Data-driven constitutive relation reveals scaling law for hydrodynamic transport coefficients

Zheng, Candi1,2; Wang, Yang2; Chen, Shiyi1

2023-01-17

10.1103/PhysRevE.107.015104

PHYSICAL REVIEW E   Impact Factor & Quartile

2470-0045

2470-0053

Finding extended hydrodynamics equations valid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models offer a new phenomenological approach to learning constitutive relations from data. Such models enable complex constitutive relations that extend Newton's law of viscosity and Fourier's law of heat conduction by regression on higher derivatives. However, the choices of derivatives in these models are ad hoc without a clear physical explanation. We investigated data-driven models theoretically on a linear system. We argue that these models are equivalent to nonlinear length scale scaling laws of transport coefficients. The equivalence to scaling laws justified the physical plausibility and revealed the limitation of data-driven models. Our argument also points out that modeling the scaling law could avoid practical difficulties in data-driven models like derivative estimation and variable selection on noisy data. We further proposed a constitutive relation model based on scaling law and tested it on the calculation of Rayleigh scattering spectra. The result shows our data-driven model has a clear advantage over the Chapman-Enskog expansion and moment methods.

SCI

English

First ; Corresponding

Physics

Physics, Fluids & Plasmas ; Physics, Mathematical

WOS:000923229600014

AMER PHYSICAL SOC

PHYSICS

Web of Science

1.Southern Univ Sci & Technol, Dept Mech & Aerosp Engn, Xueyuan Rd 1088, Shenzhen, Peoples R China
2.Hong Kong Univ Sci & Technol, Dept Math, Clear Water Bay, Hong Kong 999077, Peoples R China

Zheng, Candi,Wang, Yang,Chen, Shiyi. Data-driven constitutive relation reveals scaling law for hydrodynamic transport coefficients[J]. PHYSICAL REVIEW E,2023,107(1).

Zheng, Candi,Wang, Yang,&Chen, Shiyi.(2023).Data-driven constitutive relation reveals scaling law for hydrodynamic transport coefficients.PHYSICAL REVIEW E,107(1).

Zheng, Candi,et al."Data-driven constitutive relation reveals scaling law for hydrodynamic transport coefficients".PHYSICAL REVIEW E 107.1(2023).