Goal-Based Error Estimation for the Multi-Dimensional Diamond Difference and Box Discrete Ordinate (SN) Methods

IF 0.7 4区工程技术 Q3 MATHEMATICS, APPLIED

Journal of Computational and Theoretical Transport Pub Date : 2020-01-30 DOI:10.1080/23324309.2019.1710214

R. S. Jeffers, J. Kópházi, M. D. Eaton, F. Févotte, F. Hülsemann, J. Ragusa

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引用次数: 0

Abstract

Abstract Goal-based error estimation due to spatial discretization and adaptive mesh refinement (AMR) has previously been investigated for the one dimensional, diamond difference, discrete ordinate (1-D DD-SN) method for discretizing the Neutron Transport Equation (NTE). This paper investigates the challenges of extending goal-based error estimation to multi-dimensions with supporting evidence provided on 2-D fixed (extraneous) source and Keff eigenvalue (criticality) verification test cases. It was found that extending Hennart’s weighted residual view of the lowest order 1-D DD equations to multi-dimensions gave what has previously been called the box method. This paper shows how the box method can be extended to higher orders. The paper also shows an equivalence between the higher order box methods and the higher order DD methods derived by Hébert et al. Though, less information is retained in the final solution in the latter case. These extensions allow for the definition of dual weighted residual (DWR) error estimators in multi-dimensions for the DD and box methods. However, they are not applied to drive AMR in the multi-dimensional case due to the various challenges explained in this paper.

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多维菱形差分和盒形离散纵坐标(SN)方法的目标误差估计

摘要针对中子输运方程(NTE)的一维菱形差分离散坐标(1-D DD-SN)离散化方法，研究了基于目标的空间离散化和自适应网格细化(AMR)误差估计。本文研究了将基于目标的误差估计扩展到多维的挑战，并提供了二维固定(外来)源和Keff特征值(临界)验证测试用例的支持证据。研究发现，将Hennart的最低阶1-D DD方程的加权残差视图扩展到多维，给出了以前称为盒法的方法。本文说明了如何将盒法推广到更高阶。本文还证明了hsambert等人推导的高阶盒法与高阶DD法之间的等价性。但是，在后一种情况下，最终解决方案中保留的信息较少。这些扩展允许为DD和box方法定义多维的双加权残差(DWR)误差估计器。然而，由于本文解释的各种挑战，它们并不适用于多维情况下的驱动AMR。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Computational and Theoretical Transport Mathematics-Mathematical Physics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： Emphasizing computational methods and theoretical studies, this unique journal invites articles on neutral-particle transport, kinetic theory, radiative transfer, charged-particle transport, and macroscopic transport phenomena. In addition, the journal encourages articles on uncertainty quantification related to these fields. Offering a range of information and research methodologies unavailable elsewhere, Journal of Computational and Theoretical Transport brings together closely related mathematical concepts and techniques to encourage a productive, interdisciplinary exchange of ideas.