Dense velocity, pressure and Eulerian acceleration fields from single-instant scattered velocities through Navier–Stokes-based data assimilation

Abstract

In this study, a reconstruction procedure to infer full 3D instantaneous velocity and pressure fields from sparse velocity measurements is proposed, here focusing on the case of scattered data as provided by Particle Tracking Velocimetry (PTV). A key characteristic of the present approach is that it only relies on single-instant velocity measurements, and does not require any time-resolved or acceleration information. It is based on a strong enforcement of the Navier-Stokes equations where the partial time derivative of the velocity field, namely Eulerian acceleration, is considered as a control vector to minimize the discrepancies between the single-instant measurements and the reconstructed flow. Eulerian acceleration is thus a byproduct of the present methodology in addition to the identification of the full velocity and pressure fields. The reconstruction performances of the proposed Navier-Stokes-based data-assimilation approach for single-instant velocity measurements (NS-DA-SIM) are assessed using a numerical dataset for the 3D flow past a cylinder. Comparisons with existing data assimilation methodologies allow to further illustrate the merits of the present approach. The latter is finally applied to the instantaneous reconstruction of an experimental air jet flow from volumetric PTV data, confirming its robustness and high efficacy.

Special Issue on Machine learning and data assimilation techniques for fluid flow measurements

“…The approach provides accurate predictions of the flow statistics by solving the Reynolds-averaged Navier-Stokes (RANS) equations for incompressible turbulent flows without any a-priori turbulence model, and employing the measured mean velocity and Reynolds stresses at the domain frontier as boundary conditions. Mons et al [9] present a variational data assimilation procedure to infer 3D flow velocity, Eulerian acceleration and pressure fields from sparse single-instant velocity measurements, as those obtained by two-pulse PTV. The approach is based on the solution of the unsteady Navier-Stokes equations, whereby the Eulerian acceleration is treated as a forcing term, which is adjusted to minimize the discrepancy between the reconstructed and the measured velocities.…”