Three-dimensional numerical simulations of a flow past a non-submerged diversion dike are performed for various blockage ratios (1/6 ≤ β ≤ 1/3) and Froude numbers (0.152 ≤ Fr ≤ 0.253). The instantaneous and time-averaged flow characteristics, the evolution process of mixing layers, and the bed shear stress of the dike are analyzed. The blockage ratio β plays an important role in the momentum redistribution and turbulent kinetic energy of the diversion dike. As the blockage ratio increases, the flow velocity gradient and the vortex shedding frequency in the mixing layer significantly increase. The Froude number Fr has little effect on the flow field. A large recirculation zone is observed in the wake of the dike, and the recirculation length is more depended on the length of the dike rather than the Froude number. The bed shear stress around the dike increases significantly with the increase in the blockage ratio.

Non-equilibrium suspended sediment transport in coastal engineering is characterized by complex interactions among turbulent flows, seabed topography, and structures. This study developed a two-way coupled large eddy simulation suspended sediment transport model sedTransFoam based on the open-source OpenFOAM framework. The solver comprehensively accounts for turbulence modulation caused by high-concentration sediment and interactions between sediment. Additionally, it incorporates a flux boundary condition based on turbulent burst theory to accurately simulate instantaneous sediment transport characteristics under strong turbulence effects. The sloped terrain and pile group structure generate complex turbulence-sediment interactions, making them a classic setting for studying non-equilibrium suspended sediment transport. The solver is employed to investigate sediment dynamics, where sloped terrain and pile groups generate complex turbulence and sediment transport patterns. The simulations demonstrate that the sloped terrain induces large-scale Kelvin–Helmholtz vortices, which drive erosion through enhanced shear stress. Pile groups shift vortices toward interfaces, where shear stress and turbulent kinetic energy primarily govern sediment transport. Transverse momentum exchange is predominantly driven by turbulent mixing (accounting for approximately 75%), while high-density pile configurations increase siltation due to reduced turbulence scales.

Partially averaged Navier–Stokes (PANS) has evolved over the past two decades from a conventional RANS–DNS bridging model into a scale-resolving simulation framework with controllable turbulence resolution. By introducing the unresolved fractions of turbulent kinetic energy and dissipation, fk and fε, PANS regulates the partition between modeled and resolved turbulence. However, the turbulence resolution achieved in practical simulations is not solely determined by the prescribed parameters, but also depends on the interaction among turbulence closure, grid resolution, numerical dissipation, and physical modeling. This review summarizes the theoretical foundations, resolution-control strategies, and engineering applications of PANS, with particular emphasis on the consistency between prescribed and realized turbulence resolution. The formulation of partially averaged governing equations, closure transformations, scale relationships, and the limiting behaviors toward RANS and DNS are first discussed. Recent developments in variable-resolution formulations, commutation-error treatment, scale-supplying variables, near-wall resolution approaches, dissipation-resolution control, and variable-density extensions are subsequently reviewed. Applications to canonical turbulence, separated flows, rotating machinery, marine hydrodynamics, cavitation, heat transfer, combustion, and compressible flows are assessed in terms of turbulence statistics, coherent structures, spectral characteristics, and engineering prediction capability. Existing studies demonstrate that PANS can recover energetic unsteadiness suppressed by RANS and improve predictions of complex flows when sufficient numerical resolution and appropriate physical closures are provided. Nevertheless, reducing fk does not necessarily guarantee improved accuracy, as the prescribed resolution must be consistent with grid resolution, time-step selection, numerical schemes, boundary treatments, and multiphysics models. Future developments of PANS will focus on reliable resolution estimation, conservative variable-resolution strategies, consistent multiphysics scale closures, and systematic verification and validation procedures to establish quantitative relationships among prescribed resolution, numerical realization, and predictive accuracy.

Partially averaged Navier–Stokes (PANS) has evolved over the past two decades from a conventional RANS–DNS bridging model into a scale-resolving simulation framework with controllable turbulence resolution. By introducing the unresolved fractions of turbulent kinetic energy and dissipation, f_k and f_ε, PANS regulates the partition between modeled and resolved turbulence. However, the turbulence resolution achieved in practical simulations is not solely determined by the prescribed parameters, but also depends on the interaction among turbulence closure, grid resolution, numerical dissipation, and physical modeling. This review summarizes the theoretical foundations, resolution-control strategies, and engineering applications of PANS, with particular emphasis on the consistency between prescribed and realized turbulence resolution. The formulation of partially averaged governing equations, closure transformations, scale relationships, and the limiting behaviors toward RANS and DNS are first discussed. Recent developments in variable-resolution formulations, commutation-error treatment, scale-supplying variables, near-wall resolution approaches, dissipation-resolution control, and variable-density extensions are subsequently reviewed. Applications to canonical turbulence, separated flows, rotating machinery, marine hydrodynamics, cavitation, heat transfer, combustion, and compressible flows are assessed in terms of turbulence statistics, coherent structures, spectral characteristics, and engineering prediction capability. Existing studies demonstrate that PANS can recover energetic unsteadiness suppressed by RANS and improve predictions of complex flows when sufficient numerical resolution and appropriate physical closures are provided. Nevertheless, reducing f_k does not necessarily guarantee improved accuracy, as the prescribed resolution must be consistent with grid resolution, time-step selection, numerical schemes, boundary treatments, and multiphysics models. Future developments of PANS will focus on reliable resolution estimation, conservative variable-resolution strategies, consistent multiphysics scale closures, and systematic verification and validation procedures to establish quantitative relationships among prescribed resolution, numerical realization, and predictive accuracy. In PANS, f_k and f_ε define a scale-dependent closure rather than a scale separation set directly to the grid or filter.