Files on granular gases – Vicente Garzó
The Mathematica notebook Boltzmann.nb provides the transport coefficients for a binary mixture of inelastic hard spheres for arbitrary values of the three coefficients of normal restitution, the mass ratio, the diameter ratio, the mole fraction of one of the species, and the dimensionality of the system, as obtained from the inelastic Boltzmann equation in the first Sonine approximation.
For details on the derivation of the results, see
- V. Garzó and J. W. Dufty, Hydrodynamics for a granular mixture at low density, Phys. Fluids 14, 1476-1490 (2002).
- V. Garzó, J. M. Montanero, and J. W. Dufty, Mass and heat fluxes for a binary granular mixture at low density, Phys. Fluids 18, 083305 (2006).
- V. Garzó and J. M. Montanero, Navier-Stokes transport coefficients of d-dimensional granular binary mixtures at low density, J. Stat. Phys. 129, 27-58 (2007) [preprint arXiv: cond-mat/0604552].
The Mathematica notebook Model.nb provides the same as Boltzmann.nb, except that the results are obtained from a model of elastic hard spheres subject to the action of a friction force mimicking the effect of inelastic cooling.
For details on the derivation of the results, see
- F. Vega Reyes, V. Garzó, and A. Santos, Granular mixtures modeled as elastic hard spheres subject to a drag force, Phys. Rev. E 75, 061306-1-14 (2007) [arXiv:cond-mat/0701558].
The Mathematica notebook Write2.nb allows you to export tables of both the Boltzmann and the friction model coefficients as functions of the coefficient of restitution for a list of values of the remaining parameters of the mixture (mass ratio, diameter ratio, and mole fraction) and for a given dimensionality.
«Evaluation of the Navier-Stokes transport coefficients of a granular binary mixture from a modified Sonine approximation» by Vicente Garzó, Francisco Vega Reyes and José María Montanero.
(journal-ref: J.Fluid Mech. 623, 387 – 411 (2009); preprint: arXiv:0806.1858)
The Mathematica notebook Boltzmann12v6N.nb calculates the Navier-Stokes transport coefficients for a granular binary mixture of hard spheres/disks at low density. The coefficients are evaluated from a modified Sonine approximation, which consists in replacing the Maxwell-Boltzmann distribution weight function (used in the standard first Sonine approximation) by the homogeneous cooling state distribution for each species (see arXiv:0806.1858 for more details on the mathematical approach).
Code format: Mathematica 6
Recommended system requirements: RAM memory >= 2GB
«Mass transport of impurities in a moderately dense granular gas» by Vicente Garzó and Francisco Vega Reyes.
(journal-ref: Phys. Rev. E, in press (2009); preprint: arXiv:0812.3274)
Files:
- diffusion2dF.nb calculates the diffusion coefficient for a hard disk granular gas, using a second order sonine approach.
- diffusion3dF.nb idem for a hard spheres granular gas.
Code format: Mathematica 6
Recommended system requirements: RAM memory >= 1GB