Mean-flow Data Assimilation based on minimal correction of turbulence models: application to turbulent high-Reynolds number backward-facing step

We perform mean-flow reconstruction through variational data assimilation using Reynolds-Averaged Navier-Stokes equations closed by the Spalart-Allmaras model in a high Reynolds number Backward-Facing Step configuration. Two correction terms are used: a force term in the momentum equations and a scalar term in the turbulence model. We show that the force term perfectly reconstructs the target data but only for dense measurements, while the scalar solution is slightly less accurate, but independent of the number of measurements. An observability Gramian analysis shows that the scalar term is much less flexible than the force term.