Numerical Analysis on the Long-Time Behavior of Moving Body in a Rarefied Gas (Mathematical Analysis in Fluid and Gas Dynamics)

Abstract

We consider the unsteady motion of an infinite plate under an external elastic force acting on the plate in its perpendicular direction. The plate is immersed in a rarefied gas, and thus the plate motion is coupled with the surrounding gas behavior. We perturb the plate from its equilibrium position and release it at an initial time. Subsequently, the plate starts an oscillating motion around the equilibrium position, but the displacement from the equilibrium decays as time goes on because of the drag force exerted by the surrounding gas. We numerically analyze the long-time behavior of the plate using the Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation as the basic equation for the rarefied gas. It is shown that the displacement from the equilibrium decays as time goes on with a rate t-3/2, where t is a time variable.