A conservative scheme for a simplified granular media

Christophe Buet (1) , Stéphane Cordier (2) , Valérie dos Santos (2)

1 DAM - Direction des Applications Militaires
2 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

In this paper, we present a numerical scheme for a non linear Fokker – Planck equation of one-dimensional granular medium. We consider a kinetic description of a system of particles undergoing nearly elastic particles and interacting with a thermal bath. We construct a numerical method which preserve all the properties of the continuous model, conservation laws, and decay of the entropy. Moreover, the discreti- zation is such that, on a fixed grid, we deal with arbitrary small temperatures for the bath. Explicit and implicit time discretization are analyzed.

Mots clés: Entropy scheme; Granular media; Discretization; Q1Linear equation .; Q1Linear equation

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Buet, Stéphane Cordier, Valérie dos Santos. A conservative scheme for a simplified granular media. Transport Theory and Statistical Physics, 2004, 33, pp.2. ⟨10.1081/TT-120037804⟩. ⟨hal-00076840⟩