Comparative analysis of the numerical solution of full Boltzmann and BGK model equations for the Poiseuille flow in a planar microchannel

Abstract

The pressure driven gas flow through planar microchannel is analyzed on the basis of the full Boltzmann equation and its kinetic Bhatnagar–Gross–Krook (BGK) model provided with the Maxwell diffuse boundary condition. The implicit–explicit numerical scheme along with the discrete velocity method are implemented. The optimization of algorithms via parallel programming with MPI in the physical space has been done. Calculations are carried out for Knudsen number ranging from the free-molecular regime to the slip one and for reservoir pressure ratios leading to subsonic and supersonic flows, including flow into vacuum. The structure of the flow field as a function of pressure ratio, rarefaction parameter and channel geometry are quantified from a kinetic standpoint. The range of applicability of the BGK kinetic model for microscale computations via comparison with the full Boltzmann solution is discussed. The choice of reservoir domain size is also considered.