  In this paper we present a novel technique for the simulation of moving
boundaries and moving rigid bodies immersed in a rarefied gas using an
Eulerian-Lagrangian formulation based on least square method. The rarefied gas
is simulated by solving the Bhatnagar-Gross-Krook (BGK) model for the Boltzmann
equation of rarefied gas dynamics.
  The BGK model is solved by an Arbitrary Lagrangian-Eulerian (ALE) method,
where grid-points/particles are moved with the mean velocity of the gas.
  The computational domain for the rarefied gas changes with time due to the
motion of the boundaries. To allow a simpler handling of the interface motion
we have used a meshfree method based on a least-square approximation for the
reconstruction procedures required for the scheme.
  We have considered a one way, as well as a two-way coupling of
boundaries/rigid bodies and gas flow. The numerical results are compared with
analytical as well as with Direct Simulation Monte Carlo (DSMC) solutions of
the Boltzmann equation. Convergence studies are performed for one-dimensional
and two-dimensional test-cases. Several further test problems and applications
illustrate the versatility of the approach.
