The Partially Averaged Navier–Stokes Paradigm: Recent Advances Toward Predictive Scale-Resolving Turbulence Simulation

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. In PANS, fk and fε define a scale-dependent closure rather than a scale separation set directly to the grid or filter.