Non-uniform state-based Markov chain model to improve the accuracy of transient contaminant transport prediction

Rapid prediction of indoor airborne contaminant distribution is crucial for controlling indoor air quality. Markov chain technology, which uses matrix multiplication, is computationally efficient in this field. The combination of computational fluid dynamics (CFD) with Markov chain technology has gained significant attention among researchers. The partitioning of the indoor zone directly affects the size and values of the transition matrix, which is the core of the Markov chain and impacts both the cost and accuracy of calculations. Although coarse matrix Markov chain models incur relatively lower computational costs, effective methods for state partitioning are lacking. This study proposes an improved method for non-uniform state partitioning based on velocity to enhance the computational accuracy of Markov chain models with coarse matrices. First, we used the airflow velocity field obtained by CFD simulation to divide the states and obtain non-uniform states. Subsequently, we obtained the transition matrix corresponding to non-uniform states and applied it to the Markov chain model for predictive calculation. We compared the predictive results of the non-uniform state-based Markov chain model with experimental and CFD simulation data, which showed that the model had a good predictive performance for transient contaminant transport and that the non-uniform state partitioning method improved predictive accuracy. Additionally, we discussed the effects of different numbers of states and time steps on computational accuracy.