Evaluation of various types of wall boundary conditions for the Boltzmann equation

This paper presents the evaluation of several solid wall boundary conditions when used in the numerical solution of the Boltzmann equation using the finite-difference/ finite-volume methods. Five solid wall boundary conditions are considered: (a) adsorption, (b) specular reflection, (c) diffuse reflection, (d) Maxwellian reflection, and (e) adsorptive Maxwellian reflection. The boundary conditions are applied on a two-dimensional discretized velocity space mesh. Methods for applying the same boundary conditions on a three-dimensional velocity space grid are also presented. The boundary conditions are implemented for the numerical solution of the hypersonic rarefied flow over a flat plate using a three-dimensional generalized Boltzmann equation (GBE) solver. The derivatives that contribute to heat transfer and skin friction at the solid boundary are calculated and compared. Recommendations for further evaluation of the boundary conditions are made.