Vibrated granular gas confined by a piston

TL;DR

This paper develops a hydrodynamic model for a vibrated granular gas confined by a piston, emphasizing boundary conditions and validating predictions with molecular dynamics simulations.

Contribution

It introduces an exact boundary condition relating grain fluxes, enabling a consistent hydrodynamic description without undetermined parameters.

Findings

Good agreement between theory and simulations at low density and inelasticity.

Derived boundary conditions improve hydrodynamic modeling accuracy.

Proposed corrections extend the dilute limit theory.

Abstract

The steady state of a vibrated granular gas confined by a movable piston on the top is discussed. Particular attention is given to the hydrodynamic boundary conditions to be used when solving the inelastic Navier-Stokes equations. The relevance of an exact general condition relating the grain fluxes approaching and moving away from each of the walls is emphasized. It is shown how it can be used to get a consistent hydrodynamic description of the boundaries. The obtained expressions for the fields do not contain any undetermined parameter. Comparison of the theoretical predictions with molecular dynamics simulation results is carried out, and a good agreement is observed for low density and not too large inelasticity. A practical way of introducing small finite density corrections to the dilute limit theory is proposed, to improve the accuracy of the theory.