Numerical mathematics connecting Partial Differential Equations and Cellular Automata

• Date: 24. 2. 2022
• Time: 14:00 - 15:30
• Address:
  Sokolovská 83, Praha
• Room: K3
• Speaker: Jiří Felcman

Numerical mathematics connecting Partial Differential Equations and Cellular Automata (CA) for a pedestrian evacuation simulation is presented. The crowd flow is considered in terms of compressible fluid flow such as density, velocity and pressure. The intended direction of the escape of pedestrians in panic situations is governed by the Eikonal equation of the pedestrian flow model. A new two-dimensional CA model is proposed for the simulation of the pedestrian flow. The solution of the Eikonal equation is used to define the probability matrix whose elements express the probability of a pedestrian moving in finite set of directions. The relevant evacuation scenarios are numerically solved. Predictions of the evacuation behavior of pedestrians, for various room geometries with multiple exits, are demonstrated. The mathematical model is numerically justified by comparison of CA approach with the Finite Volume Method for the space discretization and Discontinuous Galerkin Method for the implicit time discretization of pedestrian flow model. For a short overview of CA see https://mathworld.wolfram.com/CellularAutomaton.html