We introduce a new model of traffic flow with phase transitions. The model is obtained by coupling together the classical Lighthill-Whitham-Richards (LWR) equation with the 2 × 2 system described in [A. Aw and M. Rascle, Resurrection of “second order” models of traffic flow, SIAM J. Appl. Math., 60 (2000), pp. 916–938]. We describe the solutions of the Riemann problem, and we compare the result...

This paper gives rigorous numerical analysis of the error in prediction of aeroacoustic noise via Lighthill analogy. The first fundamental and intractable problem is to predict the sound power on surfaces. We give a full analysis of three methods of prediction. The second fundamental problem is the limited regularity of the underlying turbulent flow. This is handled herein by giving a negative ...

We consider the Lighthill-Witham-Richards traffic flow model on a junction composed by one mainline, an onramp and an offramp, which are connected by a node. The onramp dynamics is modeled using an ordinary differential equation describing the evolution of the queue length. The definition of the solution of the Riemann problem at the junction is based on an optimization problem and the use of a...

Dense human flow has been a concern for the safety of public events for a long time. Macroscopic pedestrian models, which are mainly based on fluid dynamics, are often used to simulate huge crowds due to their low computational costs (COLOMBO and ROSINI, 2005). Similar approaches are used in the field of traffic simulations (LIGHTHILL and WHITHAM, 1955). A combined macroscopic simulation of veh...

This paper treats the problem of optimizing a coordinated ramp metering strategy based on a distributed macroscopic traffic model. The Lighthill, Whitham and Richards (LWR) model is extended to include on/off-ramps with on-ramp flow saturations and an optimal control formulation is proposed. Using optimization techniques in Banach spaces, a solution is shown to exist and the necessary optimalit...

Based on the low of the eighth power of speed of M.J. Lighthill this article has derived the calculating formula for the air dynamic noise power in the compressor, and analysed the factors to affect the noise, also indicated that the dynamic noise in the compressor mainly comes from the valve jet noise; the principle to reduce the dynamic noise is to get a small Reynolds number Re; the emphasis...

The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the models, we consider follow-the-leader type with different types drivers and vehicles which are distributed randomly on road. After a rescaling, show that cumulative distribution function converges solution model. We also establish connection between model so-called Lig...

The higher-order characteristic basis function method (HO-CBFM) is clearly formulated. HO-CBFM provides results accurately even if a block division is arbitrary. The HO-CBFM combined with a volume integral equation (VIE) is used in the analysis of various antennas in the vicinity of a dielectric object. The results of the numerical analysis show that the HO-CBFM can reduce the CPU time while st...

If a d-dimensional integral involves an integrand ofthe functional form F (II (x I) + f2(X2) + ... ), then one can introduce an integral transform (Fourier or Laplace or variants on those) which allows all the integrals over the coordinates XI to factor. Thus a d-dimensional integral is reduced to a one-dimensional integral over the transform variable. This is shown to be a very powerful and pr...