scholarly journals On a numerical flux for the pedestrian flow equations

2015 ◽  
Vol 11 (2) ◽  
pp. 79-96 ◽  
Author(s):  
P. Kubera ◽  
J. Felcman
Keyword(s):  
Eikonal Equation ◽  
Source Term ◽  
Operator Splitting ◽  
Pedestrian Flow ◽  
Hyperbolic Problems ◽  
Hyperbolic Problem ◽  
Flow Equations ◽  
Numerical Flux ◽  
Homogeneity Property ◽  
The Right

Abstract The pedestrian flow equations are formulated as the hyperbolic problem with a source term, completed by the eikonal equation yielding the desired direction of the pedestrian velocity. The operator splitting consisting of successive discretization of the eikonal equation, ordinary differential equation with the right hand side being the source term and the homogeneous hyperbolic system is proposed. The numerical flux of the Vijayasundaram type is proposed for the finite volume solution of the hyperbolic problem. The Vijayasundaram numerical flux, originally proposed for the hyperbolic problems possessing the homogeneity property is extended for pedestrian flow, where the homogeneity property is lost. The application of the proposed numerical flux is demonstrated on the physically relevant problem.

INTERACTIONS OF PEDESTRIANS INTERLACED IN T-SHAPED STRUCTURE USING A MODIFIED MULTI-FIELD CELLULAR AUTOMATON

2013 ◽  
Vol 24 (04) ◽  
pp. 1350024 ◽  
Author(s):  
ZHIJIAN FU ◽  
LIZHONG YANG ◽  
PING RAO ◽  
TAOLIN ZHANG
Keyword(s):  
Phase Transition ◽  
Cellular Automaton ◽  
Free Flow ◽  
Dominant Factor ◽  
Pedestrian Flow ◽  
Transition Diagram ◽  
Open Boundaries ◽  
The Right

Little work has been done before in the study of separating pedestrian flow interlaced. Under open boundaries, the interaction of separating pedestrian flow interlaced in a T-shaped structure was simulated, using a modified multi-field cellular automaton updating synchronously. The free-jammed phase transition diagram of pedestrian flow and principles of the pedestrian interference were obtained. The movement of pedestrians is free flow in the low entrance density. While it is a complete jammed flow with the entrance density increasing to a certain level and little difference existing between the left moving probability and the right moving probability. Thus, the dominant factor influencing pedestrian flow is the interference of opposite pedestrian flows due to changing movement directions. And it is changing to an incomplete jammed flow with this difference increasing. Thus, the dominant factor is changing to the interference of the coincident pedestrian flow and the limitation of the bottleneck.

scholarly journals Impact of Wind Veer and the Coriolis Force for an Idealized Farm to Farm Interaction Case

2019 ◽  
Vol 9 (5) ◽  
pp. 922 ◽  
Author(s):  
Ola Eriksson ◽  
Simon-Philippe Breton ◽  
Karl Nilsson ◽  
Stefan Ivanell
Keyword(s):  
Coriolis Force ◽  
Wind Shear ◽  
Source Term ◽  
Wind Farms ◽  
Long Distance ◽  
Large Eddy ◽  
Relative Production ◽  
The Mean ◽  
The Right ◽  
The Impact

The impact of the Coriolis force on the long distance wake behind wind farms is investigated using Large Eddy Simulations (LES) combined with a Forced Boundary Layer (FBL) technique. When using the FBL technique any mean wind shear and turbulent fluctuations can be added with body forces. The wind shear can also include the mean wind veer due to the Coriolis force. The variation of the Coriolis force due to local deviations from the mean profile, e.g., from wakes, is not taken into account in the FBL. This can be corrected for with an extra source term in the equations, hereon defined as the Coriolis correction. For a row of 4 turbines it is shown that the inclusion of the wind veer turns the wake to the right, while including the Coriolis correction turns it to the left. When including both wind veer and Coriolis correction the impact of wind veer dominates. For an idealized farm to farm interaction case, two farms of 4 ∗ 4 turbines with 6 km in between, it can be seen that when including wind veer and the Coriolis correction a approximately 3% increase in the relative production for a full wake direction can be seen and only a slightly smaller increase can be seen when including only wind veer. The results indicate that FBL can be used for studies of long distance wakes without including a Coriolis correction but efforts need to be taken to use a wind shear with a correct mean wind veer.

An approach for emotions and behavior modeling in a crowd in the presence of rare events

2016 ◽  
Vol 24 (6) ◽  
pp. 428-445 ◽  
Author(s):  
Lynda Saifi ◽  
Abdelhak Boubetra ◽  
Farid Nouioua
Keyword(s):  
Probability Theory ◽  
Walking Speed ◽  
Behavior Modeling ◽  
Personality Factors ◽  
Common Phenomenon ◽  
Pedestrian Flow ◽  
Behavioral Rules ◽  
Emotional Model ◽  
The Right ◽  
And Behavior

A common phenomenon in everyday life is that, when a strange event occurs or is announced, a regular crowd can completely change, showing different intense emotions and sometimes uncontrollable and violent emerging behavior. These emotions and behaviors that disturb the organization of a crowd are of concern in our study, and we attempt to predict these suspicious circumstances and provide help in making the right decisions at the right time. Furthermore, most of the models that address crowd disasters belong to the physical or the cognitive approaches. They study pedestrian flow and collision avoidance, etc., and they use walking speed and angle of vision. However, in this work, based on a behavioral rules approach, we aim to model emergent emotion, behavior and influence in a crowd, taking into account particularly the personality of members of the crowd. For this purpose, we have combined the OCEAN (Openness, Consciousness, Extraversion, Agreeableness, and Neuroticism) personality model with the OCC (Ortony, Clore, and Collins) emotional model to indicate the susceptibility of each of the five personality factors to feeling every emotion. Then we proposed an approach that uses first fuzzy logic for the emotional modeling of critical emotions of members of the crowd at the announcement or the presence of unusual events, in order to quantify emotions. Then, we model the behavior and the tendency towards actions using probability theory. Finally, the influence among the members of the crowd is modeled using the neighborhood principle and cellular automata.

scholarly journals A Cellular Automaton Model for Pedestrians’ Movements Influenced by Gaseous Hazardous Material Spreading

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
J. Makmul
Keyword(s):  
Cellular Automaton ◽  
Numerical Experiments ◽  
Eikonal Equation ◽  
Arrival Time ◽  
Source Term ◽  
State Transition ◽  
Hazardous Material ◽  
Advection Diffusion ◽  
Moore Neighborhood ◽  
Ca Model

A cellular automaton (CA) model is proposed to simulate the egress of pedestrians while gaseous hazardous material is spreading. The advection-diffusion with source term is used to describe the propagation of gaseous hazardous material. It is incorporated into the CA model. The navigation field in our model is determined by the solution of the Eikonal equation. The state transition of a pedestrian relies on the arrival time of cells in the Moore neighborhood. Numerical experiments are investigated in a room with multiple exits, and their results are shown.

scholarly journals A fast sweeping algorithm for accurate solution of the tilted transversely isotropic eikonal equation using factorization

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. WB1-WB8 ◽  
Author(s):  
Umair bin Waheed ◽  
Tariq Alkhalifah
Keyword(s):  
Finite Difference ◽  
Eikonal Equation ◽  
Transversely Isotropic ◽  
Accurate Solution ◽  
Computational Domain ◽  
Wave Kinematics ◽  
Source Point ◽  
Fast Sweeping ◽  
Two Factors ◽  
The Right

Traveltime computation is essential for many seismic data processing applications and velocity analysis tools. High-resolution seismic imaging requires eikonal solvers to account for anisotropy whenever it significantly affects the seismic wave kinematics. Moreover, computation of auxiliary quantities, such as amplitude and take-off angle, relies on highly accurate traveltime solutions. However, the finite-difference-based eikonal solution for a point-source initial condition has upwind source singularity at the source position because the wavefront curvature is large near the source point. Therefore, all finite-difference solvers, even the high-order ones, show inaccuracies because the errors due to source-singularity spread from the source point to the whole computational domain. We address the source-singularity problem for tilted transversely isotropic (TTI) eikonal solvers using factorization. We solve a sequence of factored tilted elliptically anisotropic (TEA) eikonal equations iteratively, each time by updating the right-hand-side function. At each iteration, we factor the unknown TEA traveltime into two factors. One of the factors is specified analytically, such that the other factor is smooth in the source neighborhood. Through this iterative procedure, we obtain an accurate solution to the TTI eikonal equation. Numerical tests show significant improvement in accuracy due to factorization. The idea can be easily extended to compute accurate traveltimes for models with lower anisotropic symmetries, such as orthorhombic, monoclinic, or even triclinic media.

A numerical investigation of flux-limited approximations for pedestrian dynamics

2017 ◽  
Vol 27 (06) ◽  
pp. 1177-1197 ◽  
Author(s):  
L. Müller ◽  
A. Meurer ◽  
F. Schneider ◽  
A. Klar
Keyword(s):  
Eikonal Equation ◽  
Particle System ◽  
Mean Field ◽  
Test Cases ◽  
Pedestrian Flow ◽  
Mean Velocity ◽  
Pedestrian Dynamics ◽  
Interacting Particle ◽  
Starting Point ◽  
Scalar Equations

A hierarchy of models for pedestrian flow with fixed speed is numerically investigated. The starting point is a microscopic model based on a stochastic interacting particle system coupled to an eikonal equation. Starting from this model a nonlocal and nonlinear flux-limited maximum-entropy equation for density and mean velocity is derived via a mean field kinetic equation. Finally, associated classical scalar equations for the density are considered for comparison. These models are compared to each other for different test cases showing the superiority of the flux-limited approach, in particular for situations with smaller values of the stochastic noise.

scholarly journals Effective Source Term Discretizations for Higher Accuracy Finite Volume Discretization of Parabolic Equations

2021 ◽  
Vol 9 (8) ◽  
pp. 366-392
Author(s):  
Yaw Kyei
Keyword(s):  
Finite Volume ◽  
Parabolic Equations ◽  
Source Term ◽  
Space Time ◽  
Local Source ◽  
Source Terms ◽  
Equation Error ◽  
Diffusive Fluxes ◽  
The Right ◽  
Volume Method

A finite volume method is applied to develop space-time discretizations for parabolic equations based on an equation error method.A space-time expansion of the local equation error based on flux integral formulation of the equation is first designed using a desiredframework of neighboring quadrature points for the solution and local source terms. The quadrature weights are then determined through aminimization process for the error which constitutes all local compact fluxes about each centroid within the computational domain.In utilizing a local source term distribution to account for diffusive fluxes, the right minimizing quadrature weights and collocationpoints including subgrid points for the source terms may be determined and optimized for higher accuracies as well as robust higher-ordercomputational convergence. The resulting local residuals form a more complete description of the truncation errors which are then utilizedto assess the computational performances of the resulting schemes. The effectiveness of the discretization method is demonstrated by theresults and analysis of the schemes.

scholarly journals Riemann Solvers for some Hyperbolic Problems with a Source Term

1999 ◽  
Vol 6 ◽  
pp. 75-90 ◽  
Author(s):  
Alain Yves Leroux
Keyword(s):  
Source Term ◽  
Hyperbolic Problems ◽  
Riemann Solvers
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