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Formation and evolution of density singularities in hydrodynamics of inelastic gases

Itzhak Fouxon·Baruch Meerson·Michael Assaf·Eli Livne
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Abstract

We use ideal hydrodynamics to investigate clustering in a gas of inelastically colliding spheres. The hydrodynamic equations exhibit a new type of finite-time density blowup, where the gas pressure remains finite. The density blowups signal formation of close-packed clusters. The blowup dynamics are universal and describable by exact analytic solutions continuable beyond the blowup time. These solutions show that dilute hydrodynamic equations yield a powerful effective description of a granular gas flow with close-packed clusters, described as finite-mass point-like singularities of the density. This description is similar in spirit to the description of shocks in ordinary ideal gas dynamics.

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Itzhak Fouxon, Baruch Meerson, Michael Assaf, Eli Livne. 2007-05-05. Formation and evolution of density singularities in hydrodynamics of inelastic gases. https://doi.org/10.1103/physreve.75.050301

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