Immersed boundary method for Boltzmann model kinetic equations and its applications to microscale gas damping

Three different immersed boundary method (IBM) formulations are presented for Boltzmann model kinetic equations such as Bhatnagar-Gross-Krook (BGK) and Ellipsoidal statistical Bhatnagar Gross-Krook (ESBGK) model equations. 1D unsteady IBM solution for a moving piston is compared with the DSMC results and 2D quasisteady microscale gas damping solutions are verifed by a conformal finite volume method solver. In the last chapter, two applications of immersed boundary methods for Boltzmann model kinetic equations are presented. Firstly, unsteady pressure distributions and damping force values are compared for the 2D application of a moving piston under a constant high-g acceleration with IB ES-BGK methods that are presented. It was shown that the coupling of damping force and acceleration force is required when the damping force gets comparable to the acceleration force reducing the velocity of the microbeam. Furthermore, all the IB ES BGK methods have similar convergence and error behavior for this unsteady application. In the second part, a sinusoidally oscillating beam flows were analyzed with these methods and damping force values and pressure distributions were presented. For oscillating flow, the IBInterrelaxation method has the fastest convergence. 2D unsteady analyses with IBM formulation are compared with FVM Conformal quasi-steady results and show that unsteady simulations predict higher damping than the steady simulations for both impulsive and oscillating motion.