“Take a deep breath. Even if the air looks clear, it’s nearly certain that you’ll inhale tens of millions of solid particles and liquid droplets. These ubiquitous specks of matter are known as aerosols, and they can be found in the air over oceans, deserts, mountains, forests, ice, and every ecosystem in between. They drift in Earth’s atmosphere from the stratosphere to the surface and range in size from a few nanometers—less than the width of the smallest viruses—to several several tens of micrometers—about the diameter of human hair. Despite their small size, they have major impacts on our climate and our health.” from Aerosols: Tiny Particles, Big Impactillu_conducting_passages.
We concentrate on therapeutic aerosols. For these aerosols to be most effective, they have to reach a certain part of the lung. So the goal is to calculate the positions where the aerosols particles end up in the lung.
The image on the right shows the respiratory system (from wikipedia). We write a model for an aerosol (air/particle mixture) in the respiratory system for a fixed or moving domain in 3D. It consists of the incompressible Navier-Stokes equations for the air and the Vlasov equation for the particles, coupled through a drag force.
In the paper Modeling and numerics for respiratory aerosols, we validate the scheme as well as the C++ code which A. Moussa developed during his PhD thesis, we verify numerical stability and compare with explicit solutions.
A 3D mesh for a bifurcation in the bronchial tree:









This mesh can be used for simulations: