The statistical overloading framework for dispersal problems - a comprehensive evaluation of the computational requirements

Accurate characterization of turbulent dispersal of aerosols and pollutants is a topic of interest involving turbulent flows in a variety of settings. In indoor settings, this finds applications in airborne disease transmission prediction, preventing occupational hazards, and improving indoor air quality.Similar applications in other avenues include managing atmospheric dispersion in urban settings and tephra dispersal. Statistical overloading is a novel computational technique that takes advantage of the one-way coupled nature of these flows to obtain converged, meaningful statistics pertaining to quantities of interest (QoI). The computational domain is overloaded with an abundance of pollutant particles that are randomly seeded over space and time to characterize variations in the QoI due to both inhomogeneity and turbulence. 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 X 10 X 3.2 m³. The resulting dataset is used to benchmark the methodology and to formulate practical guidelines for selecting key computational parameters in turbulent dispersal simulations. These include, but are not limited to, determining the minimum number of particles that must be tracked and the minimum number of independent turbulent or spatial realizations required to ensure statistically converged results to a desired level of accuracy. The guidelines are derived by combining the abundant Lagrangian statistics obtained from the simulations with statistical parameter estimation theory and scaling analysis.