Comparison of numerical solutions of the Boltzmann and the Navier–Stokes equations for a moving rigid circular body in a micro scaled cavity
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In this paper we present a simulation of a moving rigid circular body suspended in a cavity containing a rarefied gas. The rigid body moves due the flow developed in the gas by continuous uniform motion of one of the wall of the cavity. The flow in the gas is simulated by solving the Boltzmann equation using DSMC particle method. The motion of the rigid body is governed by 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 rigid body. On the other hand, the motion of rigid body influences the gas flow in its surroundings. The numerical solutions obtained for the dynamics of the rigid body by solving the Boltzmann equation implementing moment and momentum approaches in the DSMC framework are compared. Furthermore, the numerical solutions obtained by solving the Boltzmann equation implementing momentum approach in DSMC framework are compared with the solutions obtained by solving the Navier–Stokes equations using finite pointset method for small as well as large values of Knudsen numbers.
KeywordsBoltzmann equation Navier–Stokes equations Particle methods Force Torque Micro cavity flow Moving rigid body
This work is partially supported by the German research foundation, DFG grant KL 1105/20-1 and by the DAAD Ph.D. programme MIC.
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