Efficient assimilation of sparse data into RANS-based turbulent flow simulations using a discrete adjoint method

Abstract

Turbulent flow simulations based on the Reynolds-averaged Navier–Stokes (RANS) equations continue to be the workhorse approach for industrial flow problems. However, due to the inherent averaging and the closure models required for the Reynolds stresses, their accuracy is limited. Experimental data, on the other hand, represents the true flow features but is potentially only available in limited locations or at low resolution. Data assimilation (DA) can be used to combine closure models with such experimental data to obtain accurate simulation results. In this scenario, the result of the DA process can be interpreted as a physics-based interpolation and serve as a basis for further studies of the flow. Moreover, such tuned models may be used in machine learning approaches aiming at a priori closure model enhancement. The main objective of this work is to recover a spatially varying eddy viscosity correction factor from sparsely distributed reference data. We use an efficient in-house data assimilation implementation based on the discrete adjoint method for RANS simulations in OpenFOAM to recover an optimal eddy viscosity field. A gradient optimization procedure is used to minimize a velocity-based cost function with a regularization term. All the partial derivatives in the gradient computation are evaluated with an efficient semi-analytical approach at the cost of approximately one forward solution step. The effectiveness of the proposed approach is demonstrated for a periodic hill test case at Re=10595 with different spatial distributions of the reference data. The results show improvements in the agreement between simulation and reference for a range of reference data configurations and highlight the performance of linear eddy viscosity models.