Indoor ventilation is underutilized for the control of exposure to infectious pathogens. Occupancy restrictions during the pandemic showed the acute need to control detailed airflow patterns, particularly in heavily occupied spaces, such as lecture halls or offices, and not just to focus on air changes. Displacement ventilation is increasingly considered a viable energy efficient approach. However, control of airflow patterns from displacement ventilation requires us to understand them first. The challenge in doing so is that, on the one hand, detailed numerical simulations – such as direct numerical simulations (DNSs) – enable the most accurate assessment of the flow, but they are computationally prohibitively costly, thus impractical. On the other hand, large eddy simulations (LES) use parametrizations instead of explicitly capturing small-scale flow processes critical to capturing the inhomogeneous mixing and fluid–boundary interactions. Moreover, their use for generalizable insights requires extensive validation against experiments or already validated gold-standard DNSs. In this study, we start to address this challenge by employing efficient monotonically integrated LES (MILES) to simulate airflows in large-scale geometries and benchmark against relevant gold-standard DNSs. We discuss the validity and limitations of MILES. Via its application to a lecture hall, we showcase its emerging potential as an assessment tool for indoor air mixing heterogeneity.