Particle transport modeling in pulmonary airways with high-order elements

Inhaled particles can be either harmful (e.g., smoke, exhaust, viruses) or beneficial (e.g., a therapeutic drug). The accurate and computationally efficient simulation of particle transport and deposition remains a challenge because it requires the simultaneous solution of the Navier-Stokes equations and multiple advection-diffusion mass transport equations when the particles are modeled as multiple mono-dispersed populations. The solution of these equations requires that multiple length scales be resolved since the ratio of advection to diffusion varies among the different equations. Here, the spectral element method is examined because the high-order approximation provides greater flexibility in resolving multiple length scales. The problem geometry is based on the Weibel model A of the human airway for convergence tests and the first three generations of a typical rat airway for experimental validation. Particles in the size range 1 to 100 nm are simulated for deposition results. The particle concentration and flux were determined using meshes of varying coarseness to represent the geometry along with basis polynomials of order 5 to 11. The higher-order elements accurately propagate the short wavelengths contained in the advection-diffusion solution without sacrificing efficiency for the more computationally expensive Navier-Stokes solution. As the diffusion coefficient in the advection-diffusion equation decreases (i.e., particle size increases) the advantages of the spectral elements become apparent for the coupled system.