(258c) Simulation of Nanoparticle Transport In Airways Using Petrov-Galerkin Finite Element Methods

The simulation of nanoparticle transport and deposition in human airways requires the solving of multiple differential equations.  The bulk air phase is modeled using the Navier-Stokes equations in the laminar flow regime.  Transport in the particle phase is dominated by advection with diffusion being less important but non-negligible for nanoparticles (d < 1 micron).  The nanoparticle phase is typically modeled using multiple advection-diffusion equations with the diffusivity being a function of particle size and density.  The numerical challenge here is two-fold: (1) a higher-order approximation is desirable due to the large boundary layer gradients, and (2) the larger magnitude of advection relative to diffusion requires upwinding or stabilization for most numerical approaches.  Our focus is on Petrov-Galerkin finite element methods because they enable straightforward higher-order discretizations and provide stabilization for advection dominated flows.  Various Petrov-Galerkin approaches are compared, including a novel combined approach, for transport down a straight cylinder.  Using the results from straight cylinder study, the methods are then applied to multiple generations (typical 3-5) of realistic human airway geometries.  The objective is to predict optimal nanoparticle size and density for targeted drug delivery to specific regions of the airways.