Accurate And Efficient Radiation Transport In Optically Thick Media By Means Of The Symbolic Implicit Monte Carlo Method In The Difference Formulation
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Accurate And Efficient Radiation Transport In Optically Thick Media By Means Of The Symbolic Implicit Monte Carlo Method In The Difference Formulation
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Author : M. McKinley
language : en
Publisher:
Release Date : 2005
Accurate And Efficient Radiation Transport In Optically Thick Media By Means Of The Symbolic Implicit Monte Carlo Method In The Difference Formulation written by M. McKinley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with categories.
The equations of radiation transport for thermal photons are notoriously difficult to solve in thick media without resorting to asymptotic approximations such as the diffusion limit. One source of this difficulty is that in thick, absorbing media thermal emission is almost completely balanced by strong absorption. In a previous publication [SB03], the photon transport equation was written in terms of the deviation of the specific intensity from the local equilibrium field. We called the new form of the equations the difference formulation. The difference formulation is rigorously equivalent to the original transport equation. It is particularly advantageous in thick media, where the radiation field approaches local equilibrium and the deviations from the Planck distribution are small. The difference formulation for photon transport also clarifies the diffusion limit. In this paper, the transport equation is solved by the Symbolic Implicit Monte Carlo (SIMC) method and a comparison is made between the standard formulation and the difference formulation. The SIMC method is easily adapted to the derivative source terms of the difference formulation, and a remarkable reduction in noise is obtained when the difference formulation is applied to problems involving thick media.
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.
Monte Carlo Methods For Radiation Transport
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Author : Oleg N. Vassiliev
language : en
Publisher: Springer
Release Date : 2016-10-17
Monte Carlo Methods For Radiation Transport written by Oleg N. Vassiliev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-17 with Science categories.
This book is a guide to the use of Monte Carlo techniques in radiation transport. This topic is of great interest for medical physicists. Praised as a "gold standard" for accurate radiotherapy dose calculations, Monte Carlo has stimulated a high level of research activity that has produced thousands of papers within the past few years. The book is designed primarily to address the needs of an academically inclined medical physicist who wishes to learn the technique, as well as experienced users of standard Monte Carlo codes who wish to gain insight into the underlying mathematics of Monte Carlo algorithms. The book focuses on the fundamentals—giving full attention to and explaining the very basic concepts. It also includes advanced topics and covers recent advances such as transport of charged particles in magnetic fields and the grid-based solvers of the Boltzmann equation.
Methods In Monte Carlo Solution Of The Radiation Transport Equation
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Author : Malvin H. Kalos
language : en
Publisher:
Release Date : 1962
Methods In Monte Carlo Solution Of The Radiation Transport Equation written by Malvin H. Kalos and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Monte Carlo method categories.
A discussion is given of certain methods of importance sampling and scoring in the Monte Carlo solution of the radiation transport equation.
Monte Carlo Method For Solving Inverse Problems Of Radiation Transfer
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Author : V. S. Antyufeev
language : en
Publisher: Walter de Gruyter
Release Date : 2000
Monte Carlo Method For Solving Inverse Problems Of Radiation Transfer written by V. S. Antyufeev and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume in the Inverse and Ill-Posed Problems Series deals with inverse problems of radiation transfer. In particular, the following problems are considered: atmosphere optics; radiation propagation in plant canopy; tomography in scattering fields.
Radiative Transfer
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Author : Hélène Frisch
language : en
Publisher: Springer Nature
Release Date : 2022-05-26
Radiative Transfer written by Hélène Frisch and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-26 with Science categories.
This book discusses analytic and asymptotic methods relevant to radiative transfer in dilute media, such as stellar and planetary atmospheres. Several methods, providing exact expressions for the radiation field in a semi-infinite atmosphere, are described in detail and applied to unpolarized and polarized continuous spectra and spectral lines. Among these methods, the Wiener–Hopf method, introduced in 1931 for a stellar atmospheric problem, is used today in fields such as solid mechanics, diffraction theory, or mathematical finance. Asymptotic analyses are carried out on unpolarized and polarized radiative transfer equations and on a discrete time random walk. Applicable when photons undergo a large number of scatterings, they provide criteria to distinguish between large-scale diffusive and non-diffusive behaviors, typical scales of variation of the radiation field, such as the thermalization length, and specific descriptions for regions close and far from boundaries. Its well organized synthetic view of exact and asymptotic methods of radiative transfer makes this book a valuable resource for both graduate students and professional scientists in astrophysics and beyond.
Advanced Monte Carlo For Radiation Physics Particle Transport Simulation And Applications
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Author : Andreas Kling
language : en
Publisher: Springer Science & Business Media
Release Date : 2014-02-22
Advanced Monte Carlo For Radiation Physics Particle Transport Simulation And Applications written by Andreas Kling 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 2014-02-22 with Science categories.
This book focuses on the state of the art of Monte Carlo methods in radiation physics and particle transport simulation and applications. Special attention is paid to algorithm development for modeling, and the analysis of experiments and measurements in a variety of fields.
Implicit Monte Carlo Methods And Non Equilibrium Marshak Wave Radiative Transport
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Author :
language : en
Publisher:
Release Date : 1985
Implicit Monte Carlo Methods And Non Equilibrium Marshak Wave Radiative Transport written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
Two enhancements to the Fleck implicit Monte Carlo method for radiative transport are described, for use in transparent and opaque media respectively. The first introduces a spectral mean cross section, which applies to pseudoscattering in transparent regions with a high frequency incident spectrum. The second provides a simple Monte Carlo random walk method for opaque regions, without the need for a supplementary diffusion equation formulation. A time-dependent transport Marshak wave problem of radiative transfer, in which a non-equilibrium condition exists between the radiation and material energy fields, is then solved. These results are compared to published benchmark solutions and to new discrete ordinate S-N results, for both spatially integrated radiation-material energies versus time and to new spatially dependent temperature profiles. Multigroup opacities, which are independent of both temperature and frequency, are used in addition to a material specific heat which is proportional to the cube of the temperature. 7 refs., 4 figs.
Monte Carlo Simulation In The Radiological Sci
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Author : Richard L. Morin
language : en
Publisher: Springer
Release Date : 1988-07-31
Monte Carlo Simulation In The Radiological Sci written by Richard L. Morin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-07-31 with Mathematics categories.
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.