NURBS Enhanced Virtual Element Methods for the Spatial Discretization of the Multigroup Neutron Diffusion Equation on Curvilinear Polygonal Meshes

IF 0.7 4区工程技术 Q3 MATHEMATICS, APPLIED

Journal of Computational and Theoretical Transport Pub Date : 2022-06-07 DOI:10.1080/23324309.2022.2103150

John Ferguson, Mathew Eaton, J. Kópházi

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引用次数: 1

Abstract

Abstract The Continuous Galerkin Virtual Element Method (CG-VEM) is a recent innovation in spatial discretization methods that can solve partial differential equations (PDEs) using polygonal (2D) and polyhedral (3D) meshes. Recently, a new formulation of CG-VEM was introduced which can construct VEM spaces on polygons with curvilinear edges. This paper presents the application of the curved VEM to the multigroup neutron diffusion equation and demonstrates its benefits over the conventional straight-sided VEM for a number of benchmark verification test cases with curvilinear domains. These domains were constructed using a topological data-structure developed as part of this paper, based on the doubly-connected edge list, with curves and surfaces both represented using non-uniform rational B-splines (NURBS). This data-structure is used both to specify the geometry of the reactor and to represent the curvilinear polygonal mesh. We also present two separate methods of performing integrations on curvilinear polygons, one for homogeneous functions and one for non-homogeneous functions.

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曲线多边形网格上多组中子扩散方程空间离散化的NURBS增强虚拟元方法

摘要连续伽辽金虚拟单元法（CG-VEM）是空间离散化方法的最新创新，可以使用多边形（2D）和多面体（3D）网格求解偏微分方程（PDE）。最近，提出了一种新的CG-VEM公式，它可以在具有曲线边的多边形上构造VEM空间。本文介绍了曲线VEM在多组中子扩散方程中的应用，并在许多具有曲线域的基准验证测试用例中证明了其优于传统的直边VEM的优点。这些域是使用拓扑数据结构构建的，该拓扑数据结构是本文的一部分，基于双连通边列表，曲线和曲面都使用非均匀有理B样条（NURBS）表示。该数据结构用于指定反应器的几何结构和表示曲线多边形网格。我们还提出了两种在曲线多边形上进行积分的独立方法，一种用于齐次函数，另一种用于非齐次函数。

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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.