Abstract
The paper presents a discretization of the Boltzmann equation obtained by writing the collision operator in polar coordinates, discretizing the velocity moduli and introducing a suitable class of basic interpolants. The model obtained is a system of integro-differential equations with integration over suitable angular variables: one over the portion of the unit sphere between two parallels symmetric with respect to the equatorial plane perpendicular to the velocity of the field particle and one over a unit circle. The model preserves mass, momentum and energy and an H-theorem is proved.
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Preziosi, L., Longo, E. On a conservative polar discretization of the Boltzmann equation. Japan J. Indust. Appl. Math. 14, 399–435 (1997). https://doi.org/10.1007/BF03167391
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DOI: https://doi.org/10.1007/BF03167391