State Observer data assimilation for RANS with time-averaged 3D-PIV data

State observer techniques are investigated for the assimilation of three-dimensional velocity measurements into computational fluid dynamics simulations based on Reynolds-averaged Navier–Stokes (RANS) equations. The method relies on a forcing term, or observer, in the momentum equation, stemming from the difference between the computed velocity and the reference value, obtained by measurements or high-fidelity simulations. Two different approaches for the forcing term are considered: proportional and integral-proportional. This technique is demonstrated considering an experimental database that describes the time-average three-dimensional flow behind a generic car-mirror model. The velocity field is obtained by means of Robotic Volumetric PIV measurements. The effects of the different forcing terms and the spatial density of the measurement input to the numerical simulation are studied. The state observer approach forces locally the solution to comply with the reference value and the extent of the region modified by the forcing input is discussed. The velocity distribution and flow topology obtained with data assimilation are compared with attention to the object wake and the reattachment point where the largest discrepancy is observed between the different approaches. The results show that the integral term is more effective than the proportional one in reducing the mismatch between simulation and the reference data, with increasing benefits when the density of forced points, or forcing density, is increased.