Absence of inelastic collapse for a 1D gas of grains with an internal degree of freedom

Francesco Paparella, Giuseppe Passoni

Research output: Contribution to journalArticle

Abstract

In a cooling gas of rigid particles interacting with a constant coefficient of restitution, groups of particles within the gas may experience an infinite number of collisions in a finite time. This singularity, named inelastic collapse, is a shortcoming of the mathematical model, and it hampers the efforts of simulating a freely evolving, cooling granular system. After a brief review of previous works addressing the problem, we propose a one-dimensional model where a grain is seen as a pair of point masses joined by a massless, dissipative spring. We show that binary interactions of such grains are described as impacts with a constant restitution coefficient, whose expression is given in terms of the spring parameters. However, the impact is not instantaneous, but it requires a finite time. We show that in situations that would lead to inelastic collapse, multiple interactions among grains transfer kinetic energy into potential energy associated with the deformation of the springs, rather than dissipate it. This effectively avoids the collapse. Finally, we discuss the results of the simulations of a cooling granular system in comparison with other models.

Original languageEnglish (US)
Pages (from-to)218-229
Number of pages12
JournalComputers and Mathematics with Applications
Volume55
Issue number2
DOIs
StatePublished - Jan 1 2008

Fingerprint

Cooling
Degree of freedom
Internal
Gases
Coefficient of restitution
Dissipate
One-dimensional Model
Potential energy
Kinetic energy
Interaction
Instantaneous
Collision
Singularity
Mathematical Model
Mathematical models
Binary
Coefficient
Energy
Gas
Simulation

Keywords

  • Granular gas
  • Inelastic collapse
  • Restitution coefficient

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Modeling and Simulation

Cite this

Absence of inelastic collapse for a 1D gas of grains with an internal degree of freedom. / Paparella, Francesco; Passoni, Giuseppe.

In: Computers and Mathematics with Applications, Vol. 55, No. 2, 01.01.2008, p. 218-229.

Research output: Contribution to journalArticle

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