From turbulence modelling to machine learning integration in computational ship hydrodynamics using RANS

This comprehensive review examines the application of Reynolds-Averaged Navier-Stokes (RANS) modelling in computational ship hydrodynamics, starting from fundamental theory, numerical implementation, validation procedures, and diverse practical applications. The paper systematically addresses governing equations and turbulence modelling approaches, while analyzing their strengths and limitations in ship flow simulations. Detailed discussions of discretization schemes, grid generation strategies, free surface modelling techniques, and convergence algorithms provide practical guidance for CFD practitioners. The review emphasizes verification and validation methodologies through benchmark cases and uncertainty quantification, highlighting best practices from ITTC guidelines and international workshops. Extensive applications are presented across calm water resistance prediction, hull form optimization, bulbous bow design, energy-saving devices, seakeeping analysis and fluid - structure interaction. Current challenges are critically assessed, including turbulence modelling limitations, scale effects, and free surface accuracy. The integration of machine learning with RANS simulations is explored as an emerging frontier for accelerated design optimization, with particular focus on resistance prediction, hull optimization, and wake field analysis. The paper concludes with future perspectives on hybrid RANS-LES approaches, increased availability of CFD services and ultimately, AI-augmented ship design workflows, providing a comprehensive reference for researchers and engineers in computational ship hydrodynamics.