A meshfree arbitrary Lagrangian-Eulerian method for the BGK model of the Boltzmann equation with moving boundaries

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.