Modelling of respiratory aerosol dispersion using the Fully Lagrangian Approach

The airborne transmission of respiratory infections is underpinned by the behaviour of virus-carrying aerosols, and the myriad of airflow effects which influence the dispersion process, including turbulence, ventilation, and gravitational settling. Accounting for these different effects within a modelling framework forms the cornerstone of developing quantitatively accurate approaches for predicting the spatial dependence of the infectious aerosol concentration. Additionally, determination of the viral transmission also requires knowledge of the aerosol size distribution due to the variation of viral load across the range of droplet sizes. Whilst modelling of the aerosol concentration as a continuum is a popular approach to acquiring this information, some of the detailed aerosol behaviour is necessarily lost due to the averaged nature of such models. The Fully Lagrangian Approach (FLA) addresses this deficiency by retaining the information of individual aerosol trajectories within the model formulation, and the aerosol concentration is computed by applying conservation of mass along these trajectories. Recent work has further developed a methodology for the reconstruction of the aerosol concentration field from the trajectory data using the statistical learning technique of kernel regression, and the resulting model is able to provide an accurate descriptor of the aerosol concentration using only a select seeding of aerosol trajectories. The kernel regression procedure can also straightforwardly be extended to include the aerosol size, therefore enabling inference of the size distribution to be made at every point in space. In the present work the FLA is applied to the situation of aerosol exhalation into still air, with the subsequent evaporation and settling being tracked. Results are presented for the aerosol size distribution at different distances from the point of exhalation, along with the spatial statistics of aerosol concentration, average size, and polydispersity. This demonstrates the ability of the FLA to obtain detailed knowledge of the aerosol concentration and range of droplet sizes, and thereby provide insight into the evolution of the viral transmission process at a fraction of the computational expense of conventional computational fluid dynamics simulations.