On The Solution Of The Radiative Transfer Equations written by Jürgen Steinacker and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Diffusion categories.
We investigate the explicit numerical solution strategies of multi-dimensional radiative transfer equations which are commonly used, e.g., to determine the radiation emerging from astrophysical objects surrounded by absorbing and scattering matter. For explicit grid solvers, we identify numerical diffusion as a severe source of error in first-order discretization schemes, underestimated in former work about radiative transfer. Using the simple example of a beam propagating through vacuum, we illustrate the influence of the diffusion on the solution and discuss various techniques to reduce it. In view of the large required storage for implicit solvers, we propose to use second-order explicit grid techniques to solve 3D radiative transfer problems.
A Hybrid Discrete Ordinates Spherical Harmonics Method For Solution Of The Radiative Transfer Equation In Multi Dimensional Participating Media
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Author : Maathangi Sankar
language : en
Publisher:
Release Date : 2011
A Hybrid Discrete Ordinates Spherical Harmonics Method For Solution Of The Radiative Transfer Equation In Multi Dimensional Participating Media written by Maathangi Sankar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
Abstract: The Radiative Transfer Equation (RTE) is a multi-dimensional integro - differential equation. It is difficult to obtain an exact analytical solution to the RTE even for simple one - dimensional cases due of its directional nature. As a result, approximate numerical methods must be used to solve the RTE. The two most popular methods that are currently used to solve the RTE are the Method of Spherical Harmonics, PN approximation, and the Discrete Ordinates Method, DOM or SN approximation. However, neither of these methods exhibit good accuracy over the entire range of optical thickness of practical interest. The PN approximation, although it shows good accuracy for optically thick regimes, it is not accurate for optically thin media and in scenarios in which radiation propagation is strongly directional, such as that of a medium bounded by a combination of hot and cold walls. The SN method, on the other hand, does show promising accuracy over a wide range of optical thickness. However, it suffers from ray effects in optically thin media, resulting in locally unphysical solutions. In optically thick media, the strongly coupled directional equations in DOM, renders the method computationally very expensive for obtaining accurate results. Keeping in mind the advantages of each of the afore-mentioned methods and the regimes in which they are accurate, a new robust and computationally efficient hybrid method that has acceptable accuracy over a wide range of optical thickness is proposed, developed, and demonstrated in this thesis.
Radiative Transfer In Curved Media
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Author : K. K. Sen
language : en
Publisher: World Scientific
Release Date : 1990
Radiative Transfer In Curved Media written by K. K. Sen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Mathematics categories.
Most of the methods described in this book can be used with cosmetic modifications to solve transfer problems of greater complexity. All attempts have been made to make the book self-contained.
Modified Discrete Ordinates Solution Of Radiative Transfer In Multidimensional Participating Media
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Author : Mohan Ammanath Ramankutty
language : en
Publisher:
Release Date : 1994
Modified Discrete Ordinates Solution Of Radiative Transfer In Multidimensional Participating Media written by Mohan Ammanath Ramankutty and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Boundary value problems categories.
"The discrete ordinates method has evolved as a powerful tool in the analysis of radiative heat transfer in multidimensional geometries containing participating media. The discrete ordinates method does not make accurate predictions in situations involving isolated boundary sources, due to a phenomenon known as 'ray-effects'. A modified discrete ordinates (MDO) method is presented. The intensity is broken into diffuse and direct components. The direct intensity component is determined analytically, and the direct inscatter term appears as a distributed source in the transport equation for the diffuse intensity. The diffuse transport equation is solved numerically by the conventional discrete ordinates procedure. The MDO method is applied to solve the radiative transfer equation in two- and three-dimensional rectangular and cylindrical enclosures containing absorbing, emitting, and isotropically scattering media. Uniform and non-uniform diffuse loadings on the top boundary are considered. Graphical and numerical results for various geometries and loading parameters are presented. The standard discrete ordinates solution exhibits anomalies in the flux leaving the bottom. Large errors are observed when the loading area is small compared to the overall enclosure dimensions. The MDO method eliminates 'ray-effects' and significantly improves the accuracy of the predictions"--Abstract, leaf iv.
Radiative Heat Transfer
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Author : Michael F. Modest
language : en
Publisher: Academic Press
Release Date : 2013-02-20
Radiative Heat Transfer written by Michael F. Modest and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Science categories.
The third edition of Radiative Heat Transfer describes the basic physics of radiation heat transfer. The book provides models, methodologies, and calculations essential in solving research problems in a variety of industries, including solar and nuclear energy, nanotechnology, biomedical, and environmental. Every chapter of Radiative Heat Transfer offers uncluttered nomenclature, numerous worked examples, and a large number of problems—many based on real world situations—making it ideal for classroom use as well as for self-study. The book's 24 chapters cover the four major areas in the field: surface properties; surface transport; properties of participating media; and transfer through participating media. Within each chapter, all analytical methods are developed in substantial detail, and a number of examples show how the developed relations may be applied to practical problems. Extensive solution manual for adopting instructors Most complete text in the field of radiative heat transfer Many worked examples and end-of-chapter problems Large number of computer codes (in Fortran and C++), ranging from basic problem solving aids to sophisticated research tools Covers experimental methods
Computational Methods In Transport
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Author : Frank Graziani
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-02-17
Computational Methods In Transport written by Frank Graziani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-02-17 with Computers categories.
Thereexistawiderangeofapplicationswhereasigni?cantfractionofthe- mentum and energy present in a physical problem is carried by the transport of particles. Depending on the speci?capplication, the particles involved may be photons, neutrons, neutrinos, or charged particles. Regardless of which phenomena is being described, at the heart of each application is the fact that a Boltzmann like transport equation has to be solved. The complexity, and hence expense, involved in solving the transport problem can be understood by realizing that the general solution to the 3D Boltzmann transport equation is in fact really seven dimensional: 3 spatial coordinates, 2 angles, 1 time, and 1 for speed or energy. Low-order appro- mations to the transport equation are frequently used due in part to physical justi?cation but many in cases, simply because a solution to the full tra- port problem is too computationally expensive. An example is the di?usion equation, which e?ectively drops the two angles in phase space by assuming that a linear representation in angle is adequate. Another approximation is the grey approximation, which drops the energy variable by averaging over it. If the grey approximation is applied to the di?usion equation, the expense of solving what amounts to the simplest possible description of transport is roughly equal to the cost of implicit computational ?uid dynamics. It is clear therefore, that for those application areas needing some form of transport, fast, accurate and robust transport algorithms can lead to an increase in overall code performance and a decrease in time to solution.
Thermal Radiation Heat Transfer 5th Edition
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Author : John R. Howell
language : en
Publisher: CRC Press
Release Date : 2010-09-28
Thermal Radiation Heat Transfer 5th Edition written by John R. Howell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-28 with Technology & Engineering categories.
Providing a comprehensive overview of the radiative behavior and properties of materials, the fifth edition of this classic textbook describes the physics of radiative heat transfer, development of relevant analysis methods, and associated mathematical and numerical techniques. Retaining the salient features and fundamental coverage that have made it popular, Thermal Radiation Heat Transfer, Fifth Edition has been carefully streamlined to omit superfluous material, yet enhanced to update information with extensive references. Includes four new chapters on Inverse Methods, Electromagnetic Theory, Scattering and Absorption by Particles, and Near-Field Radiative Transfer Keeping pace with significant developments, this book begins by addressing the radiative properties of blackbody and opaque materials, and how they are predicted using electromagnetic theory and obtained through measurements. It discusses radiative exchange in enclosures without any radiating medium between the surfaces—and where heat conduction is included within the boundaries. The book also covers the radiative properties of gases and addresses energy exchange when gases and other materials interact with radiative energy, as occurs in furnaces. To make this challenging subject matter easily understandable for students, the authors have revised and reorganized this textbook to produce a streamlined, practical learning tool that: Applies the common nomenclature adopted by the major heat transfer journals Consolidates past material, reincorporating much of the previous text into appendices Provides an updated, expanded, and alphabetized collection of references, assembling them in one appendix Offers a helpful list of symbols With worked-out examples, chapter-end homework problems, and other useful learning features, such as concluding remarks and historical notes, this new edition continues its tradition of serving both as a comprehensive textbook for those studying and applying radiative transfer, and as a repository of vital literary references for the serious researcher.
Mathematical Models And Numerical Methods For Radiative Transfer
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Author : C. Berthon
language : en
Publisher:
Release Date : 2009
Mathematical Models And Numerical Methods For Radiative Transfer written by C. Berthon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.
Numerical Solution Methods For Radiative Transfer In Semitransparent Media
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Author : Frank Zingsheim
language : en
Publisher:
Release Date : 1999
Numerical Solution Methods For Radiative Transfer In Semitransparent Media written by Frank Zingsheim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with categories.
