Simulation of nanoparticle transport in airways using Petrov–Galerkin finite element methods

Abstract

The transport and deposition properties of nanoparticles with a range of aerodynamic diameters ( 1 nm ≤ d ≤ 150 nm) were studied for the human airways. A finite element code was developed that solved both the Navier-Stokes and advection-diffusion equations monolithically. When modeling nanoparticle transport in the airways, the finite element method becomes unstable, and, in order resolve this issue, various stabilization methods were considered in terms of accuracy and computational cost. The stabilization methods considered here include the streamline upwind, streamline upwind Petrov-Galerkin, and Galerkin least squares approaches. In order to compare the various stabilization approaches, the approximate solution from each stabilization approach was compared to the analytical Graetz solution, which is a model for monodispersed, dilute particle transport in a straight cylinder. The optimal stabilization method, especially with regard to accuracy, was found to be the Galerkin least squares approach for the Graetz problem when the Péclet number was larger than 10(4). In the human airways geometry, the Galerkin least squares stabilization approach once more provided the most accurate approximate solution for particles with an aerodynamic diameter of 10 nm or larger, but mesh size had a much greater effect on accuracy than the choice of stabilization method. The choice of stabilization method had a greater impact than mesh size for particles with an aerodynamic diameter 10 nm or smaller, but the most accurate stabilization method was streamline upwind Petrov-Galerkin in these cases.