Lattice hydrodynamic model with bidirectional pedestrian flow

The two-dimensional lattice hydrodynamic model of traffic is extended to the two-dimensional bidirectional pedestrian flow via taking four types of pedestrians into account. The stability condition and the mKdV equation to describe the density wave of pedestrian congestion are obtained by linear stability and nonlinear analysis, respectively. In addition, there exist three phase transitions among the freely moving phase, the coexisting phase and the uniformly congested phase in the phase diagram. It can also be found that the critical point ac refers to not only the fraction c1 of the eastbound and westbound pedestrians, but also the fraction c2 of the northbound and southbound pedestrians. However, the critical point ac could not appear in the phase diagram and congested crowd at any time when two fractions are equal to same value of 0.5 (c1=c2=0.5). Furthermore, numerical simulation is carried out to examine the performance of such a model and the results show coincidence with the theory analysis results.