Efficient variational data assimilation for the correction of RANS models in 2D simulations of stationary turbulent flows

The Reynolds-averaged Navier--Stokes (RANS) equations provide a computationally efficient approach to solving flow problems in engineering applications. However, the accuracy is affected by the use of closure models to represent turbulent effects. To overcome these limitations, recent contributions have explored data-driven methods such as data assimilation and machine learning.

We present an efficient variational data assimilation (DA) approach to improve steady-state two-dimensional RANS simulations based on eddy viscosity closure models. Our method introduces a divergence-free corrective forcing term based on a potential field that improves simulation accuracy while allowing coarser grid resolution. The DA implementation relies on the discrete adjoint approach and uses approximations for efficient gradient evaluation.

The implementation is based on a two-dimensional coupled RANS solver in foam-extend 5.0, and this modified solver includes specific extensions to allow the computation of the adjoint velocity and pressure as well as the adjoint gradient.

To demonstrate the advantages of our proposed approach, we compare it with alternative data assimilation methods for canonical two-dimensional turbulent flow problems. Sparsely distributed data from averaged high-fidelity simulations are used as reference data.