I wrote my bachelor thesis at the Institute of Computational Physics at the ZHAW, where I extended a macroscopic pedestrian model with equations and analysed the changes. This modification of the model allows the simulation of heterogeneous groups of people. The changes were based in the pFlow and eFlow Project. The model is based on the following two equation: \begin{equation} \tag{1} \frac{\partial\varrho_\varepsilon}{\partial t} -\varepsilon \Delta \varrho_\varepsilon + \nabla \cdot(\varrho_\varepsilon \boldsymbol{u}) = 0, \end{equation} \begin{equation} \tag{2} -\delta^2 \Delta \Psi_\delta + \frac{1}{f^2(\varrho_\varepsilon)}\Psi_\delta = 0, \end{equation} which are linked through: \begin{equation} \tag{3} \boldsymbol{u} = f(\varrho_\varepsilon) \frac{\nabla\Psi_\delta}{\Vert\nabla\Psi_\delta\Vert}. \end{equation} Since the results of the thesis will be used in a paper, the full thesis has not been published. Here is the abstract.
Simulating evacuation scenarios in advance is an important tool for identifying dangerous situations in buildings and at major events at an early stage. Additionally, during the Covid-19 pandemic, there has been an increased demand for a tool to simulate the spread of infections in crowds. This led to the development of a simulation software called eFlow, which couples a macroscopic pedestrian model with an epidemiological model. In the course of this work, we extend the existing model to allow multiple groups with different parameters to be simulated simultaneously.
First, the macroscopic pedestrian model is further developed to simulate several groups of pedestrians with different dynamics in crowds. Additionally, we extend the epidemiological model to simulate the spread of infections in groups of susceptible individuals with different probabilities of infection. The extended model is then solved using the simulation software COMSOL.
In order to describe the pedestrian dynamics and the spread of infection in heterogeneous groups, the density of people is divided into different densities and the corresponding differential equations including boundary conditions are formulated separately. With this method, the velocity for each group can be defined independently of other groups based on different crowd densities and the entrances and exits the groups can use. In the epidemiological model, the group of people susceptible to infection is divided to assign each subgroup of susceptibles its own probability of infection upon contact with an infectious person. Additionally, the group of infectious pedestrians is subdivided and given its own parameters in order to take different infectivities into account. Both extensions of the model are verified using COMSOL by comparing them with the previous models.
Compared to the previous model, the extensions allow new and more complex situations to be described. For example, it is possible to simulate how one group overtakes another or how two groups intersect. Selected situations were analysed and checked for plausibility as a proof of concept. It provides the foundation for better prediction and understanding of pedestrian dynamics and the spread of infections in crowds in the future.
Keywords: Multi-group simulation, Pedestrian dynamics, Continuum model, Spread of infection
Here you find the projects poster, which was used to present the thesis at an event from ZHAW.