发表机构
Iowa State University; Vanderbilt University; Waseda University（爱荷华州立大学; 范德堡大学; 早稻田大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文综述了计算流分析中弱施加Dirichlet边界条件，其作为变分一致近壁模型，允许壁面滑移，在粗网格上恢复准确流动量，并支撑浸没几何分析，适用于不可压缩和可压缩流动。
AI 中文摘要
强施加Dirichlet边界条件要求近壁网格高度细化，以解析陡峭的速度和热梯度。这带来了高昂的计算成本，尤其是在实际流动模拟中。弱施加边界条件通过充当变分一致的近壁模型来缓解这一负担。通过允许在固体壁面处发生受控滑移，弱施加在不可压缩和可压缩流动状态下，均能在粗糙的边界层网格上恢复准确的流动量。此外，弱边界条件是浸没几何分析的基础使能技术。由于弱算子独立于背景网格评估边界积分，可以直接在复杂几何体上进行高保真流动分析，而无需将网格拟合到表面。这一能力促进了从边界表示CAD模型、原始点云、摄影测量重建和分割医学图像的直接几何到分析工作流程。本综述考察了弱边界条件框架从标量对流扩散方程到完整Navier-Stokes方程的统一数学发展，展示了其在不可压缩和可压缩流动中的多功能性和稳健性，无论是在传统的边界拟合、滑移界面还是先进的浸没几何应用中。
英文摘要
Strongly enforced Dirichlet boundary conditions require highly refined near-wall meshes to resolve steep velocity and thermal gradients. This introduces high computational costs, especially for practical flow simulations. Weakly enforced boundary conditions alleviate this burden by acting as a variationally consistent near-wall model. By allowing a controlled slip at the solid wall, weak enforcement recovers accurate flow quantities on coarse boundary-layer meshes across both incompressible and compressible regimes. Furthermore, weak boundary conditions serve as the fundamental enabling technology for immersogeometric analysis. Because the weak operator evaluates boundary integrals independently of the background mesh, high-fidelity flow analysis can be performed directly on complex geometries without fitting a mesh to the surface. This capability has facilitated direct geometry-to-analysis workflows for boundary-representation CAD models, raw point clouds, photogrammetric reconstructions, and segmented medical images. This review examines the unified mathematical development of the weak boundary condition framework from scalar advection-diffusion equations to the full Navier-Stokes equations, illustrating its versatility and robustness across incompressible and compressible flows, whether in traditional boundary-fitted, sliding-interface, or advanced immersogeometric applications.
