Bernhoff, N. (2010) On halfspace problems for the discrete Boltzmann equation. Il nuovo cimento C, 33 (1). pp. 4754. ISSN 18269885

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Abstract
We study typical halfspace problems of rarefied gas dynamics, including the problems of Milne and Kramer, for the discrete Boltzmann equation (a general discrete velocity model, DVM, with an arbitrary finite number of velocities). Then the discrete Boltzmann equation reduces to a system of ODEs. The data for the outgoing particles at the boundary are assigned, possibly linearly depending on the data for the incoming particles. A classification of wellposed halfspace problems for the homogeneous, as well as the inhomogeneous, linearized discrete Boltzmann equation is made. In the nonlinear case the solutions are assumed to tend to an assigned Maxwellian at infinity. The conditions on the data at the boundary needed for the existence of a unique (in a neighborhood of the assigned Maxwellian) solution of the problem are investigated. In the nondegenerate case (corresponding, in the continuous case, to the case when the Mach number at the Maxwellian at infinity is different of −1, 0 and 1) implicit conditions are found. Furthermore, under certain assumptions explicit conditions are found, both in the nondegenerate and degenerate cases. An application to axially symmetric models is also studied.
Item Type:  Article 

Uncontrolled Keywords:  Kinetic and transport theory of gases ; Kinetic theory 
Subjects:  500 Scienze naturali e Matematica > 530 Fisica 
Depositing User:  Marina Spanti 
Date Deposited:  31 Mar 2020 15:16 
Last Modified:  31 Mar 2020 15:16 
URI:  http://eprints.bice.rm.cnr.it/id/eprint/16792 
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