A Rescaling Velocity Method for Dissipative Kinetic Equations - Applications to Granular Media

TL;DR

This paper introduces a novel rescaling velocity method for dissipative kinetic equations, enabling accurate long-term simulations across different regimes, especially useful for granular media and clustering phenomena.

Contribution

The paper proposes a new numerical algorithm based on relative energy scaling that effectively handles long-time behavior in dissipative kinetic equations across dilute and dense regimes.

Findings

Efficient long-time simulations of granular gases.

Accurate modeling of clustering phenomena.

Applicable to both dilute and dense regimes.

Abstract

We present a new numerical algorithm based on a relative energy scaling for collisional kinetic equations allowing to study numerically their long time behavior, without the usual problems related to the change of scales in velocity variables. It is based on the knowledge of the hydrodynamic limit of the model considered, but is able to compute solutions for either dilute or dense regimes. Several applications are presented for Boltzmann like equations. This method is particularly efficient for numerical simulations of the granular gases equation with dissipative energy: it allows to study accurately the long time behavior of this equation and is very well suited for the study of clustering phenomena.