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Article: Positivity-Preserving Discontinuous Galerkin Methods on Triangular Meshes for Macroscopic Pedestrian Flow Models

TitlePositivity-Preserving Discontinuous Galerkin Methods on Triangular Meshes for Macroscopic Pedestrian Flow Models
Authors
Issue Date25-Oct-2023
PublisherHindawi
Citation
Journal of Advanced Transportation, 2023, v. 2023 How to Cite?
Abstract

The macroscopic models for solving the pedestrian flow problem can be generally classified into two categories as follows: first-order continuum models and high-order continuum models. In first-order continuum models, the density satisfies the mass conservation law, the speed is defined by a flow-density relationship, and the desired directional motion of pedestrians is determined by an Eikonal-type equation. In contrast, in high-order models, the velocity is governed by the momentum conservation law. In this study, we summarize existing first-order and high-order models and rewrite them in the form of unified scalar or system hyperbolic conservation laws. Next, we apply high-order discontinuous Galerkin methods with a positivity-preserving limiter on unstructured triangular meshes to solve the conservation law and a second-order fast-sweeping scheme to solve the Eikonal equations. Our method can efficiently model real-life complex computational regions and avoid nonphysical solutions and simulation blow-ups. Finally, numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed solution algorithm. The numerical results validate the reliability of the proposed numerical method and highlight the advantages of triangular meshes.


Persistent Identifierhttp://hdl.handle.net/10722/339003
ISSN
2023 Impact Factor: 2.0
2023 SCImago Journal Rankings: 0.582

 

DC FieldValueLanguage
dc.contributor.authorYang, L-
dc.contributor.authorLiang, H-
dc.contributor.authorDu, J-
dc.contributor.authorWong, SC-
dc.date.accessioned2024-03-11T10:33:07Z-
dc.date.available2024-03-11T10:33:07Z-
dc.date.issued2023-10-25-
dc.identifier.citationJournal of Advanced Transportation, 2023, v. 2023-
dc.identifier.issn0197-6729-
dc.identifier.urihttp://hdl.handle.net/10722/339003-
dc.description.abstract<p>The macroscopic models for solving the pedestrian flow problem can be generally classified into two categories as follows: first-order continuum models and high-order continuum models. In first-order continuum models, the density satisfies the mass conservation law, the speed is defined by a flow-density relationship, and the desired directional motion of pedestrians is determined by an Eikonal-type equation. In contrast, in high-order models, the velocity is governed by the momentum conservation law. In this study, we summarize existing first-order and high-order models and rewrite them in the form of unified scalar or system hyperbolic conservation laws. Next, we apply high-order discontinuous Galerkin methods with a positivity-preserving limiter on unstructured triangular meshes to solve the conservation law and a second-order fast-sweeping scheme to solve the Eikonal equations. Our method can efficiently model real-life complex computational regions and avoid nonphysical solutions and simulation blow-ups. Finally, numerical examples are presented to demonstrate the accuracy and effectiveness of the proposed solution algorithm. The numerical results validate the reliability of the proposed numerical method and highlight the advantages of triangular meshes.</p>-
dc.languageeng-
dc.publisherHindawi-
dc.relation.ispartofJournal of Advanced Transportation-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.titlePositivity-Preserving Discontinuous Galerkin Methods on Triangular Meshes for Macroscopic Pedestrian Flow Models-
dc.typeArticle-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1155/2023/7245723-
dc.identifier.volume2023-
dc.identifier.eissn2042-3195-
dc.identifier.issnl0197-6729-

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