Wave-Particle Based Multiscale Modeling and Simulation of Non-equilibrium Turbulent Flows

This paper presents a novel methodology for the direct numerical modeling and simulation of turbulent flows. The kinetic model equation is firstly extended to turbulent flow with the account of coupled evolution of kinetic, thermal, and turbulent energy. Based on the kinetic model, a unified framework for the laminar and turbulent flow is constructed through wave-particle decomposition, following the coupled evolution of wave and particles. The modeling is based on the assumption that the turbulence emergence is attributed to the breakdown of continuously connected fluid elements under the cell resolution. Then, the non-equilibrium transport of discrete fluid elements carrying the turbulent kinetic energy is constructed by the particle movement. The model leverages a hybrid wave-particle representation, where wave dynamics governed by the Navier-Stokes equations provide a background flow structure, while particle transport is driven by the unresolved turbulent dynamics. Particle non-equilibrium trajectory crossing, collision, and interaction with the background wave, distinguish the current model from conventional RANS and LES methodologies for the turbulent flow simulation. Instead of the dissipation model constructed in the mixing length theory, the present model presents a upgrading non-equilibrium transport model with particle penetration and collision. The transition between laminar and turbulent states is determined by the particle density in the wave-particle decomposition inside each cell. Emphasizing genuine non-equilibrium particle transport, the proposed multiscale method demonstrates enhanced accuracy for capturing the turbulent flow, where the Reynolds stress can be directly obtained from the flow field in the study of compressible mixing layer. This work offers a versatile tool for turbulence research with potential applications in aerospace, energy systems, etc.