Nano-particle drag prediction at low Reynolds number using a direct Boltzmann–BGK solution approach

Abstract

This paper outlines a novel approach for solution of the Boltzmann–BGK equation describing molecular gas dynamics applied to the challenging problem of drag prediction of a 2D circular nano-particle at transitional Knudsen number (0.0214) and low Reynolds number (0.25–2.0). The numerical scheme utilises a discontinuous-Galerkin finite element discretisation for the physical space representing the problem particle geometry and a high order discretisation for molecular velocity space describing the molecular distribution function. The paper shows that this method produces drag predictions that are aligned well with the range of drag predictions for this problem generated from the alternative numerical approaches of molecular dynamics codes and a modified continuum scheme. It also demonstrates the sensitivity of flow-field solutions and therefore drag predictions to the wall absorption parameter used to construct the solid wall boundary condition used in the solver algorithm. The results from this work has applications in fields ranging from diagnostics and therapeutics in medicine to the fields of semiconductors and xerographics.