Modelling crowd pressure and turbulence through a mixed-type continuum approach

References

• Aw, A. A. T. M., and M. Rascle. 2000. “Resurrection of ‘Second Order’ Models of Traffic Flow.” SIAM Journal on Applied Mathematics 60 (3): 916–938. https://doi.org/10.1137/S0036139997332099.
   Web of Science ®Google Scholar
• BBC. 2015. “Hajj Stampede: At Least 717 Killed in Saudi Arabia.”
   Google Scholar
• Benedictus, L.. 2015. “Hajj Crush: How Crowd Disasters Happen, and How They Can Be Avoided.”
   Google Scholar
• Bradley, G. E.. 1993. “A Proposed Mathematical Model for Computer Prediction of Crowd Movements and Their Associated Risks.” In Proceedings of the International Conference on Engineering for Crowd Safety, 303–311. Elsevier Publishing Company London.
   Google Scholar
• Dickie, J. F., and G. K. Wanless. 1993. “Spectator Terrace Barriers.” Structural Engineer 71:216–222.
   Google Scholar
• Fruin, J.. 1993. The Causes and Prevention of Crowd Disasters, 99–108. Amsterdam, Netherlands: Elsevier.
   Google Scholar
• Fulton., A. 2022. “Seoul Crowd Crush: What We Know So Far About Halloween Deaths in Itaewon.”
   Google Scholar
• Gustafsson, B., H. Kreiss, and J. Oliger. 2013. Time Dependent Problems and Difference Methods. Vol. 2. New York: Wiley Online Library.
   Google Scholar
• Haghani, M., E. Cristiani, N. Bode, M. Boltes, and A. Corbetta. 2019. “Panic, Irrationality, and Herding: Three Ambiguous Terms in Crowd Dynamics Research.” Journal of Advanced Transportation 2019: 9267643..
   Web of Science ®Google Scholar
• Helbing, D., L. Buzna, A. Johansson, and T. Werner. 2005. “Self-Organized Pedestrian Crowd Dynamics: Experiments, Simulations, and Design Solutions.” Transportation Science 39 (1): 1–24. https://doi.org/10.1287/trsc.1040.0108.
   Web of Science ®Google Scholar
• Helbing, D., I. J. Farkas, and T. Vicsek. 2000. “Simulating Dynamical Features of Escape Panic.” Nature 407 (6803): 487–490. https://doi.org/10.1038/35035023.
   PubMed Web of Science ®Google Scholar
• Helbing, D., A. Johansson, and H. Z. Al-Abideen. 2007. “Dynamics of Crowd Disasters: An Empirical Study.” Physical Review E 75 (4): 046109. https://doi.org/10.1103/PhysRevE.75.046109.
   Web of Science ®Google Scholar
• Helbing, D., and P. Mukerji. 2012. “Crowd Disasters As Systemic Failures: Analysis of the Love Parade Disaster.” EPJ Data Science 1 (1): 1–40. https://doi.org/10.1140/epjds7.
   Web of Science ®Google Scholar
• Huang, L., T. Chen, Y. Wang, and H. Yuan. 2015. “Congestion Detection of Pedestrians Using the Velocity Entropy: A Case Study of Love Parade 2010 Disaster.” Physica A: Statistical Mechanics and Its Applications 440: 200–209. https://doi.org/10.1016/j.physa.2015.08.013.
   Web of Science ®Google Scholar
• Huang, L., S. C. Wong, M. Zhang, C. Shu, and W. H. K. Lam. 2009. “Revisiting Hughes' Dynamic Continuum Model for Pedestrian Flow and the Development of An Efficient Solution Algorithm.” Transportation Research Part B: Methodological 43 (1): 127–141. https://doi.org/10.1016/j.trb.2008.06.003.
   Web of Science ®Google Scholar
• Hughes, R. L.. 2002. “A Continuum Theory for the Flow of Pedestrians.” Transportation Research Part B: Methodological 36 (6): 507–535. https://doi.org/10.1016/S0191-2615(01)00015-7.
   Web of Science ®Google Scholar
• Jiang, Y. Q., P. Zhang, S. C. Wong, and R. X. Liu. 2010. “A Higher-Order Macroscopic Model for Pedestrian Flows.” Physica A: Statistical Mechanics and Its Applications 389 (21): 4623–4635. https://doi.org/10.1016/j.physa.2010.05.003.
   Web of Science ®Google Scholar
• Johansson, A., D. Helbing, H. Z. Al-Abideen, and S. Al-Bosta. 2008. “From Crowd Dynamics to Crowd Safety: A Video-Based Analysis.” Advances in Complex Systems 11 (4): 497–527. https://doi.org/10.1142/S0219525908001854.
   Web of Science ®Google Scholar
• Khan, S. D.. 2019. “Congestion Detection in Pedestrian Crowds Using Oscillation in Motion Trajectories.” Engineering Applications of Artificial Intelligence 85: 429–443. https://doi.org/10.1016/j.engappai.2019.07.009.
   Web of Science ®Google Scholar
• Krausz, B., and C. Bauckhage. 2012. “Loveparade 2010: Automatic Video Analysis of a Crowd Disaster.” Computer Vision Image Understanding 116 (3): 307–319. https://doi.org/10.1016/j.cviu.2011.08.006.
   Web of Science ®Google Scholar
• Langston, P. A., R. Masling, and B. N. Asmar. 2006. “Crowd Dynamics Discrete Element Multi-circle Model.” Safety Science 44 (5): 395–417. https://doi.org/10.1016/j.ssci.2005.11.007.
   Web of Science ®Google Scholar
• Lee, J. Y. S., and W. H. K. Lam. 2006. “Variation of Walking Speeds on a Unidirectional Walkway and on a Bidirectional Stairway.” Transportation Research Record 1982 (1): 122–131. https://doi.org/10.1177/0361198106198200116.
   Google Scholar
• Liang, H., J. Du, and S. C. Wong. 2021. “A Continuum Model for Pedestrian Flow with Explicit Consideration of Crowd Force and Panic Effects.” Transportation Research Part B: Methodological 149:100–117. https://doi.org/10.1016/j.trb.2021.05.006.
   Web of Science ®Google Scholar
• Liu, C., W. Song, L. Fu, L. Lian, and S. Lo. 2017. “Experimental Study on Relaxation Time in Direction Changing Movement.” Physica A: Statistical Mechanics and Its Applications 468: 44–52. https://doi.org/10.1016/j.physa.2016.10.037.
   Web of Science ®Google Scholar
• Loveparade2010doc. 2010. “Dokumentation der ereignisse zur loveparade 2010 in duisburg.” Retrieved June 29, 2022, from https://loveparade2010doku.wordpress.com/.
   Google Scholar
• Loveparade. 2011. “Kamera13-1620-1640.mp4.” Retrieved June 29, 2022, from https://www.youtube.com/watch?v=QpzISdBE3dA.
   Google Scholar
• Shu, C.. 1992. “A Numerical Method for Systems of Conservation Laws of Mixed Type Admitting Hyperbolic Flux Splitting.” Journal of Computational Physics 100 (2): 424–429. https://doi.org/10.1016/0021-9991(92)90249-X.
   Web of Science ®Google Scholar
• Smith, R. A., and L. B. Lim. 1995. “Experiments to Investigate the Level of ‘comfortable’ Loads for People Against Crush Barriers.” Safety Science 18 (4): 329–335. https://doi.org/10.1016/0925-7535(94)00052-5.
   Web of Science ®Google Scholar
• Still, G. K. 2022. “Crowd Safety and Crowd Risk Analysis.” Retrieved June 29, 2022, from http://www.gkstill.com/ExpertWitness/CrowdDisasters.html.
   Google Scholar
• Thielicke, W., and R. Sonntag. 2021. “Particle Image Velocimetry for MATLAB: Accuracy and Enhanced Algorithms in PIVlab.” Journal of Open Research Software 9: 1–14. https://doi.org/10.5334/jors.334.
   Google Scholar
• Wang, J., S. Ni, S. Shen, and S. Li. 2019. “Empirical Study of Crowd Dynamic in Public Gathering Places During a Terrorist Attack Event.” Physica A: Statistical Mechanics and Its Applications 523: 1–9. https://doi.org/10.1016/j.physa.2019.01.120.
   Web of Science ®Google Scholar
• Wang, C., L. Shen, and W. Weng. 2023. “Modelling Physical Contacts to Evaluate the Individual Risk in a Dense Crowd.” Scientific Reports 13 (1): 3929. https://doi.org/10.1038/s41598-023-31148-z.
   PubMed Web of Science ®Google Scholar
• Wong, S. C., W. L. Leung, S. H. Chan, W. H. K. Lam, N. H. C. Yung, C. Y. Liu, and P. Zhang. 2010. “Bidirectional Pedestrian Stream Model with Oblique Intersecting Angle.” Journal of Transportation Engineering 136 (3): 234–242. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000086.
   Web of Science ®Google Scholar
• Yang, L., H. Liang, J. Du, and S. C. Wong. 2023. “Positivity-Preserving Discontinuous Galerkin Methods on Triangular Meshes for Macroscopic Pedestrian Flow Models.” Journal of Advanced Transportation 2023: 7245723. https://doi.org/10.1155/2023/7245723.
   Web of Science ®Google Scholar
• Zhao, R., Q. Hu, Q. Liu, C. Li, D. Dong, and Y. Ma. 2019. “Panic Propagation Dynamics of High-Density Crowd Based on Information Entropy and Aw–Rascle Model.” IEEE Transactions on Intelligent Transportation Systems 21: 4425–4434. https://doi.org/10.1109/TITS.6979.
   Web of Science ®Google Scholar