This repository contains a brief code which aims to compare different transport methods for solving the Boltzmann transport equation when the total cross section is spatially non-uniform.
Please refer to the following article for more information: "H. Belanger et al., submitted to EPJ+ (2020)"
The example output files in the data directory contain the data sets used
to write this article. A python script is also provided there to plot the
collision density and FOM for all problems.
The code uses as one-dimensional rod geometry. The media is located in within the domain 0 <= x <= 2, with vacuum boundary conditions imposed at x=0 and x=2. Particles all enter the rod at x=0, moving in the positive direction. Despite the total cross section varying as a function of position within the rod, individual reaction channel probabilities are kept constant at all locations. The probability of absorption is 0.3, and that of scatter is 0.7. Scattering is isotropic, with equal probability of scattering in the forward or backwards direction.
Implicit capture and Russian Roulette are used for variance reduction. The survival weight is 1 while the roulette cutoff weight is 0.6. Particle spliting is also used as a variance reduction technique for the transport methods which augment particle weights. Particles with a weight w greater than or equal to 2 are split into N identical particles, each with weight w/N, where N is the rounded value of the original weight.
The transport methods evaulated in this code are based on the following works:
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Direct Sampling : F.B. Brown, W.R. Martin, Direct Sampling of Monte Carlo Flight Paths in Media with Continuously Varying Cross-Sections, in ANS Mathematics & Computation Topical Meeting (2003), Vol. 2
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Delta Tracking : E.R. Woodcock, T. Murphy, P.J. Hemmings, T.C. Longworth, Technical report. ANL-7050, ArgonneNational Laboratory, USA (1965)
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Negative Weighted Delta Tracking : D. Legrady, B. Molnar, M. Klausz, T. Major, Ann. Nucl. Energy 102, 116 (2017)
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Carter, Cashwell, and Taylor Tracking : L.L. Carter, E.D. Cashwell, W.M. Taylor, Nucl. Sci. Eng. 48, 403 (1972)
This software is distributed under the terms and conditions of the CeCILL v2.1 license. The English version is provided in the LICENSE file, and the equally valid and authenic French version is provided in LICENSE-FRENCH. This is a copyleft license, very simillar to the GNU GPL, and is compatible with both the GPLv2 and GPLv3. If you would like more information about the CeCILL license beyond that provided in the two license files, please refer to the CeCILL website.
To build and install cmmct, run the following commands:
$ mkdir build && cd build
$ cmake -DCMAKE_INSTALL_PREFIX=/path/for/binary ..
$ make
This will build a cmmct executable, with OpenMP support automatically
enabled. If you would like to dissable OpenMP, run cmake with the
-Dopenmp=off option.