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The Advancement of Stable, Efficient and Parallel Acceleration Methods for the Neutron Transport Equation

Abstract : In this paper we propose a new library of non-linear techniques for accelerating the discrete-ordinates transport equation. Two new types of nonlinear acceleration methods called Spatially Variant Rebalancing Method (SVRM) and Response Matrix Acceleration (RMA), respectively, are proposed and investigated. The first method, SVRM, is based on the computation of the zeroth and first order spatial variation of the neutron balance equation. RMA, is a DP0 method that uses knowledge of the transport operator to form a consistent relationship. Two distinct variants of RMA, called Explicit-RMA (E-RMA) and Balance (B-RMA), respectively, are derived. The convergence properties of both acceleration methods are investigated for two different iteration schemes of the method of characteristics (MOC) transport operator for a 1D slab, using spectral and Fourier analysis. Based off the results of the 1D comparison, only RMA and CMFD were implemented in the library. The performance of RMA is compared to CMFD using the C5G7, ZPPR, and UH12 3D benchmarks. Both parallel and sequential solving schemes are considered. Analysis of the results indicates that both variants of RMA have improved effectiveness and stability relative to CMFD, for optically diffusive materials. Moreover, RMA shows great improvement in stability and effectiveness when the geometry is spatially decomposed. To achieve optimal numerical performance, a combination of RMA and CMFD is suggested. Further investigation into the use and improvement of RMA is proposed. As well, many ideas for extending the features of the library are presented.
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Submitted on : Tuesday, November 26, 2019 - 3:39:08 PM
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  • HAL Id : tel-02381357, version 1

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Wesley Ford. The Advancement of Stable, Efficient and Parallel Acceleration Methods for the Neutron Transport Equation. Computational Physics [physics.comp-ph]. Université Paris Saclay (COmUE), 2019. English. ⟨NNT : 2019SACLX105⟩. ⟨tel-02381357⟩

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