FV–DG method for the pedestrian flow problem

Dolejší, Vít; Felcman, J.; Kubera, Petr

doi:10.1016/j.compfluid.2019.03.006

Cited by 6 publications

(12 citation statements)

References 10 publications

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“…The use of the Eikonal equation in the CA approach and the motivation will then be more clear. The details can be found in [9].…”

Section: Eikonal Equation Of Pedestrian Flowmentioning

confidence: 99%

“…(ϕ means the derivative with respect to the parameter σ.) It was proved in [9] that µ can be equivalently expressed as…”

Section: Eikonal Equation Of Pedestrian Flowmentioning

confidence: 99%

“…It was proved in [9], that the solution φ of the Eikonal equation (212) represents the time it takes for a pedestrian to reach an exit point in Γ o if the pedestrian follows the curve ϕ satisfying relation (2.9), i.e. φ(x)…”

Section: Eikonal Equation Of Pedestrian Flowmentioning

confidence: 99%

“…We have been interested in the solution of the pedestrian flow equations from the macroscopic point of view in several papers, namely in [9,19]. We have presented an efficient and robust algorithm for the numerical solution of the room evacuation problem.…”

Section: Introductionmentioning

confidence: 99%

“…The macroscopic model we shall use for the comparison is the two-dimensional model derived in detail in [9]. For comparison purposes, we briefly remember its construction.…”

Section: Introductionmentioning

confidence: 99%

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A cellular automaton model for a pedestrian flow problem

Felcman

Kubera

2021

Math. Model. Nat. Phenom.

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The evacuation phenomena in the two dimensional pedestrian flow model are simulated. The intended direction of the escape of pedestrians in panic situations is governed by the Eikonal equation of the pedestrian flow model. A new two-dimensional Cellular Automaton (CA) model is proposed for the simulation of the pedestrian flow. The solution of the Eikonal equation is used to define the probability matrix whose elements express the probability of a pedestrian moving in finite set of directions. The novelty of this paper lies in the construction of the density dependent probability matrix. The relevant evacuation scenarios are numerically solved. Predictions of the evacuation behavior of pedestrians, for various room geometries with multiple exists, are demonstrated. The mathematical model is numerically justified by comparison of CA approach with the Finite Volume Method for the space discretization and Discontinuous Galerkin Method for the implicit time discretization of pedestrian flow model.

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“…The use of the Eikonal equation in the CA approach and the motivation will then be more clear. The details can be found in [9].…”

Section: Eikonal Equation Of Pedestrian Flowmentioning

confidence: 99%

“…(ϕ means the derivative with respect to the parameter σ.) It was proved in [9] that µ can be equivalently expressed as…”

Section: Eikonal Equation Of Pedestrian Flowmentioning

confidence: 99%

Section: Eikonal Equation Of Pedestrian Flowmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The macroscopic model we shall use for the comparison is the two-dimensional model derived in detail in [9]. For comparison purposes, we briefly remember its construction.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations