LAUSR

Abstract Rapid contaminant transport simulation is important in emergency scenarios, and Markov chain models have shown promise in this regard. The state transfer matrix (STM) is the core of the Markov chain model and determines the simulation accuracy and computing cost. However, existing methods to calculate the STM result in significant errors or large computing costs. Using set theory, the characteristic form of the STM was investigated according to the continuity equation for incompressible fluids. Based on this form, the calculation method of the STM when the initial contaminant is distributed uniformly was improved. The performances of the original and modified methods were compared via a case study. In addition, the influence of underlying airflow grid resolution on model performance was analyzed. Finally, sensitivity analysis was conducted to determine the dominant factor. The results revealed that the STM should be constructed as an approximate doubly stochastic matrix; however, this is problematic due to the discrete underlying airflow and the associated interpolation. As an alternative, a left stochastic matrix is appropriate, with higher accuracy when the initial contaminant is uniformly distributed over a large area. Increasing the underlying airflow grid resolution can improve the model accuracy; however, a minimum grid resolution with a credible velocity field is sufficient, especially considering the computing cost. Sensitivity analysis showed that the Markov state size is the dominant factor for the accuracy and computing cost, and it should be carefully selected. This study can aid the development of a Markov chain model for airborne contaminant transport.