Velocity distribution function and effective constant restitution coefficient for granular gas of viscoelastic particles

TL;DR

This paper uses molecular dynamics simulations and kinetic theory to analyze velocity distribution functions and an effective restitution coefficient in granular gases of viscoelastic particles, highlighting the model's accuracy limitations at high dissipation.

Contribution

It introduces a simplified model of an effective constant restitution coefficient dependent on granular temperature and develops a theory for the velocity distribution function in driven viscoelastic granular gases.

Findings

Simulation results agree with theory for low dissipation

Discrepancies appear in Sonine coefficients at high dissipation

The effective restitution coefficient model accurately predicts granular temperature

Abstract

We perform large-scale event-driven Molecular dynamics (MD) simulations for granular gases of particles interacting with the impact-velocity dependent restitution coefficient. We use the simplest first-principle collision model of viscoelastic spheres. Both cases of force-free and uniformly heated gases are studied. We formulate a simplified model of an effective constant restitution coefficient, which depends on a current granular temperature and compute the effective constant restitution coefficient, using the kinetic theory. We develop a theory of the velocity distribution function for driven gases of viscoelastic particles and analyze evolution of granular temperature and of the Sonine coefficients, which characterize the form of the velocity distribution function. We observe that for not large dissipation the simulation results are in an excellent agreement with the theory for both, homogeneous cooling state and uniformly heated gases. At the same time a noticeable discrepancy between the theory and MD results for the Sonine coefficients is detected for large dissipation. We analyze the accuracy of the simplified model, based on the effective restitution coefficient and conclude that this model can accurately describe granular temperature. It provides also an acceptable accuracy for the velocity distribution function for small dissipation, but fails when dissipation is large.