Lattice hydrodynamic model for traffic flow on curved road with passing

In order to investigate the effect of passing upon traffic flow on curved road, in this paper, an extended one-dimensional lattice hydrodynamic model for traffic flow on curved road with passing is proposed. The stability condition is obtained by the use of linear stability analysis. The result of stability analysis shows that passing behavior plays an important role in influencing the stability of traffic flow as well as radian of curved road. The nonlinear wave equations including Burgers, Korteweg-de Vries and modified Korteweg-de Vries equations are derived to describe the nonlinear traffic behavior in different regions, respectively. The analytical results show that reducing the coefficient of passing may enhance the stability of traffic flow. Jamming transition occurs between uniform flow and kink jam when the coefficient of passing is less than the critical value. When the coefficient of passing is larger than the critical value, jamming transition occurs from uniform flow to irregular wave through chaotic phase with decreasing sensitivity parameter. In addition, compared with other segments of curved road, traffic flow with passing easily becomes unstable and complicated at the entrance and exit of curved road, especially at the entrance of curved road. The numerical simulations are given to illustrate and clarify the analytical results.     

An extended macroscopic model for traffic flow on curved road and its numerical simulation

Nonlinear Dynamics - In this paper, we propose a full angular velocity difference model by introducing the angular velocity and displacement on curved road. The relation of transformation of...     

Tunnel effects on ring road traffic flow based on an urgent-gentle class traffic model

To explore tunnel effects on ring road traffic flow, a macroscopic urgent-gentle class traffic model is put forward. The model identifies vehicles with urgent and gentle classes, chooses the tunnel speed limit as free flow speed to express the fundamental diagram in the tunnel, and adopts algebraic expressions to describe traffic pressure and sound speed. With two speed trajectories at the Kobotoke tunnel in Japan,the model is validated, with good agreement with observed data. Numerical results indicate that in the case of having no ramp effects, tunnel mean travel time is almost constant dependent on tunnel length.When initial density normalized by jam density is above a threshold of about 0.21, a traffic shock wave originates at the tunnel entrance and propagates backward. Such a threshold drops slightly as a result of on-ramp merging effect, the mean travel time drops as off-ramp diversion effect intensifies gradually.These findings deepen the understanding of tunnel effects on traffic flow in reality.     

Phase transitions in the two-lane density difference lattice hydrodynamic model of traffic flow

In this paper, we derive the KdV equation from the two-lane lattice hydrodynamic traffic model considering density difference effect. The soliton solution is obtained from the KdV equation. Under periodical boundary, the KdV soliton of traffic flow is demonstrated by numerical simulation. The numerical simulation result is consistent with the nonlinear analytical result. Under open system, the density fluctuation of the downstream last one lattice is designed to explore the empirical congested traffic states. A phase diagram is presented which includes free traffic, moving localized cluster, triggered stop-and-go traffic, oscillating congested traffic, and homogeneous congested traffic. Finally, the spatiotemporal evolution of all the traffic states described in phase diagram are reproduced. Results suggest that the two-lane density difference hydrodynamic traffic model is suitable to describe the actual traffic.     

Coevolution dynamics model of road surface and urban traffic structure

In this paper, a new dynamics model based on the logistic equation is proposed to capture the dynamic characteristics in the coevolution process between road surface and urban traffic structure. The stability analysis shows that ignoring the coevolution relation will lead to the disequilibrium development and cause the chaotic state of the urban transportation system eventually. To avoid the unsteadily development, a chaos control method is established. Results indicate that the suggested control model is effective in the coevolution management and control.     

KINEMATIC WAVE PROPERTIES OF ANISOTROPIC DYNAMICS MODEL FOR TRAFFIC FLOW

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A new lattice hydrodynamic model for two-lane traffic with the consideration of density difference effect

A new lattice hydrodynamic model for two-lane traffic flow is proposed by introducing the density difference effect (DDE). Using linear stability theory, stability condition of the presented model is obtained. Jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are investigated by employing nonlinear analysis. The modified KdV (mKdV) equation near the critical point is derived and the kink-antikink soliton solutions are obtained. Numerical simulations are presented to verify analytical results, showing that DDE can improve the stability of traffic flow effectively.     

Phase-plane analysis of conserved higher-order traffic flow model

The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.     

An extended continuum model incorporating the electronic throttle dynamics for traffic flow

This study develops a novel continuum model with consideration of the effect of electronic throttle (ET) dynamics to capture the behaviour of vehicles in traffic flow. In particular, the continuum model is proposed by incorporating the opening angle of ET based on the throttle-based full velocity difference model. Theoretical analyses including stability, negative velocity and shock wave are performed systematically. Numerical experiments and comparisons are conducted to verify the performance of the proposed continuum model. Results show that the steady-state performance of the proposed model is improved with respect to the stability. In addition, the proposed model is effective to rapidly dissipate the effect of external perturbation. Also, the phenomenon of negative velocity can be avoided by the proposed model.     

格子Boltzmann方法中基于内插值的曲线边界处理新方法

对格子Boltzmann方法提出了一种新的曲面边界条件处理方法。在笛卡尔坐标系中,这种处理方法是现有的格子Boltzmann方法有关边界条件处理与浸入式边界条件的混合,它采用内插值方法计算靠近物理边界的网格点速度,使其保证最低精度为二阶,然后利用格子Boltzmann方法中的边界条件技术得到相应的分布函数。由理论推导和数值计算表明,本文提出的方法比其他方法更稳定且具有二阶精度。     

Lattice Boltzmann model for nanofluids

A nanofluid is a particle suspension that consists of base liquids and nanoparticles and has great potential for heat transfer enhancement. By accounting for the external and internal forces acting on the suspended nanoparticles and interactions among the nanoparticles and fluid particles, a lattice Boltzmann model is proposed for simulating flow and energy transport processes inside the nanofluids. First, we briefly introduce the conventional lattice Boltzmann model for multicomponent systems. Then, we discuss the irregular motion of the nanoparticles and inherent dynamic behavior of nanofluids and describe a lattice Boltzmann model for simulating nanofluids. Finally, we conduct some calculations for the distribution of the suspended nanoparticles.     

A new lattice hydrodynamic model for bidirectional pedestrian flow considering the visual field effect

In this paper, a new lattice hydrodynamic model for bidirectional pedestrian flow is proposed by considering the pedestrian’s visual field effect. The stability condition of this model is obtained by the linear stability analysis. The mKdV equation near the critical point is derived to describe the density wave of pedestrian jam by applying the reductive perturbation method. The phase diagram indicates that the phase transition occurs among the freely moving phase, the coexisting phase, and the uniformly congested phase below the critical point \(a_c\) . Furthermore, the analytical results show that the visual field effect plays an important role in jamming transition. To take into account the visual information about the motion of more pedestrian in front can improve efficiently the stability of pedestrian system. In addition, the numerical simulations are in accordance with the theoretical analysis.     

Continuum modeling for two-lane traffic flow

In this paper, we study the continuum modeling of traffic dynamics for two-lane freeways. A new dynamics model is proposed, which contains the speed gradient-based momentum equations derived from a car-following theory suited to two-lane traffic flow. The conditions for securing the linear stability of the new model are presented. Numerical tests are carried out and some nonequilibrium phenomena are observed, such as small disturbance instability, stop-and-go waves, local clusters and phase transition. The project supported by the National Natural Science Foundation of China (70521001) The English text was polished by Yunming Chen.     

Solitary wave solution to Aw-Rascle viscous model of traffic flow

A traveling wave solution to the Aw-Rascle traffic flow model that includes the relaxation and diffusion terms is investigated. The model can be approximated by the well-known Kortweg-de Vries (KdV) equation. A numerical simulation is conducted by the first-order accurate Lax-Friedrichs scheme, which is known for its ability to capture the entropy solution to hyperbolic conservation laws. Periodic boundary conditions are applied to simulate a lengthy propagation, where the profile of the derived KdV solution is taken as the initial condition to observe the change of the profile. The simulation shows good agreement between the approximated KdV solution and the numerical solution.