A constitutive relation generalizing the Navier–Stokes theory to high-rate regimes

We propose a constitutive equation for flows of gases in high-rate regimes where the Navier–Stokes theory breaks down. The model generalizes the Navier–Stokes relation and agrees well with that model in all lower rate flows examined. Our proposed constitutive relation is calibrated with the method o...

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Bibliographic Details
Published in:Journal of fluid mechanics 2023-11, Vol.974, Article A30
Main Authors: Pahlani, Gunjan, Schwartzentruber, Thomas, James, Richard D.
Format: Article
Language:English
Subjects:
Argon
Compressibility
Computational fluid dynamics
Constitutive equations
Constitutive relationships
Equilibrium
Evolution
Exact solutions
Fluid dynamics
Fluid flow
Gases
Hydrodynamics
Incompressible flow
JFM Papers
Molecular dynamics
Navier-Stokes equations
Ordinary differential equations
Partial differential equations
Simulation
Strain rate
Tensors
Velocity
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Summary:We propose a constitutive equation for flows of gases in high-rate regimes where the Navier–Stokes theory breaks down. The model generalizes the Navier–Stokes relation and agrees well with that model in all lower rate flows examined. Our proposed constitutive relation is calibrated with the method of objective molecular dynamics (OMD) using families of compressible and incompressible flows of Lennard-Jones argon. The constitutive relation makes use of the higher-order objective strain rates due to Rivlin and Ericksen (J. Rat. Mech. Anal., vol. 4, 1955, pp. 323–425). The constitutive relation is fully frame-indifferent, and the macroscopic flows corresponding to the OMD simulations are exact solutions for the proposed model. The model is shown to agree with atomistic results much better than the Navier–Stokes equations in the transition regime. The success of our model indicates that it is not higher gradients that become important in the high-rate regime, but rather higher rates of change of the strain rate tensor. While somewhat more complicated to implement than the Navier–Stokes relation, the proposed model is expected to be compatible with existing methods of computational fluid dynamics and may extend those methods to higher rate regimes, while preserving their ability to handle large spatial scales.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2023.727