A Stress-Based Estimator for Pressure and Stress Recovery from Velocity Measurements
Abstract
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.
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BibTeX
@misc{barnafi2026stressbased,
title = {{A Stress-Based Estimator for Pressure and Stress Recovery from Velocity Measurements}},
author = {Nicolás Barnafi and Benjamín Cisternas and Ernesto Castillo and Felipe Galarce},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09484},
eprint = {2609.09484},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09484},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Stress-Based Estimator for Pressure and Stress Recovery from Velocity Measurements
AU - Nicolás Barnafi
AU - Benjamín Cisternas
AU - Ernesto Castillo
AU - Felipe Galarce
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09484
UR - https://arxiv.org/abs/2609.09484
AB - 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.
ER -