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

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 [Brey et al., Phys. Rev. E 70, 051301 (2004); J. Phys.: Condens. Matter 17, S2489 (2005)], 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 distribution. The structure of the transport coefficients is common in both approximations, the distinction appearing in the coefficient of the fourth cumulant $a_2$. 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.

10 pages, 6 figures; v2: slightly shortened

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• Transport properties of dense dissipitive hard-sphere fluids for arbitrary energy loss models
• First-order Chapman--Enskog velocity distribution function in a granular gas
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• Modified Sonine approximation for granular binary mixtures
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• Dynamics of Annihilation I : Linearized Boltzmann Equation and Hydrodynamics
• Mass transport of an impurity in a strongly sheared granular gas
• Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients
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• Exact transport coefficients from the inelastic rough Maxwell model of a granular gas
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• Instabilities in granular gas-solid flows
• Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. II. Stability analysis
• Kinetic model for transport in granular mixtures
• Hydrodynamic equations for a granular mixture from kinetic theory - fundamental considerations