A numerical study of the Navier-Stokes transport coefficients for 2D granular hydrodynamics

TL;DR

This study compares two theoretical models for granular flow transport coefficients using hydrodynamic simulations of the Navier-Stokes equations, revealing significant differences in temperature and diffusion predictions for inelastic granular gases.

Contribution

It introduces a comparative analysis of Jenkins-Richman and Garzó-Dufty-Lutsko theories for granular transport coefficients through numerical simulations of the Faraday instability.

Findings

Differences in temperature fields between the two models.

Heat transfer mechanisms significantly affect diffusion.

Inelasticity impacts transport properties notably.

Abstract

A numerical study is presented to analyze the thermal mechanisms of unsteady, supersonic granular flow, by means of hydrodynamic simulations of the Navier-Stokes granular equations. For this purpose a paradigmatic problem in granular dynamics such as the Faraday instability is selected. Two different approaches for the Navier-Stokes transport coefficients for granular materials are considered, namely the traditional Jenkins-Richman theory for moderately dense quasi-elastic grains, and the improved Garz\'o-Dufty-Lutsko theory for arbitrary inelasticity, which we also present here. Both solutions are compared with event-driven simulations of the same system under the same conditions, by analyzing the density, the temperature and the velocity field. Important differences are found between the two approaches leading to interesting implications. In particular, the heat transfer mechanism coupled to the density gradient which is a distinctive feature of inelastic granular gases, is responsible for a major discrepancy in the temperature field and hence in the diffusion mechanisms.