Mathematical Investigation of 1D Discontinuity Waves in Dilute Granular Gases

Abstract

The propagation of acceleration waves in dilute granular gases was investigated. Acceleration waves propagating in elastic gases, mixtures, and other materials are widely studied in the literature, but not in granular gases. A thirteen-moment theory for granular gas was considered in the framework of Grad’s theory. The spatially homogeneous solutions were determined, and the hyperbolicity of the model is discussed. The propagation of acceleration waves in a non-constant state was investigated; the amplitude of the fastest mode was derived, and the critical time was evaluated. The acceleration wave propagation velocity in inelastic gases was shown to be lower than in elastic gases.

Keywords

• acceleration waves
• Grad theory
• dilute granular gas
• stability analysis