Modeling Equations in Wave-Particle Turbulence Simulation
Recently, the wave-particle turbulence simulation (WPTS) has been proposed as a novel framework for non-equilibrium turbulence modeling and simulation. In this work, for the first time the complete model equations of WPTS are explicitly derived from the perspective of wave-particle decomposition, and the physical mechanism of each term is clearly interpreted. To extend its applicability to wall-bounded flows, the WPTS coupled with wall model is developed, and the introduction of wall model substantially alleviates the near-wall grid-resolution constraint. In the bulk region, the wave component resolves the large-scale structures, whereas the particle component accounts for subgrid-scale modeling through the non-equilibrium transport mechanism. As a result, the coupled method enables accurate predictions of the flat-plate transition on coarse-grid. In particular, the computed skin-friction coefficient and mean velocity profiles in the fully turbulent region agree well with the reference data from direct numerical simulation, and the accuracy is markedly superior to that of the gas-kinetic scheme (GKS) under the identical grid. These findings underscore the considerable promise of the multi-scale WPTS method for transitional flow simulations.