Solutions of the moment hierarchy in the kinetic theory of Maxwell models
arXiv:0903.1054 · doi:10.1007/s00161-009-0113-5
Abstract
In the Maxwell interaction model the collision rate is independent of the relative velocity of the colliding pair and, as a consequence, the collisional moments are bilinear combinations of velocity moments of the same or lower order. In general, however, the drift term of the Boltzmann equation couples moments of a given order to moments of a higher order, thus preventing the solvability of the moment hierarchy, unless approximate closures are introduced. On the other hand, there exist a number of states where the moment hierarchy can be recursively solved, the solution generally exposing non-Newtonian properties. The aim of this paper is to present an overview of results pertaining to some of those states, namely the planar Fourier flow (without and with a constant gravity field), the planar Couette flow, the force-driven Poiseuille flow, and the uniform shear flow.
26 pages, 7 figures, 6 tables; v2: Change of notation of some variables, new section and two new figures added; published in a special use of Cont. Mech. Thermodyn. devoted to the Proceedings of the Workshop on Moment Methods in Kinetic Gas Theory (November 6-8, 2008)
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Cited by in corpus (9)
- Hamiltonian and Godunov Structures of the Grad Hierarchy
- Hydrodynamics of inelastic Maxwell models
- An exact solution of the inelastic Boltzmann equation for the Couette flow with uniform heat flux
- Granular gas of inelastic and rough Maxwell particles
- Moment theories for a d-dimensional dilute granular gas of Maxwell molecules
- Collisional rates for the inelastic Maxwell model: application to the divergence of anisotropic high-order velocity moments in the homogeneous cooling state
- Exact transport coefficients from the inelastic rough Maxwell model of a granular gas
- Kinetic Theory of Soft Matter. The Penetrable-Square-Well Model
- Non-Newtonian Couette-Poiseuille flow of a dilute gas