scholarly journals Pedestrian Walking Behavior Revealed through a Random Walk Model

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Hui Xiong ◽  
Liya Yao ◽  
Huachun Tan ◽  
Wuhong Wang
Keyword(s):  
Numerical Experiments ◽  
Flow Simulation ◽  
Two Dimensional ◽  
Pedestrian Flow ◽  
Alternating Direction Implicit Method ◽  
Walking Behavior ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Continuous Time Random Walks ◽  
High Order Compact Scheme

This paper applies method of continuous-time random walks for pedestrian flow simulation. In the model, pedestrians can walk forward or backward and turn left or right if there is no block. Velocities of pedestrian flow moving forward or diffusing are dominated by coefficients. The waiting time preceding each jump is assumed to follow an exponential distribution. To solve the model, a second-order two-dimensional partial differential equation, a high-order compact scheme with the alternating direction implicit method, is employed. In the numerical experiments, the walking domain of the first one is two-dimensional with two entrances and one exit, and that of the second one is two-dimensional with one entrance and one exit. The flows in both scenarios are one way. Numerical results show that the model can be used for pedestrian flow simulation.

scholarly journals Numerical simulation for two-dimensional Riesz space fractional diffusion equations with a nonlinear reaction term

Open Physics ◽  
2013 ◽  
Vol 11 (10) ◽  
Author(s):  
Fawang Liu ◽  
Shiping Chen ◽  
Ian Turner ◽  
Kevin Burrage ◽  
Vo Anh
Keyword(s):  
Fractional Diffusion ◽  
Riesz Space ◽  
Two Dimensional ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Fractional Diffusion Equations ◽  
Reaction Term ◽  
Nonlinear Reaction ◽  
Alternating Direction ◽  
Space Fractional Diffusion Equation

AbstractFractional differential equations have attracted considerable interest because of their ability to model anomalous transport phenomena. Space fractional diffusion equations with a nonlinear reaction term have been presented and used to model many problems of practical interest. In this paper, a two-dimensional Riesz space fractional diffusion equation with a nonlinear reaction term (2D-RSFDE-NRT) is considered. A novel alternating direction implicit method for the 2D-RSFDE-NRT with homogeneous Dirichlet boundary conditions is proposed. The stability and convergence of the alternating direction implicit method are discussed. These numerical techniques are used for simulating a two-dimensional Riesz space fractional Fitzhugh-Nagumo model. Finally, a numerical example of a two-dimensional Riesz space fractional diffusion equation with an exact solution is given. The numerical results demonstrate the effectiveness of the methods. These methods and techniques can be extended in a straightforward method to three spatial dimensions, which will be the topic of our future research.

scholarly journals ALTERNATING DIRECTION METHOD FOR A TWO-DIMENSIONAL PARABOLIC EQUATION WITH A NONLOCAL BOUNDARY CONDITION

2007 ◽  
Vol 12 (1) ◽  
pp. 131-142 ◽  
Author(s):  
Mifodijus Sapagovas ◽  
Gene Kairytė ◽  
Olegas Štikonienė ◽  
Artūras Štikonas
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Sufficient Conditions ◽  
Two Dimensional ◽  
Alternating Direction Implicit Method ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Conditions Of Stability

The present paper deals with an alternating direction implicit method for a two dimensional parabolic equation in a rectangle domain with a nonlocal boundary condition in one direction. Sufficient conditions of stability for Peaceman‐Rachford method are established. Results of some numerical experiments are presented.

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