发表机构
Instituto de Ingeniería Matemática y Computacional & Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile; Center for Mathematical Modeling; School of Civil Engineering. Pontificia Universidad Católica de Valparaíso; Universidad de Santiago de Chile, Departamento de Ingeniería Mecánica; Computational Heat and Fluid Flow Lab, Universidad de Santiago de Chile; Center for Interdisciplinary Research in Biomedicine, Biotechnology and Well-Being (CID3B). Pontificia Universidad Católica de Valparaíso（智利天主教大学数学与计算工程研究所及生物科学学院; 数学建模中心; 瓦尔帕莱索天主教大学土木工程学院; 智利圣地亚哥大学机械工程系; 智利圣地亚哥大学计算热流体流动实验室; 瓦尔帕莱索天主教大学生物医学、生物技术与健康跨学科研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一种基于应力-速度公式的压力恢复方法，从速度测量中计算应力场并后处理得到压力，理论证明收敛与稳定性，数值验证在对流流动和低分辨率下优于现有方法。
AI 中文摘要
从速度测量中非侵入性地估计压力场是一个长期存在的工程问题。我们提出、分析并测试了一种压力恢复方法，该方法从速度测量中计算完整的应力场，并将压力估计作为廉价的后期处理步骤。该方法依赖于纳维-斯托克斯方程的一阶应力-速度公式，我们证明该公式通过构造方式考虑了测量速度场中偏离不可压缩性的情况。此外，我们从理论上建立了有限元（FE）逼近格式的收敛性、应力恢复相对于有限分辨率速度测量的稳定性，并在数值上验证了这一理论。我们的结果表明，所提出的估计器在对流流动状态下具有鲁棒性，并在降低空间分辨率时保持准确性，优于最先进的压力恢复策略。
英文摘要
Non-invasive pressure field estimation from velocity measurements is a longstanding engineering problem. We propose, analyze, and test a pressure-recovery method that computes a full stress field from velocity measurements, and leaves the pressure estimation as a cheap post-processing step. The method relies on a stress-velocity first order formulation of the Navier-Stokes equations, and we show that the formulation accounts for deviations from incompressibility in the measured velocity field by construction. In addition, we theoretically establish the convergence of the finite element (FE) approximation scheme, the stability of the stress recovery with respect to finite-resolution velocity measurements, and then validate this theory numerically. Our results show that the proposed estimator is robust in convective flow regimes and remains accurate at reduced spatial resolution, improving upon state-of-the-art pressure-recovery strategies.
