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Title: A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report

Abstract

The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S N) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S N regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S N is well suited for by themselves. The fully coupled Monte Carlo/S N technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an S N calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary S N region. The Monte Carlo and S N regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the S N code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the responsemore » matrices and volumetric sources, and linkage subrountines to carry out the interface flux iterations. The common angular boundary fluxes are included in the S N code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating S N calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. However, the routines have been successfully vectorized, with approximately a factor of five increase in speed over the non-vectorized version.« less

Authors:
 [1]
  1. Univ. of Arizona, Tucson, AZ (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Arizona Univ., Tucson, AZ (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
10136650
Report Number(s):
LA-SUB-94-61
ON: DE94009071; TRN: 94:007477
DOE Contract Number:
W-7405-ENG-36
Resource Type:
Thesis/Dissertation
Resource Relation:
Other Information: DN: Thesis submitted by R.S. Baker to the University of Arizona, Tucson, AZ; TH: Thesis (Ph.D.); PBD: 1990
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; 97 MATHEMATICS AND COMPUTING; NEUTRON TRANSPORT THEORY; MONTE CARLO METHOD; ITERATIVE METHODS; CROSS SECTIONS; BENCHMARKS; RESPONSE MATRIX METHOD; PROGRESS REPORT; 663610; 990200; NEUTRON PHYSICS; MATHEMATICS AND COMPUTERS

Citation Formats

Baker, Randal Scott. A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report. United States: N. p., 1990. Web. doi:10.2172/10136650.
Baker, Randal Scott. A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report. United States. doi:10.2172/10136650.
Baker, Randal Scott. Mon . "A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report". United States. doi:10.2172/10136650. https://www.osti.gov/servlets/purl/10136650.
@article{osti_10136650,
title = {A fully coupled Monte Carlo/discrete ordinates solution to the neutron transport equation. Final report},
author = {Baker, Randal Scott},
abstractNote = {The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (SN) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and SN regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor SN is well suited for by themselves. The fully coupled Monte Carlo/SN technique consists of defining spatial and/or energy regions of a problem in which either a Monte Carlo calculation or an SN calculation is to be performed. The Monte Carlo region may comprise the entire spatial region for selected energy groups, or may consist of a rectangular area that is either completely or partially embedded in an arbitrary SN region. The Monte Carlo and SN regions are then connected through the common angular boundary fluxes, which are determined iteratively using the response matrix technique, and volumetric sources. The hybrid method has been implemented in the SN code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and volumetric sources, and linkage subrountines to carry out the interface flux iterations. The common angular boundary fluxes are included in the SN code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating SN calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. However, the routines have been successfully vectorized, with approximately a factor of five increase in speed over the non-vectorized version.},
doi = {10.2172/10136650},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Mon Jan 01 00:00:00 EST 1990},
month = {Mon Jan 01 00:00:00 EST 1990}
}

Thesis/Dissertation:
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  • The neutron transport equation is solved by a hybrid method that iteratively couples regions where deterministic (S{sub N}) and stochastic (Monte Carlo) methods are applied. Unlike previous hybrid methods, the Monte Carlo and S{sub N} regions are fully coupled in the sense that no assumption is made about geometrical separation or decoupling. The hybrid method provides a new means of solving problems involving both optically thick and optically thin regions that neither Monte Carlo nor S{sub N} is well suited for by themselves. The fully coupled Monte Carlo/S{sub N} technique consists of defining spatial and/or energy regions of a problemmore » in which either a Monte Carlo calculation or an S{sub N} calculation is to be performed. The hybrid method has been implemented in the S{sub N} code TWODANT by adding special-purpose Monte Carlo subroutines to calculate the response matrices and volumetric sources, and linkage subroutines to carry out the interface flux iterations. The common angular boundary fluxes are included in the S{sub N} code as interior boundary sources, leaving the logic for the solution of the transport flux unchanged, while, with minor modifications, the diffusion synthetic accelerator remains effective in accelerating the S{sub N} calculations. The special-purpose Monte Carlo routines used are essentially analog, with few variance reduction techniques employed. The hybrid method is capable of solving forward, inhomogeneous source problems in X {minus} Y and R {minus} Z geometries. This capability includes multigroup problems involving upscatter and fission in non-highly multiplying (k{sub eff} {le} .8) systems. The hybrid method has been applied to several simple test problems with good results.« less
  • A method for applying the discrete ordinates method for solution of the neutron transport equation in arbitary two-dimensional meshes has been developed. The finite difference approach normally used to approximate spatial derivatives in extrapolating angular fluxes across a cell is replaced by direct solution of the characteristic form of the transport equation for each discrete direction. Thus, computational cells are not restricted to the traditional shape of a mesh element within a given coordinate system. However, in terms of the treatment of energy and angular dependencies, this method resembles traditional discrete ordinates techniques. Using the method developed here, a generalmore » two-dimensional space can be approximated by an irregular mesh comprised of arbitrary polygons. The present work makes no assumptions about the orientations or the number of sides in a given cell, and computes all geometric relationships between each set of sides in each cell for each discrete direction. A set of non-reentrant polygons can therefore be used to represent any given two dimensional space. Results for a number of test problems have been compared to solutions obtained from traditional methods, with good agreement. Comparisons include benchmarks against analytical results for problems with simple geometry, as well numerical results obtained from traditional discrete ordinates methods by applying the ANISN and TWOTRAN computer programs. Numerical results were obtained for problems ranging from simple one-dimensional geometry to complicated multidimensional configurations. These results have demonstrated the ability of the developed method to closely approximate complex geometrical configurations and to obtain accurate results for problems that are extremely difficult to model using traditional methods.« less
  • The fundamental motivation for the research presented in this dissertation was the need to development a more accurate prediction method for characterization of mixed radiation fields around medical electron accelerators (MEAs). Specifically, a model is developed for simulation of neutron and other particle production from photonuclear reactions and incorporated in the Monte Carlo N-Particle (MCNP) radiation transport code. This extension of the capability within the MCNP code provides for the more accurate assessment of the mixed radiation fields. The Nuclear Theory and Applications group of the Los Alamos National Laboratory has recently provided first-of-a-kind evaluated photonuclear data for a selectmore » group of isotopes. These data provide the reaction probabilities as functions of incident photon energy with angular and energy distribution information for all reaction products. The availability of these data is the cornerstone of the new methodology for state-of-the-art mutually coupled photon-neutron transport simulations. The dissertation includes details of the model development and implementation necessary to use the new photonuclear data within MCNP simulations. A new data format has been developed to include tabular photonuclear data. Data are processed from the Evaluated Nuclear Data Format (ENDF) to the new class ''u'' A Compact ENDF (ACE) format using a standalone processing code. MCNP modifications have been completed to enable Monte Carlo sampling of photonuclear reactions. Note that both neutron and gamma production are included in the present model. The new capability has been subjected to extensive verification and validation (V&V) testing. Verification testing has established the expected basic functionality. Two validation projects were undertaken. First, comparisons were made to benchmark data from literature. These calculations demonstrate the accuracy of the new data and transport routines to better than 25 percent. Second, the ability to calculate radiation dose due to the neutron environment around a MEA is shown. An uncertainty of a factor of three in the MEA calculations is shown to be due to uncertainties in the geometry modeling. It is believed that the methodology is sound and that good agreement between simulation and experiment has been demonstrated.« less
  • An algebraic equivalence between the point-energy and multigroup forms of the Boltzmann transport equation is demonstrated which allows the development of a discrete-energy, discrete-ordinates method for the solution of radiation transport problems.
  • A new algorithm is presented that applies the Green's Function Monte Carlo method to the Schroedinger Equation in imaginary time for atomic and molecular systems and that samples accurately the Coulomb singularity. The algorithm is applied to obtain the ground state energies of the following atomic systems: H; the hydrogenic ions Be/sup +3/ and O/sup +7/; helium; and the helium-like ions Be/sup +2/, N/sup +5/, and O/sup +6/. The results compare favorably to the experimental ground state energies.