Toward generalisable turbulence modelling via radial-basis-function-based corrections using data assimilation with fused multi-fidelity observations

This paper employs the ensemble-based data assimilation method to develop a closed-form correction term for the Spalart–Allmaras (S–A) turbulence model to enhance predictive accuracy in separated flows through model-form uncertainty reduction. A compact radial-basis-function expression is proposed as correction model to supersede conventional modification procedures in classic field inversion and machine learning frameworks, achieving computational economy through spatially bounded correction regions. The correction model is derived via the Ensemble Kalman method with effective utilisation of synthesised observations based on the multi-fidelity data aggregation. The modified compact expression trained on a single case is systematically evaluated against unseen separation scenarios and the results show that the developed model can improve the prediction accuracy of flow separation in different validation cases, and the effectiveness of the method is verified. Compared with other black-box models, the correction based on the radial-basis-function form offers reduced complexity and high suitability for direct integration into numerical solvers. This approach facilitates cost-effective data assimilation and enables dynamic adaptation of the correction, thereby enhancing the generalisation capability for similar flow separation conditions.