利用施瓦茨-克里斯托弗映射进行等时几何分析的边界参数匹配

IF 8.7 2区 工程技术 Q1 Mathematics Engineering with Computers Pub Date : 2024-07-03 DOI:10.1007/s00366-024-02020-z
Ye Ji, Matthias Möller, Yingying Yu, Chungang Zhu
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引用次数: 0

摘要

等几何分析带来了工程学科计算模拟与几何设计整合的范式转变。这种技术需要对物理域进行适合分析的参数化,以充分利用计算机辅助设计和计算机辅助工程分析之间的协同作用。现有方法通常固定边界参数,导致在流体通道和管状反应器等细长几何形状中面临挑战。本文针对边界参数匹配问题提出了一种创新解决方案,专为适合分析的参数化而设计。我们采用了复杂的施瓦茨-克里斯托弗映射技术,该技术在计算边界对应关系时非常重要。精炼的边界曲线重参数化过程对此进行了补充。我们的双策略方法保持了输入物理域的几何精确性和连续性,克服了现有重新参数化技术经常遇到的局限性。通过采用我们提出的边界参数匹配方法,我们表明,即使是简单的线性插值方法,也能有效地构建令人满意的、适合分析的参数化。与传统方法相比,我们的方法有了显著改进,能够生成适合分析且几何精确的模型,这对于确保获得精确的模拟结果至关重要。数值实验表明,所提出的方法能够提高等距几何分析工作流程的质量和可靠性。
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Boundary parameter matching for isogeometric analysis using Schwarz–Christoffel mapping

Isogeometric analysis has brought a paradigm shift in integrating computational simulations with geometric designs across engineering disciplines. This technique necessitates analysis-suitable parameterization of physical domains to fully harness the synergy between Computer-Aided Design and Computer-Aided Engineering analyses. Existing methods often fix boundary parameters, leading to challenges in elongated geometries such as fluid channels and tubular reactors. This paper presents an innovative solution for the boundary parameter matching problem, specifically designed for analysis-suitable parameterizations. We employ a sophisticated Schwarz–Christoffel mapping technique, which is instrumental in computing boundary correspondences. A refined boundary curve reparameterization process complements this. Our dual-strategy approach maintains the geometric exactness and continuity of input physical domains, overcoming limitations often encountered with the existing reparameterization techniques. By employing our proposed boundary parameter matching method, we show that even a simple linear interpolation approach can effectively construct a satisfactory analysis-suitable parameterization. Our methodology offers significant improvements over traditional practices, enabling the generation of analysis-suitable and geometrically precise models, which is crucial for ensuring accurate simulation results. Numerical experiments show the capacity of the proposed method to enhance the quality and reliability of isogeometric analysis workflows.

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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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