An open-source adjoint-based field inversion tool for data-driven RANS modelling

This paper presents an open-source tool for using high-fidelity simulation or experimental data to improve steady-state Reynolds-averaged Navier--Stokes (RANS) turbulence models. The field inversion approach employed, involves perturbations of the production term in the model transport equation through a spatial field and the iterative optimisation of this field such that the error between model prediction and data is minimised. This highly dimensional inverse problem requires the adjoint method for efficient gradient-based optimisation. It has been successfully applied to reconstruct turbulent mean flows with limited data. However, the implementation is a high barrier to entry as the intrusive development process involves the CFD solver, the adjoint solutions, and the optimiser, making it a time-consuming and laborious task. In this work we integrate open-source codes to enable a flexible framework for field inversion application, open to all interested CFD practitioners. The software capabilities are demonstrated using three flow cases where traditional turbulence models (Spalart--Allmaras and Wilcox k-omega for this work) perform poorly due to flow separation and adverse pressure gradients. The data used include wind-tunnel experiments and direct numerical simulations, and field inversion scenarios considered integral (e.g. lift coefficient), surface (e.g. skin friction), and volume (e.g. velocity profiles) data, in order of decreasing sparsity.