Rongjun Cheng

Nonlinear density wave investigation for an extended car-following model considering driver’s memory and jerk

Based on the two velocity difference model (TVDM), an extended car-following model is developed to investigate the effect of driver’s memory and jerk on traffic flow in this paper. By using linear stability analysis, the stability conditions are derived. And through nonlinear analysis, the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are obtained, respectively. The mKdV equation is constructed to describe the traffic behavior near the critical point. The evolution of traffic congestion and the corresponding energy consumption are discussed. Numerical simulations show that the improved model is found not only to enhance the stability of traffic flow, but also to depress the energy consumption, which are consistent with the theoretical analysis.

An extended car-following model considering random safety distance with different probabilities

Because of the difference in vehicle type or driving skill, the driving strategy is not exactly the same. The driving speeds of the different vehicles may be different for the same headway. Since the optimal velocity function is just determined by the safety distance besides the maximum velocity and headway, an extended car-following model accounting for random safety distance with different probabilities is proposed in this paper. The linear stable condition for this extended traffic model is obtained by using linear stability theory. Numerical simulations are carried out to explore the complex phenomenon resulting from multiple safety distance in the optimal velocity function. The cases of multiple types of safety distances selected with different probabilities are presented. Numerical results show that the traffic flow with multiple safety distances with different probabilities will be more unstable than that with single type of safety distance, and will result in more stop-and-go phenomena.

Nonlinear analysis of an improved continuum model considering headway change with memory

Considering the effect of headway changes with memory, an improved continuum model of traffic flow is proposed in this paper. By means of linear stability theory, the new model’s linear stability w...

Meshless analysis of two-dimensional two-sided space-fractional wave equation based on improved moving least-squares approximation

ABSTRACT The Space-fractional wave equations (SFWE) have been found to be very adequate in describing anomalous transport and dispersion phenomena. Due to the non-local property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model. In this paper, a meshless analysis of two-dimensional two-sided SFWE is proposed based on the improved moving least-squares (IMLS) approximation. The trial function for the SFWE is constructed by the IMLS approximation, where the resulting algebraic equation system to obtain the shape functions is no more ill conditioned and has high computational efficiency. The Riemann–Liouville operator is discretized by the Grünwald formula. The centre difference method and the strong-forms of the SFWE are used to obtain the final fully discrete algebraic equation. And the essential boundary conditions can be directly and easily imposed on as a finite element method. Due to the adoption of IMLS approximation and strong-forms, this method will be highly accurate and efficient. Numerical results demonstrate that this method is highly accurate and computationally efficient for SFWE. Moreover, the convergence and error estimate have been analysed in our study.

Numerical treatment for solving two-dimensional space-fractional advection–dispersion equation using meshless method

Space-fractional advection–dispersion equation (SFADE) can describe particle transport in a variety of fields more accurately than the classical models of integer-order derivative. Because of nonlocal property of integro-differential operator of space-fractional derivative, it is very challenging to deal with fractional model, and few have been reported in the literature. In this paper, a numerical analysis of the two-dimensional SFADE is carried out by the element-free Galerkin (EFG) method. The trial functions for the SFADE are constructed by the moving least-square (MLS) approximation. By the Galerkin weak form, the energy functional is formulated. Employing the energy functional minimization procedure, the final algebraic equations system is obtained. The Riemann–Liouville operator is discretized by the Grunwald formula. With center difference method, EFG method and Grunwald formula, the fully discrete approximation schemes for SFADE are established. Comparing with exact results and available results ...

High-order numerical modeling for two-dimensional two-sided space-fractional wave equation based on meshless method

The Grunwald formula is the traditional method to deal with Riemann–Liouville fractional derivative, while its convergence is only O(h). In this paper, a high-order polynomial approximation is presented for the Riemann–Liouville fractional derivative. The quadratic polynomial functions and their fractional derivatives with explicit expressions are constructed to approximate the fractional derivative instead of Grunwald formula or shifted Grunwald formula. We proved that this technique has convergence of O(h3−α). Based on the MLS approximation and the high-order polynomial approximation and center difference method, a meshless analysis is proposed for the two-dimensional two-sided space-fractional wave equations (SFWE). The SFWE is found to be very adequate in describing anomalous transport and dispersion phenomena. In the meshless method, the trial function for the SFWE is constructed by the MLS approximation and the Riemann–Liouville fractional derivative is approximated by the high-order polynomial approximation, and the essential boundary conditions can be directly and easily imposed on as finite element method. This technique avoids singular integral, and has high accuracy and efficiency. Numerical results demonstrate that this method is highly accurate and computationally efficient for space-fractional wave equations.