解决半空间吃传导问题的稳定高效无限无网格方法

IF 8.7 2区 工程技术 Q1 Mathematics Engineering with Computers Pub Date : 2024-03-23 DOI:10.1007/s00366-024-01960-w
Kuan-Chung Lin, Ting-Wei Chen, Huai-Liang Hsieh
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引用次数: 0

摘要

本研究介绍了一种创新的动态无限无网格方法,用于稳健高效地解决半空间问题。该方法将节点积分再现核粒子法与人工边界定义的半空间离散化无缝结合。无限无网格形状函数是利用一维再现核形状函数结合边界奇异核方法唯一构建的,确保了人工边界上的 Kronecker delta 特性。结合波传递函数,所提出的方法能有效地模拟耗散作用。无穷域模拟采用了虚节点法,并通过牛顿-科茨积分进行了增强。为确保求解的稳定性和收敛性,我们的方法基于域积分法的 Galerkin 弱形式。为了应对不稳定性和不精确性的挑战,我们整合了稳定的符合节点积分法和自然稳定的节点积分法。我们通过各种基准问题验证了所提出方法的功效,初步结果表明该方法具有卓越的精度和稳定性。
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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A stable and efficient infinite meshfree approach for solving half-space eat conduction problems

This study introduces an innovative dynamic infinite meshfree method for robust and efficient solutions to half-space problems. This approach seamlessly couples this method with the nodal integral reproducing kernel particle method to discretize half-spaces defined by an artificial boundary. The infinite meshfree shape function is uniquely constructed using the 1D reproducing kernel shape function combined with the boundary singular kernel method, ensuring the Kronecker delta property on artificial boundaries. Coupled with the wave-transfer function, the proposed approach models dissipation actions effectively. The infinite domain simulation employs the dummy node method, enhanced by Newton–Cotes integrals. To ensure solution stability and convergence, our approach is based on the Galerkin weak form of the domain integral method. To combat the challenges of instability and imprecision, we integrated the stabilized conforming nodal integration method and the naturally stable nodal integration. The proposed methods efficacy is validated through various benchmark problems, with preliminary results showcasing superior precision and stability.

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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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