Inelastic collisional effect on a dilute granular shock layer with a heated wall

Area of Science:

• Physics
• Chemical Engineering
• Materials Science

Background:

• Granular gases exhibit complex behaviors due to inelastic collisions.
• Understanding shock layers is crucial for various industrial and astrophysical applications.
• Kinetic theory provides a framework for modeling dilute granular systems.

Purpose of the Study:

• To numerically investigate the effect of inelastic collisions on shock layers in dilute granular gases.
• To formulate and analyze an inelastic Bhatnagar-Gross-Krook (BGK) type equation for granular gases.
• To compare the BGK model with the inelastic Boltzmann equation and Direct Simulation Monte Carlo (DSMC) methods.

Main Methods:

• Formulation of an inelastic BGK-type equation based on granular gas kinetic theory.
• Generalization of the BGK equation for hard-sphere particles to inverse power law (IPL) molecules.
• Numerical simulations using the formulated BGK equation and the DSMC method.

Main Results:

• The BGK model confirms non-equilibrium contributions to the cooling rate in the weakly inelastic regime when collision frequency depends on particle velocity.
• DSMC simulations show higher negative high-velocity tails in the shock wave generation regime compared to the BGK model.
• The discrepancy is attributed to the inelastic collisional gain term from the Boltzmann equation, absent in the proposed BGK model.

Conclusions:

• The developed inelastic BGK-type equation captures key aspects of inelastic collisional effects in granular gas shock layers.
• The study highlights the importance of the collision gain term for accurately predicting high-velocity distribution tails.
• Further refinement of kinetic models is needed to fully incorporate inelastic collisional effects for improved accuracy.