A novel construction of thermodynamically compatible models and its correspondence with Boltzmann-equation-based moment-closure hierarchies

Liu Hong Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Zaibao Yang Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Yi Zhu Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China Wen-An Yong Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing 100084, China

Analysis of PDEs mathscidoc:2204.03010

Journal of Non-Equilibrium Thermodynamics, 40, (4), 247-256, 2015.8
In this article, we propose a novel approach to construct macroscopic balance equations and constitutive equations describing various irreversible phenomena. It is based on the general principles of non-equilibrium thermodynamics and consists of four basic steps: picking suitable state variables, choosing a strictly concave entropy function, properly separating entropy fuxes and production rates, and determining a dissipation matrix. Our approach takes advantage of both extended irreversible thermodynamics and GENERIC formalisms and shows a direct correspondence with Levermore’s moment-closure hierarchies for the Boltzmann equation. As a direct application, a new ten-moment model beyond the classical hierarchies is constructed and is shown to recover the Euler equations in the equilibrium state. These interesting results may put various macroscopic modeling approaches, starting from the general principles of non-equilibrium thermodynamics, on a solid microscopic foundation based on the Boltzmann equation.
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@inproceedings{liu2015a,
  title={A novel construction of thermodynamically compatible models and its correspondence with Boltzmann-equation-based moment-closure hierarchies},
  author={Liu Hong, Zaibao Yang, Yi Zhu, and Wen-An Yong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428152347378653151},
  booktitle={Journal of Non-Equilibrium Thermodynamics},
  volume={40},
  number={4},
  pages={247-256},
  year={2015},
}
Liu Hong, Zaibao Yang, Yi Zhu, and Wen-An Yong. A novel construction of thermodynamically compatible models and its correspondence with Boltzmann-equation-based moment-closure hierarchies. 2015. Vol. 40. In Journal of Non-Equilibrium Thermodynamics. pp.247-256. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220428152347378653151.
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