The statistical overloading framework for accurate evaluation of pollutant dispersal with rigorous uncertainty estimation

Accurate characterization of turbulent dispersal of aerosols and pollutants is a topic of interest involving turbulent flows in a variety of indoor and outdoor settings. For the case of a ventilated indoor space, the stochastic nature of the dispersal process results in variations due to factors such as turbulent transport and spatial inhomogeneity. Statistical overloading is a novel technique wherein the computational domain is overloaded with an abundance of pollutant particles that are randomly seeded over space and time. This would allow us to capture quantities of interest, such as mean and variation of pollutant concentration, to any desired accuracy for all possible pollutant release and sensing locations, using just one master simulation. In this study, the statistical overloading framework is employed for the case of turbulent dispersal in ventilated indoor spaces using Euler–Lagrange LES simulations in a canonical room of dimensions $10\times 10\times 3.2{\text{m}}^3$. We establish clear guidelines for selecting computational parameters involved in designing turbulent dispersal simulations, with potential applications to other challenges involving aerosol, particulate, or pollutant dispersal. These parameters include, but are not limited to, the minimum number of particles to be tracked during the simulation and the minimum number of turbulent/spatial realizations required to achieve converged statistics to any specified level of accuracy. We leverage the extensive Lagrangian statistics obtained from Euler–Lagrange simulations, combined with well-established statistical theory, to derive the aforementioned guidelines and requirements.