Bayesian optimisation of a roof extension/spoiler on a simplified vehicle, employing wall-resolved large eddy simulation

A benchmark road vehicle geometry – the square-back Windsor body with wheels and at zero yaw angle – is simulated using high-fidelity wall-resolved large eddy simulation. Passive control for drag reduction, in the form of optimisation of its rear roof extension, is performed. The rear roof extension is parameterised by its taper penetration distance, angle of incidence and length. This optimisation process uses Gaussian process-based surrogate modelling combined with Bayesian optimisation (Kriging), guided by an expected improvement criterion. The optimisation converged in six iterations (60 simulations), achieving a $6.5\,\%$ drag reduction. Six distinct drag-reduction mechanisms were identified: diffuser-induced pressure recovery, base-size reduction, vertical wake balance modification, separation effects, recirculation region core relocation and spanwise re-symmetrisation. Rather than isolating individual mechanisms, the study reveals how they interact when multiple geometric parameters are varied concurrently, providing a system-level picture that yields practical design rules. The optimal configuration was found at a roof extension angle of incidence corresponding to the onset of separation, with taper penetration distance and extension length at their maximum values within the analysed domain. These findings establish a robust framework for aerodynamic optimisation and reinforce the effectiveness of Bayesian optimisation in Computational Fluid Dynamics-based design. In this way, the work bridges fundamental wake studies with applied design practice, showing how coupled wake–geometry interactions can be harnessed for improved aerodynamic performance.