Pedestrian Evacuation Modelled by a Conservation Law with a Two-inflection-point Flux Function
(2019) In Master's Theses in Mathematical Sciences NUMM11 20191Mathematics (Faculty of Engineering)
- Abstract
- When designing a building one must consider safety aspects. One such aspect is that in the case of an emergency people should be able to efficiently evacuate the building. In this paper we investigate how the width-profile of a corridor leading to an exit might affect the efficiency of evacuation. We model the dynamics of crowds using a continuum model, leading to a one-dimensional non-linear hyperbolic conservation law, a type of partial differential equation. The width-profile of the corridor is given by a two-parameter function, and we seek the best choice of these parameters.
In the first part of the Msc thesis we introduce the model, along with the theory needed to find exact solutions. In the second part we investigate how... (More) - When designing a building one must consider safety aspects. One such aspect is that in the case of an emergency people should be able to efficiently evacuate the building. In this paper we investigate how the width-profile of a corridor leading to an exit might affect the efficiency of evacuation. We model the dynamics of crowds using a continuum model, leading to a one-dimensional non-linear hyperbolic conservation law, a type of partial differential equation. The width-profile of the corridor is given by a two-parameter function, and we seek the best choice of these parameters.
In the first part of the Msc thesis we introduce the model, along with the theory needed to find exact solutions. In the second part we investigate how solutions behave near the boundary, and use this to find an exact solution when the width is constant. We then classify all stationary solution, when the width is non-constant. In the third part we investigate the conservation law numerically, using Godunov's method.
The numerical results suggest that the optimum choice of width-prole is to let the corridor have a convex profile with as large width in the entry to the corridor as possible. However, if one scales the density such that the maximum rate of people entering the corridor is constant, the variance is only temporary. The model also breaks down as the width at the entry increases, as one can no longer assume that people only move
in one direction. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/8974950
- author
- Lindell, Henrik LU
- supervisor
-
- Stefan Diehl LU
- organization
- course
- NUMM11 20191
- year
- 2019
- type
- H2 - Master's Degree (Two Years)
- subject
- keywords
- Numerical analysis, Applied mathematics, Hyperbolic conservation laws, Finite volume methods, Partial differential equations, Pedestrian dynamics, Modeling
- publication/series
- Master's Theses in Mathematical Sciences
- report number
- LUNFNA-3027-2019
- ISSN
- 1404-6342
- other publication id
- 2019:E14
- language
- English
- id
- 8974950
- date added to LUP
- 2019-07-15 10:54:21
- date last changed
- 2019-07-15 10:54:21
@misc{8974950,
abstract = {{When designing a building one must consider safety aspects. One such aspect is that in the case of an emergency people should be able to efficiently evacuate the building. In this paper we investigate how the width-profile of a corridor leading to an exit might affect the efficiency of evacuation. We model the dynamics of crowds using a continuum model, leading to a one-dimensional non-linear hyperbolic conservation law, a type of partial differential equation. The width-profile of the corridor is given by a two-parameter function, and we seek the best choice of these parameters.
In the first part of the Msc thesis we introduce the model, along with the theory needed to find exact solutions. In the second part we investigate how solutions behave near the boundary, and use this to find an exact solution when the width is constant. We then classify all stationary solution, when the width is non-constant. In the third part we investigate the conservation law numerically, using Godunov's method.
The numerical results suggest that the optimum choice of width-prole is to let the corridor have a convex profile with as large width in the entry to the corridor as possible. However, if one scales the density such that the maximum rate of people entering the corridor is constant, the variance is only temporary. The model also breaks down as the width at the entry increases, as one can no longer assume that people only move
in one direction.}},
author = {{Lindell, Henrik}},
issn = {{1404-6342}},
language = {{eng}},
note = {{Student Paper}},
series = {{Master's Theses in Mathematical Sciences}},
title = {{Pedestrian Evacuation Modelled by a Conservation Law with a Two-inflection-point Flux Function}},
year = {{2019}},
}