Asymptotic expansion and Padé approximants for gravity-driven flow of a heated granular gas: Competition between inelasticity and forcing, up to Burnett order

Rongali, Ramakrishna; Alam, Meheboob

doi:10.1103/physreve.98.052144

Cited by 5 publications

(1 citation statement)

References 45 publications

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“…Significant development of methods to obtain constitutive equations or related macroscopic models comes from the community of researchers studying granular flows (Saha & Alam 2016, 2017; Rongali & Alam 2018 a , b ). The study of normal stress effects and the derivation of constitutive relations is in the spirit of the present work.…”

Section: Introductionmentioning

confidence: 99%

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

Pahlani,

Schwartzentruber,

James

2023

J. Fluid Mech.

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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.

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