Numerical simulation of a moving rigid body in a rarefied gas

Abstract

In this paper we present a numerical scheme to simulate a moving rigid body with arbitrary shape suspended in a rarefied gas. The rarefied gas is simulated by solving the Boltzmann equation using a DSMC particle method. The motion of the rigid body is governed by the Newton–Euler equations, where the force and the torque on the rigid body are computed from the momentum transfer of the gas molecules colliding with the body. On the other hand, the motion of the rigid body influences the gas flow in its surroundings. We validate the numerical scheme by considering a moving piston problem in 1D and the Einstein relation for Brownian motion of the suspended particle in 3D. In the piston problem it is shown that the equilibrium position of the moving piston converges to the analytical solution for a wide range of Knudsen numbers. In the case of Brownian motion the translational as well as the rotational degrees of freedom are taken into account. In this case it is shown that the numerically computed translational and rotational diffusion coefficients converge to the theoretical values. Finally, the motion of an object of complex shape under the influence of a thermophoretic force is investigated.