Mean-flow reconstruction of unsteady flows via data assimilation: PINN vs variational methods.

Successful application of data-assimilation methods for fluid dynamics problems can lead to a significant reduction in costs associated with acquiring experimental data in wind tunnels or performing expensive fluid simulations. The aim of this work is to leverage experimental sparse mean flow measurements on the surface or in the unsteady wake of a body, in order to extract flow information that is not available in the measurements or in the under-determined governing Reynolds-Averaged Navier-Stokes (RANS) equations. This can be beneficial for super-resolving mean flow fields, extending the measurements and filling missing gaps, inferring pressure information and inferring closure terms for the RANS equations. In this work, two different techniques are employed to perform mean-flow data assimilation; a variational adjoint-based approach and Physics Informed Neural Networks (PINNs). Although the PINN and variational approaches aim to solve the data-assimilation problem by leveraging available data and governing equations to maximize a cost functional, there are key differences that affect the accuracy of the assimilation procedure. A thorough comparison of variational and PINN data assimilation methods will be presented for laminar and turbulent regimes.