Modeling turbulent diffusion and advection of indoor air contaminants by Markov chains

Turbulent eddy diffusion models are used to describe a continuous concentration gradient with distance from an in-room contaminant emission source. A refined diffusion model termed the Drivas model also accounts for contaminant reflection by wall surfaces and partially accounts for removal by exhaust air. This article develops two models based on Markov chains to describe indoor air contaminant dispersion by turbulent diffusion and advection, and removal by the exhaust airflow. Markov model I is equivalent to the Drivas model and is computationally simple. Markov model II can provide more realism by accounting for the locations of air inlets and outlets, advective flow patterns, in-room reflective surfaces, and contaminant removal mechanisms at specific room positions. The price paid for this greater realism is greater computational complexity. Both Markov models are explicitly probabilistic and estimate the expected concentration values at given room positions.