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