A thermodynamics-based turbulence model for isothermal compressible flows
Abstract
This study presents a new turbulence model for isothermal compressible flows. The model is derived by combining the Favre averaging and the Conservation-dissipation formalism -- a newly developed thermodynamics theory. The latter provides a systematic methodology to construct closure relations that intrinsically satisfy the first and second laws of thermodynamics. The new model is a hyperbolic system of first-order partial differential equations. It has a number of numerical advantages, and addresses some drawbacks of classical turbulence models by resolving the non-physical infinite information propagation paradox of the parabolic-type models and accurately capturing the interaction between compressibility and turbulence dissipation. Furthermore, we show the compatibility of the proposed model with Prandtl's one-equation model for incompressible flows by deliberately rescaling the model and studying its low Mach number limit.
Cite
@article{arxiv.2504.18755,
title = {A thermodynamics-based turbulence model for isothermal compressible flows},
author = {Zhiting Ma and Wen-An Yong and Yi Zhu},
journal= {arXiv preprint arXiv:2504.18755},
year = {2025}
}