A Nonlinear Degenerate Advection-Diffusion Model for Crowd Instability and Stampede Risk Prediction

Key Points

• This research aims to develop a nonlinear model to predict crowd instability and identify high-risk areas during stampedes.
• Developed a nonlinear advection-diffusion system for pedestrian density ρ(x, t) capturing various behavioral regimes.
• Incorporated components such as harmonic potential fields, density-dependent velocity, weak diffusion, and a smooth superquadratic pressure law.
• Introduced a risk functional R(x, t) to identify regions at high risk based on density and velocity gradients.
• Successfully modeled three behavioral regimes: potential-driven flow at low density, diffusive spreading at moderate density, and nonlinear compression at high density.
• The risk functional detects high-risk regions quickly by monitoring changes in density and velocity gradients effectively.
• Provided a computationally efficient alternative to traditional agent-based simulations, maintaining crucial instability mechanisms.