A Particle Representation Model for Compressible Homogeneous Turbulence

This work introduces a new stochastic particle representation model (PRM) with transport equations derived in analogy to the rapid distortion theory for compressible homogeneous turbulence. By leveraging the equation of state and conservation of entropy, this model uses 5 fewer transport variables compared to past models for homogeneous compressible turbulence (Yu and Girimaji, Physics of Fluids, 2007) by relating the fluctuating pressure to the dilatational component of the velocity fluctuation. The compressible PRM is an exact representation of compressible turbulence at high distortion that only requires approximation in evaluating the integrals through numerical methods. Different methods for approximating the integrals with respect to the wavevector, such as Monte Carlo integration or quadrature, are examined. Results are compared to rapid distortion theory/DNS calculations and past compressible particle representation modeling attempts for axial compression, sheared compression, and pure shear cases. Furthermore, extension to inhomogenous turbulence is briefly discussed.