Inflow Outflow Effect and Shock Wave Analysis in a Traffic Flow Simulation

Ali, Ahsan; Andallah, Laek Sazzad

doi:10.4236/ajcm.2016.62007

Cited by 5 publications

(4 citation statements)

References 10 publications

(10 reference statements)

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“…The numerical schemes given in Table 1 are implemented using the following Table 1. 2) The initial density of vehicles in this study is taken as in [18], 3) The boundary condition is considered as constants:…”

Section: Traffic Flow With Constant Speedmentioning

confidence: 99%

One-Dimensional Explicit Tolesa Numerical Scheme for Solving First Order Hyperbolic Equations and Its Application to Macroscopic Traffic Flow Model

Hundesa¹,

Lemecha²,

Koya³

2019

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In this paper, a new numerical scheme for solving first-order hyperbolic partial differential equations is proposed and is implemented in the simulation study of macroscopic traffic flow model with constant velocity and linear velocity-density relationship. Macroscopic traffic flow model is first developed by Lighthill Whitham and Richards (LWR) and used to study traffic flow by collective variables such as flow rate, velocity and density. The LWR model is treated as an initial value problem and its numerical simulations are presented using numerical schemes. A variety of numerical schemes are available in literature to solve first order hyperbolic equations. Of these the well-known ones include one-dimensional explicit: Upwind, Downwind, FTCS, and Lax-Friedrichs schemes. Having been studied carefully the space and time mesh sizes, and the patterns of all these schemes, a new scheme has been developed and named as one-dimensional explicit Tolesa numerical scheme. Tolesa numerical scheme is one of the conditionally stable and highest rates of convergence schemes. All the said numerical schemes are applied to solve advection equation pertaining traffic flows. Also the one-dimensional explicit Tolesa numerical scheme is another alternative numerical scheme to solve advection equation and apply to traffic flows model like other well-known one-dimensional explicit schemes. The effect of density of cars on the overall interactions of the vehicles along a given length of the highway and time are investigated. Graphical representations of density profile, velocity profile, flux profile, and in general the fundamental diagrams of vehicles on the highway with different time levels are illustrated. These concepts and results have been arranged systematically in this paper.

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Section: Traffic Flow With Constant Speedmentioning

confidence: 99%

One-Dimensional Explicit Tolesa Numerical Scheme for Solving First Order Hyperbolic Equations and Its Application to Macroscopic Traffic Flow Model

Hundesa¹,

Lemecha²,

Koya³

2019

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“…It is used as a model to test several numerical methods since it includes a convection term and a viscosity term . In fact, Burgers' equation represents one dimensional Navier-Stokes equation when pressure and force terms are dropped from Navier-Stokes equation [6,9]. Another importance of this equation is that it allows us to compare the quality of numerical method applied to a nonlinear equation.…”

Section: Introductionmentioning

confidence: 99%

Numerical Study of the Characteristics of Shock and Rarefaction Waves for Nonlinear Wave Equation

Hasan¹,

Takia²,

Rahaman³

et al. 2022

AJASR

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In everyday life human faces shock waves and rarefaction largely in their surroundings. Hence it's necessary to know the behavior of these waves to protect destructive effects. The aim of this work to observe the propagation of shock and rarefaction waves in various dynamics due to solve non-linear hyperbolic inviscid Burgers' equation numerically. The models adopted here two numerical schemes which enable us to solve non-linear hyperbolic Burgers' equation numerically. The first order explicit upwind scheme (EUDS) and second order Lax-Wendroff schemes are used to solve this equation to improve our understanding of the numerical diffusion (smearing) and oscillations that can be present when using such schemes. In order to understand the behavior of the solution we use method of characteristics to find the exact solution of inviscid Burgers' equation. Numerical solutions are studied for different initial conditions and the shock and rarefaction waves are investigated for Riemann problem. We present stability analysis of the schemes and establish stability condition which leads to determine time step selection in terms of spatial step size with maximum initial value. Numerical result for these schemes are compared with an exact solution of inviscid Burgers' equation in terms of accuracy by error estimation. The numerical features of the rate of convergence are presented graphically. This analysis helps us to understand a wide range of physical phenomenon of the properties of wave as well as saves in several aspects in real life.

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“…The third is the use of Greenshields model in macrotransportation planning. Since the Greenshields model is simple in form and convenient for the derivation and analysis of theoretical formulas, although it has some shortcomings in its application, it is still widely used in the study of road traffic flow and is a very important model [15][16][17][18][19]. The relationship of velocity-density in ship traffic flow is similar to that in road traffic flow, but the influence factors of the former has some difference from the latter.…”

Section: Introductionmentioning

confidence: 99%

Research on the impact of ship traffic flow on the restricted channel segment of the middle Yangtze River based on traffic wave theory

Liu

Lodewijks

2021

SN Appl. Sci.

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On the basis of the influence of dry season on ship traffic flow, the gathering and dissipating process of ship traffic flow was researched with Greenshields linear flow—density relationship model, the intrinsic relationship between the ship traffic congestion state and traffic wave in the unclosed restricted channel segment was emphatically explored when the ship traffic flow in a tributary channel inflows, and the influence law of multiple traffic waves on the ship traffic flow characteristics in unclosed restricted segment is revealed. On this basis, the expressions of traffic wave speed and direction, dissipation time of queued ships and the number of ships affected were provided, and combined with Monte Carlo method, the ship traffic flow simulation model in the restricted channel segment was built. The simulation results show that in closed restricted channel segment the dissipation time of ships queued is mainly related to the ship traffic flow rate of segments A and C, and the total number of ships affected to the ship traffic flow rate of segment A. And in unclosed restricted channel segment, the dissipation time and the total number of ships affected are also determined by the meeting time of the traffic waves in addition to the ship traffic flow rate of segments. The research results can provide the theoretical support for further studying the ship traffic flow in unclosed restricted channel segment with multiple tributaries Article Highlights The inflow of tributaries' ship traffic flows has an obvious impact on the traffic conditions in the unenclosed restricted channel segment. The interaction and influence between multiple ship traffic waves and the mechanism of generating new traffic waves are explained. The expression of both dissipation time of queued ships and the total number of ships affected in the closed and unclosed restricted channel segment are given.

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Inflow Outflow Effect and Shock Wave Analysis in a Traffic Flow Simulation

Cited by 5 publications

References 10 publications

One-Dimensional Explicit Tolesa Numerical Scheme for Solving First Order Hyperbolic Equations and Its Application to Macroscopic Traffic Flow Model

One-Dimensional Explicit Tolesa Numerical Scheme for Solving First Order Hyperbolic Equations and Its Application to Macroscopic Traffic Flow Model

Numerical Study of the Characteristics of Shock and Rarefaction Waves for Nonlinear Wave Equation

Research on the impact of ship traffic flow on the restricted channel segment of the middle Yangtze River based on traffic wave theory

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