A new three-dimensional method of characteristics for the neutron transport calculation

Liu, Zhouyu; Wu, Hongchun; Cao, Liangzhi; Chen, Qichang; Li, Yunzhao

doi:10.1016/j.anucene.2010.09.021

Cited by 47 publications

(7 citation statements)

References 5 publications

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“…In Equation 1, represents the spatial vector, represents the angular vector that is comprised of both an azimuthal and polar angle, denotes the neutron energy group index, and is the source term which contains both the fission and scattering terms. The method can be applied in 1D [18], 2D, and 3D [19,20,21,22] applications. The focus of the MOC equations in this paper is on flat source, 2D-radial applications.…”

Section: Iia the Methods Of Characteristics (Moc)mentioning

confidence: 99%

Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC

Stimpson

Collins

Kochunas

2017

Annals of Nuclear Energy

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The MPACT code, being developed collaboratively by the University of Michigan and Oak Ridge National Laboratory, is the primary deterministic neutron transport solver being deployed within the Virtual Environment for Reactor Applications (VERA) as part of the Consortium for Advanced Simulation of Light Water Reactors (CASL). In many applications of the MPACT code, transport-corrected scattering has proven to be an obstacle in terms of stability, and considerable effort has been made to try to resolve the convergence issues that arise from it. Most of the convergence problems seem related to the transport-corrected cross sections, particularly when used in the 2D method of characteristics (MOC) solver, which is the focus of this work. In this paper, the stability and performance of the 2-D MOC solver in MPACT is evaluated for two iteration schemes: Gauss-Seidel and Jacobi. With the Gauss-Seidel approach, as the MOC solver loops over groups, it uses the flux solution from the previous group to construct the inscatter source for the next group. Alternatively, the Jacobi approach uses only the fluxes from the previous outer iteration to determine the inscatter source for each group. Consequently for the Jacobi iteration, the loop over groups can be moved from the outermost loop-as is the case with the Gauss-Seidel sweeper-to the innermost loop, allowing for a substantial increase in efficiency by minimizing the overhead of retrieving segment, region, and surface index information from the ray tracing data. Several test problems are assessed: (1) Babcock & Wilcox 1810 Core I, (2) Dimple S01A-Sq, (3) VERA Progression Problem 5a, and (4) VERA Problem 2a. The Jacobi iteration exhibits better stability than Gauss-Seidel, allowing for converged solutions to be obtained over a much wider range of iteration control parameters. Additionally, the MOC solve time with the Jacobi approach is roughly 2.0-2.5× faster per sweep. While the performance and stability of the Jacobi iteration are substantially improved compared to the Gauss-Seidel iteration, it does yield a roughly 8-10% increase in the overall memory requirement.

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Section: Iia the Methods Of Characteristics (Moc)mentioning

confidence: 99%

Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC

Stimpson

Collins

Kochunas

2017

Annals of Nuclear Energy

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“…The 3DMOC code is a coupling of 3D method of characteristics and the common geometry module [16]. This arrangement allows CAD models to be analyzed without using the common approach of surface equations or Boolean operations in the input card.…”

Section: The 3dmoc Codementioning

confidence: 99%

“…However, direct MOC calculations for 3D problems require a tremendous amount of memory and very long computing time. Therefore, a 3D modular ray tracing technique [16] is adopted in the 3DMOC code, which can not only hold the geometry flexibility of the MOC but also reduce the tremendous memory requirement. For the modular ray tracing technique, the object geometry is dissected into many cuboid cells by a background mesh.…”

Section: The 3dmoc Codementioning

confidence: 99%

Study on three-dimensional heterogeneous calculation of ITER test blanket module with deterministic method

Zhang

Cao

et al. 2013

Fusion Engineering and Design

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“…The coarse mesh finite difference (CMFD) method (Smith, 1984), has been widely used with pronounced success for reactor analysis for the last several decades. As a low-order acceleration scheme, CMFD solves the diffusion-like equation on a coarse mesh and it is very effective at accelerating the MOC calculation (Liu et al, 2011;Kochunas et al, 2013). However, CMFD can introduce numerical instabilities in optically thick regions which results in a degradation in performance or even a failure to convergence.…”

Section: Introductionmentioning

confidence: 99%

GPU Based Two-Level CMFD Accelerating Two-Dimensional MOC Neutron Transport Calculation

et al. 2020

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The Graphics Processing Units (GPUs) are increasingly becoming the primary computational platform in the scientific fields, due to its cost-effectiveness and massively parallel processing capability. On the other hand, the coarse mesh finite difference (CMFD) method has been one of the most popular techniques to accelerate the neutron transport calculation. The GPU is employed into the method of characteristics (MOC) accelerated by two-level CMFD to solve the neutron transport equation. In this work, the Jacobi method, the successive over-relaxation (SOR) method with red-black ordering, and the preconditioned generalized minimum residual (PGMRES) method are applied to solve the linear system under the framework of CMFD. The performance of these linear system solvers is characterized on both CPU (Central Processing Unit) and GPU. The two-dimensional (2-D) C5G7 benchmark problem and an extended mock quarter-core problem are tested to verify the accuracy and efficiency of the algorithm with double precision, as well as the feasibility of massive parallelization. Numerical results demonstrate that the desired accuracy is maintained. Moreover, the results show that the few-group CMFD acceleration is effective to accelerate the multi-group CMFD calculation. The PGMRES method shows remarkable convergence characteristics compared to the Jacobi and the SOR methods. However, the SOR method shows better performance on GPU for solving the linear system of CMFD calculation, which reaches about 2,400x speedup on GPU with two-level CMFD acceleration compared to the CPU-based MOC calculation.

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A new three-dimensional method of characteristics for the neutron transport calculation

Cited by 47 publications

References 5 publications

Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC

Improvement of transport-corrected scattering stability and performance using a Jacobi inscatter algorithm for 2D-MOC

Study on three-dimensional heterogeneous calculation of ITER test blanket module with deterministic method

GPU Based Two-Level CMFD Accelerating Two-Dimensional MOC Neutron Transport Calculation

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