Unsteady flows of a rarefied gas in a full space caused by an oscillatory motion of an infinitely wide plate in its normal direction is investigated numerically on the basis of the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation. The present notes aim at showing the properties and difficulties inherent to moving boundary problems in kinetic theory of gases using a simple one-dimensional setting.
As the first step, a rarefied polyatomic gas in a long and straight circular tube is considered, and the flow caused by a small uniform pressure gradient (Poiseuille flow) and the flow induced by a small uniform temperature gradient along the tube (thermal transpiration) are investigated, using the ellipsoidal statistical (ES) model of the Boltzmann equation for a polyatomic gas. It is shown that the solutions to these problems can be reduced to those based on the Bhatnagar-Gross-Krook (BGK) model...
We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity to the limiting velocity and prove that, under suitable smallness assumptions, the approach...
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