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Title: Improvement of the 2D/1D Method in MPACT Using the Sub-Plane Scheme

Abstract

Oak Ridge National Laboratory and the University of Michigan are jointly developing the MPACTcode to be the primary neutron transport code for the Virtual Environment for Reactor Applications (VERA). To solve the transport equation, MPACT uses the 2D/1D method, which decomposes the problem into a stack of 2D planes that are then coupled with a 1D axial calculation. MPACT uses the Method of Characteristics for the 2D transport calculations and P3 for the 1D axial calculations, then accelerates the solution using the 3D Coarse mesh Finite Dierence (CMFD) method. Increasing the number of 2D MOC planes will increase the accuracy of the alculation, but will increase the computational burden of the calculations and can cause slow convergence or instability. To prevent these problems while maintaining accuracy, the sub-plane scheme has been implemented in MPACT. This method sub-divides the MOC planes into sub-planes, refining the 1D P3 and 3D CMFD calculations without increasing the number of 2D MOC planes. To test the sub-plane scheme, three of the VERA Progression Problems were selected: Problem 3, a single assembly problem; Problem 4, a 3x3 assembly problem with control rods and pyrex burnable poisons; and Problem 5, a quarter core problem. These three problemsmore » demonstrated that the sub-plane scheme can accurately produce intra-plane axial flux profiles that preserve the accuracy of the fine mesh solution. The eigenvalue dierences are negligibly small, and dierences in 3D power distributions are less than 0.1% for realistic axial meshes. Furthermore, the convergence behavior with the sub-plane scheme compares favorably with the conventional 2D/1D method, and the computational expense is decreased for all calculations due to the reduction in expensive MOC calculations.« less

Authors:
 [1];  [1];  [2]
  1. ORNL
  2. University of Michigan
Publication Date:
Research Org.:
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Consortium for Advanced Simulation of LWRs (CASL)
Sponsoring Org.:
USDOE
OSTI Identifier:
1344278
DOE Contract Number:
AC05-00OR22725
Resource Type:
Conference
Resource Relation:
Conference: M&C 2017 - International Conference on Mathematics & Computational Methods Applied to Nuclear Science & Engineering, Jeju, South Korea, 20170416, 20170420
Country of Publication:
United States
Language:
English

Citation Formats

Graham, Aaron M, Collins, Benjamin S, and Downar, Thomas. Improvement of the 2D/1D Method in MPACT Using the Sub-Plane Scheme. United States: N. p., 2017. Web.
Graham, Aaron M, Collins, Benjamin S, & Downar, Thomas. Improvement of the 2D/1D Method in MPACT Using the Sub-Plane Scheme. United States.
Graham, Aaron M, Collins, Benjamin S, and Downar, Thomas. 2017. "Improvement of the 2D/1D Method in MPACT Using the Sub-Plane Scheme". United States. doi:.
@article{osti_1344278,
title = {Improvement of the 2D/1D Method in MPACT Using the Sub-Plane Scheme},
author = {Graham, Aaron M and Collins, Benjamin S and Downar, Thomas},
abstractNote = {Oak Ridge National Laboratory and the University of Michigan are jointly developing the MPACTcode to be the primary neutron transport code for the Virtual Environment for Reactor Applications (VERA). To solve the transport equation, MPACT uses the 2D/1D method, which decomposes the problem into a stack of 2D planes that are then coupled with a 1D axial calculation. MPACT uses the Method of Characteristics for the 2D transport calculations and P3 for the 1D axial calculations, then accelerates the solution using the 3D Coarse mesh Finite Dierence (CMFD) method. Increasing the number of 2D MOC planes will increase the accuracy of the alculation, but will increase the computational burden of the calculations and can cause slow convergence or instability. To prevent these problems while maintaining accuracy, the sub-plane scheme has been implemented in MPACT. This method sub-divides the MOC planes into sub-planes, refining the 1D P3 and 3D CMFD calculations without increasing the number of 2D MOC planes. To test the sub-plane scheme, three of the VERA Progression Problems were selected: Problem 3, a single assembly problem; Problem 4, a 3x3 assembly problem with control rods and pyrex burnable poisons; and Problem 5, a quarter core problem. These three problems demonstrated that the sub-plane scheme can accurately produce intra-plane axial flux profiles that preserve the accuracy of the fine mesh solution. The eigenvalue dierences are negligibly small, and dierences in 3D power distributions are less than 0.1% for realistic axial meshes. Furthermore, the convergence behavior with the sub-plane scheme compares favorably with the conventional 2D/1D method, and the computational expense is decreased for all calculations due to the reduction in expensive MOC calculations.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2017,
month = 1
}

Conference:
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  • As part of its initiative to provide multiphysics simulations of nuclear reactor cores, the Consortium for Advanced Simulation of Light Water Reactors (CASL) is developing the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). The MPACT code, which is the primary neutron transport solver of VERA-CS, employs the two-dimensional/one-dimensional (2D/1D) method to solve 3-dimensional neutron transport problems and provide sub-pin-level resolution of the power distribution. While 2D method of characteristics is used to solve for the transport effects within each plane, 1D-nodal methods are used axially. There have been extensive studies of the 2D/1D method with a variety nodal methods,more » and the P 3/SP 3 solver has proved to be an effective method of providing higher-fidelity solutions while maintaining a low computational burden.The current implementation in MPACT wraps a one-node nodal expansion method (NEM) kernel for each moment, iterating between them and performing multiple sweeps to resolve flux distributions. However, it has been observed that this approach is more sensitive to convergence problems. This paper documents the theory and application two new nodal P 3/SP 3 approaches to be used within the 2D/1D method in MPACT. These two approaches aim to provide enhanced stability compared with the pre-existing one-node approach. Results from the HY-NEM-SP 3 solver show that the accuracy is consistent with the one-node formulations and provides improved convergence for some problems; but the solver has issues with cases in thin planes. Although the 2N-SENM-SP 3 solver is still under development, it is intended to resolve the issues with HY-NEM-SP 3 but it will incur some additional computational burden by necessitating an additional 1D-CMFD-P 3 solver to generate the second moment cell-averaged scalar flux.« less
  • The MPACT transport code is being jointly developed by Oak Ridge National Laboratory and the University of Michigan to serve as the primary neutron transport code for the Virtual Environment for Reactor Applications Core Simulator. MPACT uses the 2D/1D method to solve the transport equation by decomposing the reactor model into a stack of 2D planes. A fine mesh flux distribution is calculated in each 2D plane using the Method of Characteristics (MOC), then the planes are coupled axially through a 1D NEM-Pmore » $$_3$$ calculation. This iterative calculation is then accelerated using the Coarse Mesh Finite Difference method. One problem that arises frequently when using the 2D/1D method is that of control rod cusping. This occurs when the tip of a control rod falls between the boundaries of an MOC plane, requiring that the rodded and unrodded regions be axially homogenized for the 2D MOC calculations. Performing a volume homogenization does not properly preserve the reaction rates, causing an error known as cusping. The most straightforward way of resolving this problem is by refining the axial mesh, but this can significantly increase the computational expense of the calculation. The other way of resolving the partially inserted rod is through the use of a decusping method. This paper presents new decusping methods implemented in MPACT that can dynamically correct the rod cusping behavior for a variety of problems.« less