Multifidelity sensitivity analysis with flow-aware RANS model coefficients

Sensitivity analysis, the gradient of a quantity of interest with respect to input parameters, is essential for optimization and uncertainty quantification. However, for turbulent flows, high-fidelity approaches like DNS and LES are often computationally prohibitive for extensive sensitivity studies, and their corresponding adjoint methods can suffer from instabilities due to the chaotic nature of these flows. Conversely, standard RANS models suffer from closure approximations which can compromise the accuracy of sensitivity estimates. To address this, this study presents a multifidelity framework that integrates DNS/LES accuracy with RANS efficiency and adjoint stability. This approach calibrates a RANS closure model using a single DNS/LES simulation at a nominal condition. The calibration introduces flow-state-dependent closure model coefficients which we refer to as a flow-aware RANS model. Adjoint methods are used to efficiently compute the gradients of a cost function against these numerous spatial coefficients, and a neural network is trained to map the local flow state to the calibrated RANS coefficients. Our approach prioritizes accuracy around the nominal state, essential for sensitivity, over broader generality. The framework's effectiveness is demonstrated in uniform and variable-area non-periodic channel flows using a flow-aware Prandtl model.