浸没流分析中的精确壁面剪应力及其在基于点云的CFD中的应用

中文摘要 AI 辅助

基于点云的CFD能够直接在从三维扫描和医学成像获得的离散点上进行流动分析，绕过了表面重建、几何清理和贴体网格生成。该方法源自浸没几何分析，将点云浸入背景网格中，并通过基于Nitsche的弱边界条件（BC）在离散点上强制执行无滑移条件。该框架能够提供精确的速度场、压力分布和积分载荷；然而，局部壁面剪应力（WSS）的精确预测仍然是一个关键挑战。几何体任意地与背景网格相交，产生缺乏一致梯度评估所需正则性的切割单元。弱边界条件的稳定项加剧了该问题，其在对称Nitsche公式中的参数估计依赖于切割配置，并影响计算WSS的牵引力的变分一致定义。在本工作中，我们提出了一种新方法，用于在浸没流分析中获得精确的壁面剪应力，并应用于基于点云的CFD，采用非对称Nitsche公式结合近壁建模，以及具有牵引力兼容性的基于补丁的应力恢复方法。该方法在典型基准测试中得到验证，并应用于球体周围的湍流流动和患者特异性主动脉，与参考结果展现出极好的一致性。

英文摘要

Point cloud-based CFD enables flow analysis directly on discrete points obtained from 3D scanning and medical imaging, bypassing surface reconstruction, geometry cleanup, and boundary-fitted mesh generation. Derived from immersogeometric analysis, the method immerses the point cloud in a background mesh and enforces no-slip conditions on discrete points through a Nitsche-based weak boundary condition (BC). The framework delivers accurate velocity fields, pressure distribution, and integrated loads; however, accurate prediction of the local wall shear stress (WSS) has remained a critical challenge. The geometry intersects the background mesh arbitrarily, producing cut elements that lack the regularity required for consistent gradient evaluation. The issue is compounded by the stabilization term of the weak BC, whose parameter estimation in the symmetric Nitsche formulation is dependent on the cut configuration and affects the variationally consistent definition of traction from which the WSS is computed. In this work, we propose a new method to obtain accurate wall shear stress in immersed flow analysis with application to point cloud-based CFD, using a non-symmetric Nitsche's formulation with near-wall modeling and a patch-based stress recovery approach with traction compatibility. The method is validated on canonical benchmarks and applied to turbulent flow past a sphere and to a patient-specific aorta, showcasing excellent agreement with reference results.

发表机构

• Iowa State University（爱荷华州立大学）

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