Open Access
Issue |
Math. Model. Nat. Phenom.
Volume 16, 2021
Modelling and Simulations of Fluid Flows
|
|
---|---|---|
Article Number | 11 | |
Number of page(s) | 18 | |
DOI | https://doi.org/10.1051/mmnp/2021002 | |
Published online | 03 March 2021 |
- S. Bandini, G. Mauri and R. Serra, Cellular automata: From a theoretical parallel computational model to its application to complex systems. Parallel Comput. 27 (2001) 539–553. [Google Scholar]
- N. Bellomo and Ch. Dogbé, On the modelling crowd dynamics from scaling to hyperbolic macroscopic models. Math. Models Methods Appl. Sci. 18 (2008) 1317–1345. [Google Scholar]
- N. Bellomo, A. Marasco and A. Romano, From the modelling of driver’s behavior to hydrodynamics models and problems of traffic flow. Nonlinear Anal. RWA 3 (2002) 339–363. [Google Scholar]
- S. Buchmueller and U. Weidmann, Parameters of pedestrians, in: Pedestrian Traffic and Walking Facilities. Technical report, Schriftenreihe des IVT, ETH Zurich (2006). [Google Scholar]
- C. Burstedde, K. Klauck, A. Schadschneider and J. Zittartz, Simulation of pedestrian dynamics using a two-dimensional cellular automaton. Physica A 295 (2001) 507–525. [Google Scholar]
- E. Cristiani, B. Piccoli and A. Tosin, Multiscale Modeling of Pedestrian Dynamics. Springer International Publishing (2014). [Google Scholar]
- F. Dietrich and G. Köster, Gradient navigation model for pedestrian dynamics. Phys. Rev. E 89 (2014) 062801. [Google Scholar]
- C. Dogbe, On the modelling of crowd dynamics by generalized kinetic models. J. Math. Anal. Appl. 387 (2012) 512–532. [Google Scholar]
- V. Dolejší, J. Felcman and P. Kubera, FV–DG method for the Pedestrian flow problem. Comput, Fluids 183 (2019) 1–15. [Google Scholar]
- M.H. Dridi, Simulation of high density pedestrian flow: Microscopic model. Open J. Modell. Simul. 3 (2015) 81–95. [Google Scholar]
- M. Feistauer, J. Felcman and I. Straškraba Mathematical and computational methods for compressible flow. Clarendon Press (2003). [Google Scholar]
- J. Felcman and P. Kubera, Eikonal equation based cellular automaton for a pedestrian evacuation problem. In T. E. Simos and Ch. Tsitouras, editors, ICNAAM 2019 AIP Conference Proceedings. American Institute of Physics (2019) 1–4. [Google Scholar]
- Z. Fu, X. Zhan, L. Luo, A. Schadschneider and J. Chen, Modeling fatigue of ascending stair evacuation with modified fine discrete floor field cellular automata. Phys. Lett. A 383 (2019) 1897–1906. [Google Scholar]
- J. Gao, J. He and J. Gong, A simplified method to provide evacuation guidance in a multi-exit building under emergency. Physica A 545 (2020) 123554. [Google Scholar]
- D. Helbing and P. Molnár, Social force model for pedestrian dynamics. Phys. Rev. E 51 (1995) 4282–4286. [Google Scholar]
- Y. Jiang, B. Chen, X. Li and Z. Ding, Dynamic navigation field in the social force model for pedestrian evacuation. Appl. Math. Modell. 80 (2020) 815–826. [Google Scholar]
- Y.Q. Jiang, P. Zhang, S.C. Wong and R.X. Liu, A higher-order macroscopic model for pedestrian flows. Physica A 389 (2010) 4623–4635. [Google Scholar]
- A. Kirchner and A. Schadschneider, Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics. Physica A 312 (2002) 260–276. [Google Scholar]
- P. Kubera and J. Felcman, On a numerical flux for the pedestrian flow equations. JAMSI 11 (2015) 79–96. [Google Scholar]
- Y. Li, M. Chen, Z. Dou, X. Zheng, Y. Cheng and A. Mebarki, A review of cellular automata models for crowd evacuation. Physica A 526 (2019) 120752. [Google Scholar]
- R. Liu, Z. Fu, A. Schadschneider, Q. Wen, J. Chen and S. Liu, Modeling the effect of visibility on upstairs crowd evacuation by a stochastic ffca model with finer discretization. Physica A 531 (2019) 121723. [Google Scholar]
- H.J. Payne, Models of freeway traffic and control. Simulation Councils, Incorporated (1971). [Google Scholar]
- T. Petrášová Application of the Dijkstra’s algorithm in the pedestrian flow problem. Bc thesis, Charles University in Prague (2016). [Google Scholar]
- K. Rendán Rozo, J. Arellana, A. Santander-Mercado and M. Jubiz-Diaz, Modelling building emergency evacuation plans considering the dynamic behaviour of pedestrians using agent-based simulation. Saf. Sci. 113 (2019) 276–284. [Google Scholar]
- A. Seyfried, B. Steffen and T. Lippert, Basics of modelling the pedestrian flow. Physica A 368 (2006) 232–238. [Google Scholar]
- L. Tan, M. Hu and H. Lin, Agent-based simulation of building evacuation: combining human behavior with predictable spatial accessibility in a fire emergency. Inf. Sci. 295 (2015) 53–66. [Google Scholar]
- M. Twarogowska, P. Goatin and R. Duvigneau, Macroscopic modeling and simulation of room evacuation. Appl. Math. Modell. (2014) 5781–5795. [Google Scholar]
- G.B. Whitham, Linear and nonlinear waves. Pure and applied mathematics, Wiley (1974). [Google Scholar]
- P. Zhang, X.-X. Jian, S.C. Wong and K. Choi, Potential field cellular automata model for pedestrian flow. Phys. Rev. E 85 (2012) 021119. [Google Scholar]
- Hk. Zhao, A fast sweeping method for Eikonal equations. Math. Comput. 74 (2005) 603–627. [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.