Some Approximations To The Radiative Transfer Equation And Their Applications
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Some Approximations To The Radiative Transfer Equation And Their Applications
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Author : Qiwei Sheng
language : en
Publisher:
Release Date : 2013
Some Approximations To The Radiative Transfer Equation And Their Applications written by Qiwei Sheng and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Fokker-Planck equation categories.
Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and so on. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables. This high dimensionality and presence of integral term present a serious challenge when one tries to solve the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation have been introduced. One among them is to use approximations of RTE. Various approximations of RTE have been proposed in the literature. These include, but are certainly not limited to, the delta-Eddington approximation, the Fokker-Planck approximation, the Boltzmann-Fokker-Planck approximation, the generalized Fokker-Planck approximation, the Fokker-Planck-Eddington approximation and the generalized Fokker-Planck-Eddington approximation. The Fokker-Planck approximation and differential approximation have received particular attention in the literature due to their relatively high accuracy, relatively low computational cost, and flexibility to potential large scale parallel computing. In this thesis we present a well-posed result for the Fokker-Planck equation that may be used to approximate the radiative transfer equation in highly forward-peaked media. Then we study the differential approximation of radiative transfer (RT/DA) equations. Well-posedness of these approximations is studied. A convergent iteration method for the RT/DA equation is presented. Then we turn to a study of RT/DA based inverse problems. The inverse problems are ill-posed and regularization is needed in solving the inverse problems. We present an existence result for solutions of regularized formulations of the inverse problems. Finally examples are included to illustrate numerical results in solving the inverse problems.
Discontinuous Galerkin Methods For The Radiative Transfer Equation And Its Approximations
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Author : Joseph A. Eichholz
language : en
Publisher:
Release Date : 2011
Discontinuous Galerkin Methods For The Radiative Transfer Equation And Its Approximations written by Joseph A. Eichholz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Galerkin methods categories.
Radiative transfer theory describes the interaction of radiation with scattering and absorbing media. It has applications in neutron transport, atmospheric physics, heat transfer, molecular imaging, and others. In steady state, the radiative transfer equation is an integro-differential equation of five independent variables. This high dimensionality and presence of integral term present a serious challenge when trying to solve the equation numerically. Over the past 50 years, several techniques for solving the radiative transfer equation have been introduced. These include, but are certainly not limited to, Monte Carlo methods, discrete-ordinate methods, spherical harmonics methods, spectral methods, finite difference methods, and finite element methods. Methods involving discrete ordinates have received particular attention in the literature due to their relatively high accuracy, flexibility, and relatively low computational cost. In this thesis we present a discrete-ordinate discontinuous Galerkin method for solving the radiative transfer equation. In addition, we present a generalized Fokker-Planck equation that may be used to approximate the radiative transfer equation in certain circumstances. We provide well posedness results for this approximation, and introduce a discrete-ordinate discontinuous Galerkin method to approximate a solution. Theoretical error estimates are derived, and numerical examples demonstrating the efficacy of the methods are given.
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.
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.
Radiative Transfer In Coupled Environmental Systems
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Author : Knut Stamnes
language : en
Publisher: John Wiley & Sons
Release Date : 2016-03-18
Radiative Transfer In Coupled Environmental Systems written by Knut Stamnes and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-18 with Science categories.
This book is dedicated to the formulation and solution of forward and inverse problems related to coupled media, and provides examples of how to solve concrete problems in environmental remote sensing of coupled atmosphere-surface systems. The authors discuss radiative transfer in coupled media such as the atmosphere-ocean system with Lambertian as well non-Lambertian reflecting surfaces at the lower boundary. The spectral range from the ultraviolet to the microwave region of the electromagnetic spectrum is considered, as are multi-spectral as well as hyperspectral remote sensing, while solutions of the forward problem for unpolarized and polarized radiation are discussed in detail.
Approximations To The Theory Of Radiative Transfer In Dense Media Appropriate To Medical Applications
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Author : Ashok Tiwary
language : en
Publisher:
Release Date : 1996
Approximations To The Theory Of Radiative Transfer In Dense Media Appropriate To Medical Applications written by Ashok Tiwary and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.
Radiation Transfer
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Author : L. A. Apresyan
language : en
Publisher: Routledge
Release Date : 2019-07-16
Radiation Transfer written by L. A. Apresyan and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-16 with Technology & Engineering categories.
The authors expound on non-traditional phenomena for transfer theory, which are nevertheless of considerable interest in wave measurements, and bring the advances of transfer theory as close as possible to the practical needs of those working in all areas of wave physics. The book opens with a historical overview of the topic, then moves on to examine the phenomenological theory of radiative transport, blending traditional theory with original ideas. The transport equation is derived from first principles, and the ensuing discussion of the diffraction content of the transport equation and non-classical radiometry is illustrated by practical examples from various fields of physics. Popular techniques of solving the transport equation are discussed, paying particular attention to wave physics and computing the coherence function. The book also examines various problems which are no longer covered by the traditional radiative transfer theory, such as enhanced backscattering and weak localization phenomena, nonlinear transport problems and kinetic equations for waves. This monograph bridges the gap between the simple power balance description in radiative transfer theory and modern coherence theory. It will be of interest to researchers and professionals working across a wide range of fields from optics, acoustics and radar theory to astrophysics, radioastronomy and remote sensing, as well as to students in these areas.
Light Scattering Reviews 5
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Author : Alexander A. Kokhanovsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-05
Light Scattering Reviews 5 written by Alexander A. Kokhanovsky 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 2010-08-05 with Science categories.
Light scattering by densely packed inhomogeneous media is a particularly ch- lenging optics problem. In most cases, only approximate methods are used for the calculations. However, in the case where only a small number of macroscopic sc- tering particles are in contact (clusters or aggregates) it is possible to obtain exact results solving Maxwell’s equations. Simulations are possible, however, only for a relativelysmallnumberofparticles,especiallyiftheirsizesarelargerthanthewa- length of incident light. The ?rst review chapter in PartI of this volume, prepared by Yasuhiko Okada, presents modern numerical techniques used for the simulation of optical characteristics of densely packed groups of spherical particles. In this case, Mie theory cannot provide accurate results because particles are located in the near ?eld of each other and strongly interact. As a matter of fact, Maxwell’s equations must be solved not for each particle separately but for the ensemble as a whole in this case. The author describes techniques for the generation of shapes of aggregates. The orientation averaging is performed by a numerical integration with respect to Euler angles. The numerical aspects of various techniques such as the T-matrix method, discrete dipole approximation, the ?nite di?erence time domain method, e?ective medium theory, and generalized multi-particle Mie so- tion are presented. Recent advances in numerical techniques such as the grouping and adding method and also numerical orientation averaging using a Monte Carlo method are discussed in great depth.
Radiation In Enclosures
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Author : Aristide Mbiock
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Radiation In Enclosures written by Aristide Mbiock 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 2012-12-06 with Science categories.
During the last half century, the development and testing of prediction models of combustion chamber performance have been an ongoing task at the International Flame Research Foundation (IFRF) in IJmuiden in the Netherlands and at many other research organizations. This task has brought forth a hierarchy of more or less standard numerical models for heat transfer predictions, in particular for the prediction of radiative heat transfer. Unfortunately all the methods developed, which certainly have a good physical foundation, are based on a large number of extreme sim plifications or uncontrolled assumptions. To date, the ever more stringent requirements for efficient production and use of energy and heat from com bustion chambers call for prediction algorithms of higher accuracy and more detailed radiative heat transfer calculations. The driving forces behind this are advanced technology requirements, the costs of large-scale experimen tal work, and the limitation of physical modeling. This interest is growing more acute and has increased the need for the publication of a textbook for more accurate treatment of radiative transfer in enclosures. The writing of a textbook on radiative heat transfer, however, in ad dition to working regularly on other subjects is a rather difficult task for which some years of meditation are necessary. The book must satisfy two requirements which are not easily reconciled. From the mathematical point of view, it must be written in accordance with standards of mathemati cal rigor and precision.
The Mathematics Of Radiative Transfer
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Author : I. W. Busbridge
language : en
Publisher: Cambridge University Press
Release Date : 2008-11-27
The Mathematics Of Radiative Transfer written by I. W. Busbridge and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-11-27 with Science categories.
This tract gives a simple but rigorous treatment of some of the mathematical problems that arise in the theory of the transfer of radiation through the atmosphere of a star. Similar problems occur in the theory of the diffusion of neutrons and in the study of temperature-wave flow in solids; so the solutions found in one theory can often be applied in the others. Dr Busbridge's starting-point is the equation of transfer. The first section provides the auxiliary mathematics, and the second discusses the Milne equations. Some unsolved and incompletely solved problems are considered in an appendix. The language and notation of astrophysics is used throughout, for brevity and simplicity, but translation into other notations is usually fairly easy. Over the years the subject had grown considerably, and several outstanding problems have been solved, though the total amount of rigorous work is small. This tract will help to clear up confusions which exist and will provide an introduction to some of the more powerful mathematical techniques available.