Some New Techniques In Numerical Simulation Of Pedestrian Flows

The purpose of pedestrian flow simulation is to reproduce pedestrian motion by modeling and simulation methods in order to study a variety of typical problems in pedestrian flows. In this thesis, several new numerical methods for pedestrian flows are proposed for several crucial problems. The development of related study is firstly reviewed and some basic methods are summarized. On this basis, the main contributions are made as follows.1. A floor field cellular automaton model for bi-directional pedestrian flow is presented and then applied to the research of counter flow and intersecting flow.A bi-directional pedestrian flow model is established to reflect real interaction between pedestrians by introducing improved dynamic fields. The dynamic field of one group is set by referring another’s in order to reflect the following and conflict-avoiding behavior of pedestrians. The intensity of the conflict is related to the intersecting angle between two moving directions. This setting makes the model appropriate to any bi-directional pedestrian flow problems. The existence of position-changing behavior is also assumed in this model. In addition, the improvement of dissipation is consistent with pedestrians’ psychology of avoiding conflicts. After applying the model to counter flow, the influences of model parameters, such as dynamic field strength, average density and dynamic field dissipation-decay on the lane formation phase, are analyzed. These model parameters affect the numbers of lanes, position-changing and probability of lane formation. The influence of dynamic field on the lane formation phases is connected with the average density, which is significant only in high-density area. The dissipation and decay of dynamic field directly affect the stability of the lanes and indirectly affect the probability of lane formation and number of lanes. In the numerical experiments, it is also found that the average number of position-changing can be used to distinguish stable and metastable lane formation phases. As for intersecting flow, our model reproduces the quasi-steady state and pedestrians’ detour and path-crossing behavior. Specifically, when the density continues to increase, pedestrians choose to walk along the existing paths to cross the interaction zone of the facility.2. Social force is introduced to cellular automaton model for pedestrian flow and two composite models are designed. After discussing the two fundamental diagrams, the pedestrian evacuation and counter flow on bottleneck with the new models are studied in detail.Two composite models are designed by integrating the social force into the cellular automaton model, named as the basic composite model and S-RCA model. The basic composite model is based on static field. This model introduces the concept of minimum step wise, pedestrian vision and benefit-cost ratio in order to truly reflect the characteristics of pedestrian movement. Pedestrian’s moving probability is assumed to be related to social force components. The S-RCA model is constructed by using the principles of RCA model, in which pedestrians can move in arbitrary direction and at arbitrary velocity. The driving force is expressed as a function of equivalent density, which can avoid unrealistic unlimited acceleration behavior. In addition, the S-RCA model limits the force in the range of vision, which reduces the calculation cost. The fundamental diagrams for the basic model are in agreement with the observed data for some parameters in experiments, which shows the rationality of the model. Moreover, the fundamental diagram also reflects the influence of pedestrian vision and the dual character of following behavior on average speed. In particular, the fundamental diagram of S-RCA model is similar to the one obtained by Helbing. The numerical results reveal the relationship between pedestrian vision and average speed: only in the low density range pedestrian vision would improve the movement efficiency, and appropriate space helps to improve the speed of the pedestrian flow, and too small or too large space would negatively affect the speed. These conclusions are consistent with common knowledge. When S-RCA model applied to the bottleneck evacuation problem, nemerical experiments results show that pedestrian vision’s impact on evacuation efficiency is relate to bottleneck width. The distence between pedestrians has two-side influence on evacuation efficiency. The bottleneck flow of the nemerical experiments are basically consistent with the results of Nagai. And the impact of the initial pedestrian flow density on bottleneck flow is also verified. Spatial distributions of evacuation time in several classical conditions are acquired in the experiments. The results show that the distribution of evacuation time is closely related to the bottleneck width, pedestrian vision and repulsive force. Then the counter flow on bottleneck is investigated with the S-RCA model by employing the newly-designed unsymmetrical factor. Numerical results show that there exist three typical phases, which are deadlock, oscillation flow and two-way free flow. And the probabilities of the three phases are related to bottleneck width, pedestrian repulsion(space between pedestrians) and unsymmetrical factor.3. Relaxation-WENO scheme is introduced to numerical simulation of fluid dynamics model for pedestrian flows. It is demonstrated that the lane formation phase produced by fluid dynamics model is sensitive to the initial-boundary conditions.The relaxation-WENO scheme is used to the numerical simulation of RDUO model. The conservation equation is rewritten as a relaxation system with linear convection term and nonlinear stiff term, in order to make the upwind discretization for convection term in high-resolution schemes such as WENO,which considerably simplifies the numerical scheme. The counter flows under different initial-boundary conditions are simulated by using this scheme. The results show that the lane formation phase is sestive to the initial-boundary conditions, which extends the existing conclusions in this field. Under one kind of initial-boundary condition, the inflow of the pedestrian flow directly influences the relative speed of the pedestrians and indirectly influences the lane formation. Under another initial-boundary conditions, the intensity of the interaction between the pedestrians only has influence on the lane formation in the low-density area.Finally, the key research directions in future work and problems to be solved are presented after the summation of our work.