Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

Fan, Wesley C.; Drumm, Clifton Russell; Powell, Jennifer L.

doi:10.2172/800996

Cited by 3 publications

(2 citation statements)

References 3 publications

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“…The EOP equations solve the RTE with the radiance only over half of the angular domain, making the simulation speed faster when compared to the SAAF formula. However, the boundary conditions may pose challenges for the solution when photons propagate in a void region (Fan et al 2002). 1)) is an integro-differential equation of five independent variables: three dimensions, angle and time.…”

Section: Radiative Transfer Equation (Rte)mentioning

confidence: 99%

Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update

Darne¹,

Lu²,

2013

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Emerging fluorescence and bioluminescence tomography approaches have several common, yet several distinct features from established emission tomographies of PET and SPECT. Although both nuclear and optical imaging modalities involve counting of photons, nuclear imaging techniques collect the emitted high energy (100-511 keV) photons after radioactive decay of radionuclides while optical techniques count low-energy (1.5-4.1 eV) photons that are scattered and absorbed by tissues requiring models of light transport for quantitative image reconstruction. Fluorescence imaging has been recently translated into clinic demonstrating high sensitivity, modest tissue penetration depth, and fast, millisecond image acquisition times. As a consequence, the promise of quantitative optical tomography as a complement of small animal PET and SPECT remains high. In this review, we summarize the different instrumentation, methodological approaches and schema for inverse image reconstructions for optical tomography, including luminescence and fluorescence modalities, and comment on limitations and key technological advances needed for further discovery research and translation.

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Section: Radiative Transfer Equation (Rte)mentioning

confidence: 99%

Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update

Darne¹,

Lu²,

2013

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“…al. derived an operator form of the SAAF equation angularly discretised using discrete ordinates (S N ) and with anisotropic scattering [19]. Ackroyd developed another variational derivation by considering relaxed forms of the SAAF equation based on trial functions and vectors for the reaction and leakage rates respectively, spatially discretised using FEs [20].…”

Section: Introductionmentioning

confidence: 99%

A geometry conforming isogeometric method for the self-adjoint angular flux (SAAF) form of the neutron transport equation with a discrete ordinate (SN) angular discretisation

Latimer

Kópházi

Eaton

et al. 2020

Annals of Nuclear Energy

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This paper presents the application of isogeometric analysis (IGA) to the spatial discretisation of the multi-group, self-adjoint angular flux (SAAF) form of the neutron transport equation with a discrete ordinate (S N) angular discretisation. The IGA spatial discretisation is based upon non-uniform rational B-spline (NURBS) basis functions for both the test and trial functions. In addition a source iteration compatible maximum principle is used to derive the IGA spatially discretised SAAF equation. It is demonstrated that this maximum principle is mathematically equivalent to the weak form of the SAAF equation. The rate of convergence of the IGA spatial discretisation of the SAAF equation is analysed using a method of manufactured solutions (MMS) verification test case. The results of several nuclear reactor physics verification benchmark test cases are analysed. This analysis demonstrates that for higher-order basis functions, and for the same number of degrees of freedom, the FE based spatial discretisation methods are numerically less accurate than IGA methods. The difference in numerical accuracy between the IGA and FE methods is shown to be because of the higher-order continuity of NURBS basis functions within a NURBS patch as well as the preservation of both the volume and surface area throughout the solution domain within the IGA spatial discretisation. Finally, the numerical results of applying the IGA SAAF method to the OECD/NEA, seven-group, two-dimensional C5G7 quarter core nuclear reactor physics verification benchmark test case are presented. The results, from this verification benchmark test case, are shown to be in good agreement with solutions of the first-order form as well as the second-order even-parity form of the neutron transport equation for the same order of discrete ordinate (S N) angular approximation.

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Axially Quadratic Discontinuous Finite Elements for Neutron Transport Reactor Simulations

Turner¹

2019

Transactions of the American Nuclear Society - Volume 121

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Discrete Ordinates Approximations to the First- and Second-Order Radiation Transport Equations

Cited by 3 publications

References 3 publications

Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update

Small animal fluorescence and bioluminescence tomography: a review of approaches, algorithms and technology update

A geometry conforming isogeometric method for the self-adjoint angular flux (SAAF) form of the neutron transport equation with a discrete ordinate (SN) angular discretisation

Axially Quadratic Discontinuous Finite Elements for Neutron Transport Reactor Simulations

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