A.I. Delis

TVD SCHEMES FOR OPEN CHANNEL FLOW

SUMMARY The Saint Venant equations for modelling flow in open channels are solved in this paper, using a variety of total variation diminishing (TVD) schemes. The performance of second- and third-order-accurate TVD schemes is investigated for the computation of free-surface flows, in predicting dam-breaks and extreme flow conditions created by the river bed topography. Convergence of the schemes is quantified by comparing error norms between subsequent iterations. Automatically calculated time steps and entropy corrections allow high CFL numbers and smooth transition between different conditions. In order to compare different approaches with TVD schemes, the most accurate of each type was chosen. All four schemes chosen proved acceptably accurate. However, there are important differences between the schemes in the occurrence of clipping, overshooting and oscillating behaviour and in the highest CFL numbers allowed by a scheme. These variations in behaviour stem from the different orders and inherent properties of the four schemes.

A Generalized Relaxation Method for Transport and Diffusion of Pollutant Models in Shallow Water

Abstract We present a numerical method based on finite difference relaxation approximations for computing the transport and diffusion of a passive pollutant by a water flow. The flow is modeled by the well-known shallow water equations and the pollutant propagation is described by a transport equation. The previously developed nonoscillatory relaxation scheme is generalized to cover problems with pollutant trans- port, in one and two dimensions and source terms, resulting in a class of methods of the first and the second order of accuracy in space and time. The methods are based on the classical relaxation models combined with a Runge-Kutta time splitting scheme, where neither Riemann solvers nor characteristic decompositions are needed. Numerical results are presented for several benchmark test problems. The schemes presented are verified by comparing the results with documented ones, proving that no special treatment is needed for the transport equation in order to obtain accurate results.

Macroscopic Modelling and Simulation of ACC and CACC Traffic

The incorporation of a macroscopic approach reflecting Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC) traffic dynamics in a gas-kinetic (GKT) traffic flow model is presented. The approach is a novel one and is based on the introduction of a relaxation term that satisfies the time/space-gap principle of ACC or CACC systems. The relaxation time is assigned on multiple leading vehicles in the CACC case, whereas in the ACC case this relaxation time is only assigned to the direct leading vehicle. Numerical simulations investigate the effect of ACC and CACC to traffic flow macroscopic stability with respect to perturbations introduced in a ring road and to flow characteristics in open freeways with merging flows at an on-ramp. Following from the results, it can be deduced that CACC vehicles increase the stabilization of traffic flow, compared to ACC ones. Further, the proposed CACC approach can further improve the dynamic equilibrium capacity and traffic dynamics, especially at on-ramp bottlenecks.

Calibration of a second-order traffic flow model using a metamodel-assisted Differential Evolution algorithm

With the increasingly widespread use of traffic flow simulation models, several questions concerning the reliability, efficiency and accuracy of such models need to be addressed convincingly. In general, the most time-efficient traffic flow models are based on the macroscopic approach to describe traffic dynamics. Macroscopic models reproduce the evolution of aggregated traffic characteristics over time and space with respect to observable variables, such as flow and speed, requiring much less computational time, compared to microscopic ones. This work assesses a second-order macroscopic gas-kinetic traffic flow (GKT) model and its numerical implementation using real traffic data from a motorway network in the U.K., where recurrent congestion originated from high on-ramp flows during the morning peak hours is observed. A parallel, metamodel-assisted Differential Evolution (DE) algorithm is employed for the calibration of the model parameters, and numerical simulations demonstrate that the DE algorithm can be a very promising method for the calibration of such traffic flow models.

Simulation of the penetration rate effects of ACC and CACC on macroscopic traffic dynamics

A macroscopic approach modeling the penetration rate of Adaptive Cruise Control (ACC) and Cooperative Adaptive Cruise Control (CACC) vehicles and its effect on traffic dynamics is investigated. Modeling is based on the introduction of a relaxation term in a gas-kinetic traffic flow (GKT) model that satisfies the time-gap principle of ACC or CACC systems and allows for consideration of mixed traffic of manual and ACC/CACC vehicles. The relaxation time is assigned to multiple leading vehicles in the CACC case; whereas in the ACC case only relates to the direct leading vehicle. Numerical simulations investigate the effect of the penetration rates of ACC and CACC equipped vehicles to traffic flow macroscopic stability, with respect to perturbations introduced in a ring road, and to flow characteristics in an open freeway with merging flow at an on-ramp.

Stability Analysis of a Macroscopic Traffic Flow Model for Adaptive Cruise Control Systems

Since the early days of traffic engineering, traffic flow stability has attracted a lot of attention, as the frequent occurrence of traffic jams, caused by small perturbations in traffic flow such as a sudden deceleration of a vehicle, deteriorate the performance of traffic flow and the utilization of the available infrastructure. Such traffic jams are usually related to instabilities in traffic flow, resulting in the formation of stop-and-go waves, propagating upstream the traffic flow. Emerging technologies in the field of Vehicle Automation and Communication Systems (VACS), such as Adaptive Cruise Control (ACC) systems, appear to be a remedy to reduce the amplitude or to eliminate the formation of such traffic instabilities. To this end, this work aims to derive a stability threshold of a novel macroscopic model, developed to simulate the flow of ACC-equipped vehicles, and study the impact of such vehicles on the stabilization of the traffic flow, with respect to small perturbations. The adopted macroscopic approach reflecting ACC traffic dynamics is based on the gas-kinetic (GKT) traffic flow model. The analytic results show that ACC vehicles enhance the stabilization of the traffic flow; the instability region is very narrow and by reducing the ACC time-gap setting it moves to higher values of density.Copyright

A Macroscopic Multi-Lane Traffic Flow Model for ACC/CACC Traffic Dynamics

An extended second-order macroscopic traffic flow model is presented that describes multi-lane traffic dynamics and also incorporates the effects of adaptive cruise control (ACC) or cooperative ACC (CACC). The extended model equations stem from a recently proposed multi-lane gas-kinetic traffic flow (GKT) model that can simulate lane changes due to vehicle interactions as well as spontaneous ones. The proposed extension that models the effects of ACC/CACC satisfies the time-gap principle of such systems on each lane and allows for consideration of mixed traffic comprising both manual and ACC/CACC vehicles. Numerical simulations are performed for a particular three-lane motorway stretch in the United Kingdom, where recurrent traffic congestion is observed during the morning peak hours, so as to compare the effects of ACC/CACC in the traffic flow conditions with those resulting from manual driving.

Using synchronous and asynchronous parallel Differential Evolution for calibrating a second-order traffic flow model

Abstract Given the importance of the credibility and validity required by macroscopic traffic flow models in performing real-word simulations, the necessity of including an accurate, computationally fast, and reliable constrained optimization scheme appears to be mandatory to ensure that the traffic flow characteristics are accurately represented by such models. To this end, a parallel, synchronous or asynchronous, metamodel-assisted Differential Evolution (DE) algorithm is employed for the calibration of a second-order macroscopic gas-kinetic traffic flow (GKT) model using real traffic data from Attiki Odos freeway in Athens, Greece. Two Artificial Neural Networks, a Multi-layer Perceptron and a Radial Basis Function network, are used as surrogate models to decrease the computation time of the evaluation phase of the DE optimizer. The parallelization of the DE algorithm is performed using the Message Passing Interface (MPI). Numerical simulations are performed, which demonstrate that the DE algorithm can be effectively used for the search of the global optimal model parameters in the GKT model, while appears to be a promising method for the calibration of other similar traffic models.

Macroscopic Modelling and Simulation of Multi-lane Traffic

In this work a macroscopic lane-changing model is incorporated to a single-class second-order gas-kinetic (GKT) traffic flow model to simulate multi-lane traffic flow dynamics. The lane-changing terms, simulating lane-changes due to vehicle interactions as well as spontaneous ones, are introduced as source and sink terms into the traffic flow equations. The numerical integration is based on an accurate and robust high-resolution finite volume relaxation scheme, where the nonlinear system of the macroscopic partial differential equations are first recast to a diagonilizable semi-linear system. A fifth order in space WENO scheme is used for spatial discretization, while time integration is based on a high-order implicit-explicit Runge-Kutta method. Numerical simulations, considering a two-lane highway flow where a bottleneck is formed due to a lane closure, demonstrate the ability of the proposed methodology to efficiently simulate the corresponding traffic dynamics.

Relaxation approximations to second-order traffic flow models by high-resolution schemes

A relaxation-type approximation of second-order non-equilibrium traffic models, written in conservation or balance law form, is considered. Using the relaxation approximation, the nonlinear equations are transformed to a semi-linear diagonilizable problem with linear characteristic variables and stiff source terms with the attractive feature that neither Riemann solvers nor characteristic decompositions are in need. In particular, it is only necessary to provide the flux and source term functions and an estimate of the characteristic speeds. To discretize the resulting relaxation system, high-resolution reconstructions in space are considered. Emphasis is given on a fifth-order WENO scheme and its performance. The computations reported demonstrate the simplicity and versatility of relaxation schemes as numerical solvers.