在具有奇点和任意域的周扩散动态模型中执行局部边界条件

IF 8.7 2区 工程技术 Q1 Mathematics
Jiangming Zhao, Siavash Jafarzadeh, Ziguang Chen, Florin Bobaru
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引用次数: 0

摘要

摘要 在周动力学(PD)模型中经常需要在自由表面施加局部边界条件和减轻表面效应。虚构节点法(FNM)用厚度等于 PD 水平面尺寸的虚构薄层 "扩展 "域,是实现这些目的的常用技术。然而,FNM 通常仅限于具有简单几何形状的域。在此,我们介绍一种基于镜像的 FNM 算法,该算法可应用于任意几何形状的畴。该算法基于在每个虚构节点上近似域边界的 "广义"(或非局部)法向量,自动确定(给定域中)所有虚构节点的镜像节点。我们在一个经典扩散问题的周动态模型中测试了这种新算法,该模型的边界上有一个通量奇点。我们发现,其他类型的 FNM 会 "污染 "远离奇点的解,而基于镜像的 FNM 则不会,此外,在水平线归零的极限情况下,它向经典解的收敛速度明显更快。新算法随后被用于在具有曲线边界和相交裂缝的域中求解基于镜像的 FNM 扩散问题。所提出的算法极大地提高了任意形状域边界附近的精确度,包括具有拐角、缺口和裂缝尖端的域。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Enforcing local boundary conditions in peridynamic models of diffusion with singularities and on arbitrary domains

Enforcing local boundary conditions in peridynamic models of diffusion with singularities and on arbitrary domains

Abstract

Imposing local boundary conditions and mitigating the surface effect at free surfaces in peridynamic (PD) models are often desired. The fictitious nodes method (FNM) “extends” the domain with a thin fictitious layer of thickness equal to the PD horizon size, and is a commonly used technique for these purposes. The FNM, however, is limited, in general, to domains with simple geometries. Here we introduce an algorithm for the mirror-based FNM that can be applied to arbitrary domain geometries. The algorithm automatically determines mirror nodes (in the given domain) of all fictitious nodes based on approximating, at each fictitious node, the “generalized” (or nonlocal) normal vector to the domain boundary. We tested the new algorithm for a peridynamic model of a classical diffusion problem with a flux singularity on the boundary. We show that other types of FNMs exhibit “pollution” of the solution far from the singularity point, while the mirror-based FNM does not and, in addition, shows a significantly faster rate of convergence to the classical solution in the limit of the horizon going to zero. The new algorithm is then used for mirror-based FNM solutions of diffusion problems in domains with curvilinear boundaries and with intersecting cracks. The proposed algorithm significantly improves the accuracy near boundaries of domains of arbitrary shapes, including those with corners, notches, and crack tips.

Graphical Abstract

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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
期刊介绍: Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.
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