On the Eikonal Equation in the Pedestrian Flow Problem
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F44555601%3A13440%2F17%3A43893493" target="_blank" >RIV/44555601:13440/17:43893493 - isvavai.cz</a>
Alternative codes found
RIV/00216208:11320/17:10332292 RIV/68407700:21340/17:00318701
Result on the web
<a href="http://dx.doi.org/10.1063/1.4992707" target="_blank" >http://dx.doi.org/10.1063/1.4992707</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4992707" target="_blank" >10.1063/1.4992707</a>
Alternative languages
Result language
angličtina
Original language name
On the Eikonal Equation in the Pedestrian Flow Problem
Original language description
We consider the Pedestrian Flow Equations (PFEs) as the coupled system formed by the Eikonal equation and the first order hyperbolic system with the source term. The hyperbolic system consists of the continuity equation and momentum equation of fluid dynamics. Specifying the social and pressure forces in the momentum equation we come to the assumption that each pedestrian is trying to move in a desired direction (e.g. to the exit in the panic situation) with a desired velocity, where his velocity and the direction of movement depend on the density of pedestrians in his neighborhood. In [1] we used the model, where the desired direction of movement is given by the solution of the Eikonal equation (more precisely by the gradient of the solution). Here we avoid the solution of the Eikonal equation, which is the novelty of the paper. Based on the fact that the solution of the Eikonal equation has the meaning of the shortest time to reach the exit, we define explicitly such a function in the framework of the Dijkstra's algorithm for the shortest path in the graph. This is done at the discrete level of the solution. As the graph we use the underlying triangulation, where the norm of each edge is density depending and has the dimension of the time. The numerical examples of the solution of the PFEs with and without the solution of the Eikonal equation are presented.
Czech name
—
Czech description
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Classification
Type
D - Article in proceedings
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA13-00522S" target="_blank" >GA13-00522S: Qualitative analysis and numerical solution of problems of flows in generally time-dependent domains with various boundary conditions</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2016 (ICNAAM-2016)
ISBN
978-0-7354-1538-6
ISSN
0094-243X
e-ISSN
neuvedeno
Number of pages
4
Pages from-to
"nestrankovano"
Publisher name
AMER INST PHYSICS, 2 HUNTINGTON QUADRANGLE, STE 1NO1, MELVILLE, NY 11747-4501 USA
Place of publication
NY, USA
Event location
Rhodes, GREECE
Event date
Sep 19, 2016
Type of event by nationality
EUR - Evropská akce
UT code for WoS article
000410159800517