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Modified Sonine approximation for the Navier–Stokes transport coefficients of a granular gas

Author

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  • Garzó, Vicente
  • Santos, Andrés
  • Montanero, José María

Abstract

Motivated by the disagreement found at high dissipation between simulation data for the heat flux transport coefficients and the expressions derived from the Boltzmann equation by the standard first Sonine approximation [J.J. Brey, M.J. Ruiz-Montero, Phys. Rev. E 70 (2004) 051301, J.J. Brey, M.J. Ruiz-Montero, P. Maynar, M.I. García de Soria, J. Phys. Condens. Matter 17 (2005) S2489], we implement in this paper a modified version of the first Sonine approximation in which the Maxwell–Boltzmann weight function is replaced by the homogeneous cooling state (HCS) distribution. The structure of the transport coefficients is common in both approximations, the distinction appearing in the coefficient of the fourth cumulant a2. Comparison with computer simulations shows that the modified approximation significantly improves the estimates for the heat flux transport coefficients at strong dissipation. In addition, the slight discrepancies between simulation and the standard first Sonine estimates for the shear viscosity and the self-diffusion coefficient are also partially corrected by the modified approximation. Finally, the extension of the modified first Sonine approximation to the transport coefficients of the Enskog kinetic theory is presented.

Suggested Citation

  • Garzó, Vicente & Santos, Andrés & Montanero, José María, 2007. "Modified Sonine approximation for the Navier–Stokes transport coefficients of a granular gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 94-107.
    • Handle: RePEc:eee:phsmap:v:376:y:2007:i:c:p:94-107
    DOI: 10.1016/j.physa.2006.10.081
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    References listed on IDEAS

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    1. Montanero, José María & Santos, Andrés & Garzó, Vicente, 2007. "First-order Chapman–Enskog velocity distribution function in a granular gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 75-93.
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    1. Montanero, José María & Santos, Andrés & Garzó, Vicente, 2007. "First-order Chapman–Enskog velocity distribution function in a granular gas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 75-93.
    2. Garzó, Vicente, 2015. "Stability of freely cooling granular mixtures at moderate densities," Chaos, Solitons & Fractals, Elsevier, vol. 81(PB), pages 497-509.
    3. Abourabia, A.M. & Morad, A.M., 2015. "Exact traveling wave solutions of the van der Waals normal form for fluidized granular matter," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 333-350.

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