Abstract:
In this thesis, we explore the modeling and application of the pedestrian fl w
model proposed by Roger L. Hughes in 2002, a system of a hyperbolic conservation law to describe
crowd densities (ρ) and an Eikonal equation to describe the path
potential (φ) of this crowd:
ρt − div(ρf 2(ρ)∇φ) = 0
||∇φ|| =1 f(p)
Throughout this work, we explain this model in the context of a one dimensional
walking facility, like a bridge or a hallway, and a two dimensional one, such as an open room with
obstacles and obstructions. We revisit the motivation for the model, as well as properties and
qualities of the resulting weak entropy so- lutions, some of which will aid in understanding
numerical results. After this, we describe numerical methods to use in order to solve the eikonal
equation for the path potential, then use this quantity to solve the conservation law for the
density after a certain time step. With these methods established, we proceed to provide meaningful
simulations in both the 1D and 2D cases, describing what our results mean from a mathematical
perspective, then a real-life explanation, alongside a brief critique of the simulated situations
with comments on how to improve the walking facility conditions from a design perspective.
