Comparing calculation methods of state transfer matrix in Markov chain models for indoor contaminant transport

Fast and accurate prediction of indoor airborne contaminant distribution is of great significance to the safety and health of occupants. Several Markov chain models have been developed and proved to be the potential solutions. However, there is a lack of comparison in terms of accuracy, computing cost, and robustness among these models, which limits their practical application. To this end, this study compared the performance of three Markov chain models, in which the state transfer matrix was calculated based on different principles, i.e., Markov chain model with flux-based method, with Lagrangian tracking, and with set theory approach. The investigation was conducted in a 2D ventilated cavity and a two-zone ventilated chamber. The simulation by Eulerian model for contaminant and experimental data were used as the benchmarks for the 2D and 3D cases, respectively. It is revealed that all three Markov chain models can provide a correct prediction. In the 2D case, the Markov chain model with set theory approach is the most accurate, followed by Lagrangian tracking. In the 3D case, the accuracy of Markov chain models with flux-based method and Lagrangian tracking is comparable. The Markov chain model with Lagrangian tracking is the fastest, and the time step size in this model can be relatively large. Finally, the selection guideline is given for the application of Markov chain models in different scenarios.