State-observer-based data assimilation for the correction of turbulent pressure in numerical simulations

Assimilation of experimental measurements with computational fluid dynamics (CFD) to improve simulation accuracy has steadily developed over the past years (Li et al., 2022, Zauner et al., 2022). However, recent efforts have focused solely on correcting the solenoidal component of the Reynolds stress tensor with data assimilation. Therefore, this work explores the assimilation of surface pressure measurements to rectify the dilatational part of the Reynolds stress tensor, also known as the turbulent pressure (Perot and Moin, 1996). The proposed state-observer-based data assimilation (SODA) expands upon the proportional-integral-derivative (PID) SODA developed by Neeteson and Rival (2020) to include additional correction terms in both the momentum and pressure equations to achieve turbulent pressure correction. The novel SODA is benchmarked against synthetic and real-world measurements with a focus on separated flow scenarios to demonstrate its ability to reconstruct mean fields with improved accuracy and convergence over conventional CFD methods.