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Shock Propagation in the Hard Sphere Gas in Two Dimensions: Comparison Between Simulations and Hydrodynamics

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Abstract

We study the radial distribution of pressure, density, temperature and flow velocity fields at different times in a two dimensional hard sphere gas that is initially at rest and disturbed by injecting kinetic energy in a localized region through large scale event driven molecular dynamics simulations. For large times, the growth of these distributions are scale invariant. The hydrodynamic description of the problem, obtained from the continuity equations for the three conserved quantities—mass, momentum, and energy—is identical to those used to describe the hydrodynamic regime of a blast wave propagating through a medium at rest, following an intense explosion, a classic problem in gas dynamics. Earlier work showed that the results from simulations matched well with the predictions from hydrodynamics in two dimensions, but did not match well in three dimensions. To resolve this contradiction, we perform large scale simulations in two dimensions, and show that like in three dimensions, hydrodynamics does not describe the simulation data well. To account for this discrepancy, we check in our simulations the different assumptions of the hydrodynamic approach like local equilibrium, existence of an equation of state, neglect of heat conduction and viscosity.

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Acknowledgements

The simulations were carried out on the supercomputer Nandadevi at The Institute of Mathematical Sciences.

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Authors and Affiliations

  1. The Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai, 600113, India

    Jilmy P. Joy & R. Rajesh

  2. Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai, 400094, India

    Jilmy P. Joy & R. Rajesh

  3. Department of Physics, St. Thomas College (Autonomous), Thrissur, Kerala, 680001, India

    Jilmy P. Joy

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  1. Jilmy P. Joy
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  2. R. Rajesh
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Correspondence to R. Rajesh.

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Communicated by Abhishek Dhar.

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Joy, J.P., Rajesh, R. Shock Propagation in the Hard Sphere Gas in Two Dimensions: Comparison Between Simulations and Hydrodynamics. J Stat Phys 184, 3 (2021). https://doi.org/10.1007/s10955-021-02790-6

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