Source Tilting Within The Difference Formulation For Radiation Transport
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Source Tilting Within The Difference Formulation For Radiation Transport
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Author :
language : en
Publisher:
Release Date : 2006
Source Tilting Within The Difference Formulation For Radiation 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 2006 with categories.
We apply a heuristic technique known as 'source tilting' to a Monte Carlo solution for radiation transport, in the difference formulation, that otherwise employs a piecewise-constant treatment of the material temperature. Source tilting improves the accuracy of the piecewise-constant treatment, reducing the excessive energy flow that occurs in the thick limit. An analysis of the cause of excessive energy flow suggests an interpolation scheme that removes this defect, obtaining the correct diffusion limit flux between zones. The results obtained with our interpolation scheme agree almost identically to those of a self-consistent piecewise-linear treatment of the difference formulation while avoiding its additional costs. The resulting method is capable of providing robust and accurate calculations for problems involving optically thick zones. We comment on the monotonicity issues that arise when employing this transport method.
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.
Generalized Reference Fields And Source Interpolation For The Difference Formulation Of Radiation Transport
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Author :
language : en
Publisher:
Release Date : 2009
Generalized Reference Fields And Source Interpolation For The Difference Formulation Of Radiation 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 2009 with categories.
In the difference formulation for the transport of thermally emitted photons, the photon intensity is defined relative to a reference field, the black body at the local material temperature. This choice of reference field combines the separate emission and absorption terms that nearly cancel, removing the dominant cause of noise in the Monte Carlo solution of thick systems, but introduces time and space derivative source terms that can not be determined until the end of the time step. The space derivative source term can also lead to noise induced crashes under certain conditions where the real physical photon intensity differs strongly from a black body at the local material temperature. In this paper, we consider a difference formulation relative to the material temperature at the beginning of the time step, or in cases where an alternative temperature better describes the radiation field, that temperature. The result is a method where iterative solution of the material energy equation is efficient and noise induced crashes are avoided. We couple our generalized reference field scheme with an ad hoc interpolation of the space derivative source, resulting in an algorithm that produces the correct flux between zones as the physical system approaches the thick limit.
An Evaluation Of The Difference Formulation For Photon Transport In A Two Level System
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Author :
language : en
Publisher:
Release Date : 2004
An Evaluation Of The Difference Formulation For Photon Transport In A Two Level System written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
In this paper we extend the difference formulation for radiation transport to the case of a single atomic line. We examine the accuracy, performance and stability of the difference formulation within the framework of the Symbolic Implicit Monte Carlo method. The difference formulation, introduced for thermal radiation by some of the authors, has the unique property that the transport equation is written in terms that become small for thick systems. We find that the difference formulation has a significant advantage over the standard formulation for a thick system. The correct treatment of the line profile, however, requires that the difference formulation in the core of the line be mixed with the standard formulation in the wings and this may limit the advantage of the method. We bypass this problem by using the gray approximation. We develop three Monte Carlo solution methods based on different degrees of implicitness for the treatment of the source terms, and we find only conditional stability unless the source terms are treated fully implicitly.
An Evaluation Of The Difference Formulation For Photon Transport In A Two Level System
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Author : M. S. McKinley
language : en
Publisher:
Release Date : 2004
An Evaluation Of The Difference Formulation For Photon Transport In A Two Level System written by M. S. McKinley and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with categories.
In this paper we extend the difference formulation for radiation transport to the case of a single atomic line. We examine the accuracy, performance and stability of the difference formulation within the framework of the Symbolic Implicit Monte Carlo method. The difference formulation, introduced for thermal radiation by some of the authors, has the unique property that the transport equation is written in terms that become small for thick systems. We find that the difference formulation has a significant advantage over the standard formulation for a thick system. The correct treatment of the line profile, however, requires that the difference formulation in the core of the line be mixed with the standard formulation in the wings, and this may limit the advantage of the method. We bypass this problem by using the gray approximation. We develop three Monte Carlo solution methods based on different degrees of implicitness for the treatment of the source terms, and we find only conditional stability unless the source terms are treated fully implicitly.
Generalized Subtraction Schemes For The Difference Formulation In Radiation Transport
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Author :
language : en
Publisher:
Release Date : 2008
Generalized Subtraction Schemes For The Difference Formulation In Radiation 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 2008 with categories.
In the difference formulation for the transport of thermally emitted photons, the photon intensity is defined relative to a reference field, the black body at the local material temperature. This choice of reference field removes the cancellation between thermal emission and absorption that is responsible for noise in the Monte Carlo solution of thick systems, but introduces time and space derivative source terms that can not be determined until the end of the time step. It can also lead to noise induced crashes under certain conditions where the real physical photon intensity differs strongly from a black body at the local material temperature. In this report, we consider a difference formulation relative to the material temperature at the beginning of the time step, and in the situations where the radiation intensity more closely follows a temperature other than the local material temperature, that temperature. The result is a method where iterative solution of the material energy equation is efficient and noise induced crashes are avoided. To support our contention that the resulting generalized subtraction scheme is robust, and therefore suitable for practical use, we perform a stability analysis in the thick limit where instabilities usually occur.
The Adjoint Difference Method And Its Application To Deep Penetration Radiation Transport
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Author : Thomas Joseph Hoffman
language : en
Publisher:
Release Date : 1971
The Adjoint Difference Method And Its Application To Deep Penetration Radiation Transport written by Thomas Joseph Hoffman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with categories.
The problem of determining the effect of interest in a geometrically complex object (vehicle) far removed from the radiation source is important in the area of radiation transport. The direct solution to this problem involves a deep-penetration, Monte Carlo calculation. Calculations of this type are always costly, and often impossible. To deal with this problem, the adjoint difference method was developed. This method decomposes the original problem into two independent calculations: A geometrically simple (one- or two-dimensional) deep-penetration calculation that is independent of the vehicle; A localized, three-dimensional calculation that is independent of the radiation source. (Author).
A Comparison Of Radiation Transport Methods In Axisymmetric Geometries
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Author : John L Giuliani (Jr)
language : en
Publisher:
Release Date : 1986
A Comparison Of Radiation Transport Methods In Axisymmetric Geometries written by John L Giuliani (Jr) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with categories.
The radiative transfer equation with a fixed source and fixed absorption is studied in axisymmetric geometries. A comparison of solutions for several model problems is presented using two different numerical schemes. The first scheme uses the radiation diffusion approximation with flux-limiting; the second, a multi-directional ray trace. The underlying spatial grid over which the solutions are calculated is a distorted set of quadrilaterals for application to two dimensional, Lagrangian, radiation-hydrodynamic codes. The results of the numerical solutions indicate that both schemes are accurate in radiating, optically thick regions. In source-free, purely absorbing regions, the accuracy decreases, but much more so for the diffusion approach than the ray tracing one. The major advantages of the latter approach over the former are; (i) the accuracy can be easily improved by increasing the number of rays for example, and (ii) computation time can be shorter for multi frequency calculations with more than about 10 frequencies.
Measure Of Diffusion Model Error For Thermal Radiation Transport
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Author : Akansha Kumar
language : en
Publisher:
Release Date : 2013
Measure Of Diffusion Model Error For Thermal Radiation Transport written by Akansha Kumar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with categories.
The diffusion approximation to the equation of transfer (Boltzmann transport equation) is usually applied to media where scattering dominates the interactions. Diffusion approximation helps in significant savings in terms of code complexity and computational time. However, this approximation often has significant error. Error due to the inherent nature of a physics model is called model error. Information about the model error associated with the diffusion approximation is clearly desirable. An indirect measure of model error is a quantity that is related in some way to the error but not equal to the error. In general, indirect measures of error are expected to be less costly than direct measures. Perhaps the most well-known indirect measure of the diffusion model error is the variable-Eddington tensor. This tensor provides a great deal of information about the angular dependence of the angular intensity solution, but it is not always simple to interpret. We define a new indirect measure of the diffusion model error called the diffusion model error source (DME source). When this DME source is added to the diffusion equation, the transport solution for the angular-integrated intensity is obtained. In contrast to the variable-Eddington tensor, our DME source is a scalar that is conceptually easy to interpret. In addition to defining the DME source analytically, we show how to generate this source numerically relative to the Sn radiative transfer equations with linear-discontinuous spatial discretization. This numerical source is computationally tested and shown to reproduce the Sn solution for a number of problems. Our radiative transfer model solves a coupled, time dependent, multi-frequency, 1-D slab equation and material heat transfer equation. We then use diffusion approximation to solve the same problem. The difference due to this approximation can be modelled by a "diffusion source". The diffusion source is defined as an amount of inhomogeneous source that, when added to a diffusion calculation, gives a solution for the angle-integrated intensity that is equal to the transport solution. The electronic version of this dissertation is accessible from http://hdl.handle.net/1969.1/149531
Collective Phenomena In Synchrotron Radiation Sources
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Author : Shaukat Khan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-01-19
Collective Phenomena In Synchrotron Radiation Sources written by Shaukat Khan 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 2007-01-19 with Science categories.
This book helps dispel the notion that collective phenomena, which have become increasingly important in modern storage rings, are an obscure and inaccessible topic. The book serves as a valuable guide on how to improve synchrotrons and other storage rings. Despite an emphasis on synchrotron light sources, the basic concepts presented here are valid for other facilities as well.