Performance of three-dimensional nodal discrete ordinates methods

Badruzzaman, Ahmed

doi:10.1016/0149-1970(86)90020-x

Cited by 13 publications

(4 citation statements)

References 5 publications

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“…To construct the LTS N nodal solution for problem (1) we begin performing the transverse integration of this equation. This procedure yields to the set of the ensuing two coupled S N equations,…”

Section: The Lts N Nodal Solution In a Rectangular Domainmentioning

confidence: 99%

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An overview of the Boltzmann transport equation solution for neutrons, photons and electrons in Cartesian geometry

Rodriguez

Vilhena

Bodmann

2011

Progress in Nuclear Energy

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Questions regarding accuracy and efficiency of deterministic transport methods are still on our mind today, even with modern supercomputers. The most versatile and widely used deterministic methods are the P N approximation, the S N method (discrete ordinates method) and their variants. In the discrete ordinates (S N) formulations of the transport equation, it is assumed that the linearized Boltzmann equation only holds for a set of distinct numerical values of the direction-of-motion variables. In this work, looking forward to confirm the capabilities of deterministic methods in obtaining accurate results, we present a general overview of deterministic methods to solve the Boltzmann transport equation for neutral and charged particles. First, we describe a review in the Laplace transform technique applied to S N two dimensional transport equation in a rectangular domain considering Compton scattering. Next, we solved the Fokker-Planck (FP) equation, an alternative approach for the Boltzmann transport equation, assuming a monoenergetic electron beam in a rectangular domain. The main idea relies on applying the P N approximation, a recent advance in the class of deterministic methods, in the angular variable, to the two dimensional Fokker-Planck equation and then applying the Laplace Transform in the spatial x-variable. Numerical results are given to illustrate the accuracy of deterministic methods presented.

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Section: The Lts N Nodal Solution In a Rectangular Domainmentioning

confidence: 99%

“…The Boltzmann equation is an integro-differential equation representing a wide range of transport problems from astrophysics to traffic low [1]. Elegant analytical and numerical techniques have been developed to solve the Boltzmann equation for a broad class of transport and radiative transfer problems.…”

Section: Introductionmentioning

confidence: 99%

An overview of the Boltzmann transport equation solution for neutrons, photons and electrons in Cartesian geometry

Rodriguez

Vilhena

Bodmann

2011

Progress in Nuclear Energy

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“…The most widely applicable method, the discrete ordi nates SN method (96), has until recently been limited to 2-dimensional geometries since the number of unknowns and computer storage require ments were prohibitively large in three dimensions. These limitations are being addressed by the availability of supercomputers in conjunction with the development of accurate, spatial coarse-mesh methods to solve the transport equation in three dimensions (97)(98)(99).…”

Section: Deterministic Me Thodsmentioning

confidence: 99%

Nuclear Techniques For Subsurface Geology

Ellis¹

1987

Annual Review of Nuclear and Particle Science

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“…However, as such methods are computationally very expensive due to their statistical nature, the development of alternative, deterministic methods was a challenging alternative. Computational techniques such as the nodal discrete‐ordinates methods were implemented in the 1980s, showing their reduced computational times in relation to the previous Monte‐Carlo techniques (Badruzzaman 1986). Deterministic codes, such as the finite‐element/spherical‐harmonics code developed by de Oliveira (1986), have also recently been applied to nuclear well‐logging problems, with the results successfully compared to both Monte‐Carlo and other deterministic (discrete‐ordinance) simulations (Kodeli et al 2001).…”

Section: Introductionmentioning

confidence: 99%

Energy Group optimization for forward and inverse problems in nuclear engineering: application to downwell‐logging problems

Aristodemou

Pain

Oliveira

et al. 2006

Geophysical Prospecting

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A B S T R A C TSimulating radiation transport of neutral particles (neutrons and γ -ray photons) within subsurface formations has been an area of research in the nuclear well-logging community since the 1960s, with many researchers exploiting existing computational tools already available within the nuclear reactor community. Deterministic codes became a popular tool, with the radiation transport equation being solved using a discretization of phase-space of the problem (energy, angle, space and time). The energy discretization in such codes is based on the multigroup approximation, or equivalently the discrete finite-difference energy approximation. One of the uncertainties, therefore, of simulating radiation transport problems, has become the multigroup energy structure. The nuclear reactor community has tackled the problem by optimizing existing nuclear cross-sectional libraries using a variety of group-collapsing codes, whilst the nuclear well-logging community has relied, until now, on libraries used in the nuclear reactor community. However, although the utilization of such libraries has been extremely useful in the past, it has also become clear that a larger number of energy groups were available than was necessary for the well-logging problems. It was obvious, therefore, that a multigroup energy structure specific to the needs of the nuclear well-logging community needed to be established. This would have the benefit of reducing computational time (the ultimate aim of this work) for both the stochastic and deterministic calculations since computational time increases with the number of energy groups.We, therefore, present in this study two methodologies that enable the optimization of any multigroup neutron-γ energy structure. Although we test our theoretical approaches on nuclear well-logging synthetic data, the methodologies can be applied to other radiation transport problems that use the multigroup energy approximation. The first approach considers the effect of collapsing the neutron groups by solving the forward transport problem directly using the deterministic code EVENT, and obtaining neutron and γ -ray fluxes deterministically for the different group-collapsing *

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Performance of three-dimensional nodal discrete ordinates methods

Cited by 13 publications

References 5 publications

An overview of the Boltzmann transport equation solution for neutrons, photons and electrons in Cartesian geometry

An overview of the Boltzmann transport equation solution for neutrons, photons and electrons in Cartesian geometry

Nuclear Techniques For Subsurface Geology

Energy Group optimization for forward and inverse problems in nuclear engineering: application to downwell‐logging problems

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