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Data-driven constitutive relation reveals scaling law for hydrodynamic transport coefficients
Candi Zheng1,2, Yang Wang2, Shiyi Chen1
1Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Xueyuan Rd 1088, Shenzhen, China.
Physical Review. E
|February 17, 2023
Summary
Data-driven models for extended hydrodynamics were found to be equivalent to nonlinear scaling laws. This provides physical justification and suggests modeling scaling laws can overcome data-driven model limitations.
Area of Science:
- Fluid dynamics
- Statistical mechanics
- Computational physics
Background:
- Extended hydrodynamics equations are needed for gas regimes from dense to rarefied.
- Accurate constitutive relations for stress and heat flux are crucial for these equations.
- Data-driven models offer a phenomenological approach to learn these relations.
Purpose of the Study:
- To theoretically investigate data-driven models for constitutive relations.
- To establish a physical basis for data-driven models in fluid dynamics.
- To propose an alternative modeling approach based on scaling laws.
Main Methods:
- Theoretical analysis of data-driven models on a linear system.
- Establishing equivalence between data-driven models and nonlinear length scale scaling laws.
- Developing and testing a constitutive relation model based on scaling laws.
Main Results:
- Data-driven models are equivalent to nonlinear length scale scaling laws of transport coefficients.
- This equivalence justifies the physical plausibility and highlights limitations of data-driven models.
- A scaling law-based model demonstrated advantages over Chapman-Enskog and moment methods in Rayleigh scattering calculations.
Conclusions:
- Data-driven models in fluid dynamics can be understood as nonlinear scaling laws.
- Modeling scaling laws offers a physically grounded alternative to direct data-driven approaches.
- The proposed scaling law model shows improved performance for calculating Rayleigh scattering spectra.
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