Dynamics of rarefied granular gases

Area of Science:

• Physics
• Fluid Dynamics
• Kinetic Theory

Background:

• Traditional gas-dynamic equations often rely on constitutive relations.
• Understanding systems of inelastic hard spheres requires advanced kinetic theory approaches.

Purpose of the Study:

• To present general bidimensional gas-dynamic equations derived from kinetic theory.
• To incorporate the fourth cumulant (kappa) as a dynamic field for enhanced system description.
• To analyze the role of kappa in specific gas-dynamic scenarios.

Main Methods:

• Derivation of bidimensional gas-dynamic equations from kinetic theory.
• Inclusion of the fourth cumulant (kappa) as a dynamic field.
• Analysis of two examples: homogeneous cooling state and a steadily heated system (with/without gravity).

Main Results:

• The derived equations include 9 hydrodynamic fields, extending standard models.
• Consistent description of the homogeneous cooling state with added transient behavior details.
• Demonstration of non-Fourier heat transport in a system with gravity when kappa is included.
• Favorable comparison of a gravity-free perturbative solution with molecular dynamics (MD) observations.
• Observation that kappa is non-homogeneous in both gravitational cases.
• Analytic extension suggests a divergent situation for exothermic collisions (restitution coefficient > 1), observed in MD.

Conclusions:

• The new gas-dynamic equations provide a more comprehensive framework for low-density inelastic hard sphere systems.
• The inclusion of kappa as a dynamic field reveals non-Fourier transport and complex behaviors.
• The formalism accurately predicts phenomena observed in molecular dynamics simulations, including divergence in specific collision scenarios.