Intersection modeling using a convergent scheme based on Hamilton-Jacobi equation

AbstractThis paper presents a convergent scheme for Hamilton-Jacobi (HJ) equations posed on a junction. The general aim of the approach is to develop a framework using similar tools to the variational principle in traffic theory to model intersections taking in account many incoming and outgoing roads. Then a time-explicit numerical scheme is proposed. It is based on the very classical Godunov scheme. The proposed model could be characterized as a pointwise model of intersection without any internal state. Moreover, our model respects the invariance principle. This scheme is applied to the cases of diverge junctions. The goal is to know how to manage the fluxes in order to maximize the flow through the junction

A variational formulation for higher order macroscopic traffic flow models: numerical investigation

This paper deals with numerical methods providing semi-analytic solutions to a wide classofmacroscopictrafficflow modelsfor piecewiseaffine initial andboundaryconditions. In a very recent paper, a variational principle has been proved for models of the Generic Second Order Modeling (GSOM) family, yielding an adequate framework for effective numerical methods. Any model of the GSOM family can be recast into its Lagrangian form as a Hamilton-Jacobi equation (HJ) for which the solution is interpreted as the position of vehicles. This solution can be computed thanks to Lax-Hopf like formulas and a generalization of the inf-morphism property. The efficiency of this computational method is illustrated through a numerical example and finally a discussion about future developments is provided

Benchmark values for the Soret, thermal diffusion and diffusion coefficients of three binary organic liquid mixtures

With the aim of providing reliable benchmark values, we have measured the Soret, diffusion and thermal diffusion coefficients of the three binary mixtures of dodecane, isobutylbenzene and 1,2,3,4 tetrahydronaphthalene for a concentration of 50 wt% at a temperature of 25°C. The experimental techniques applied by the five participating laboratories are transient holographic gratings, annular and parallelepipedic thermogravitational columns, and vertical parallelepipedic columns with velocity amplitude determination by laser doppler velocimetry. The systems have also been studied in a annular thermogravitational column filled with a porous medium in the gap. There is a good agreement between the different experiments with deviations of the order of a few per cent in most cases (8.5% at most). The numerical values are tabulated in the paper

Benchmark values for the Soret, thermal diffusion and diffusion coefficients of three binary organic liquid mixtures

With the aim of providing reliable benchmark values, we have measured the Soret, diffusion and thermal diffusion coefficients of the three binary mixtures of dodecane, isobutylbenzene and 1,2,3,4 tetrahydronaphthalene for a concentration of 50 wt% at a temperature of 25°C. The experimental techniques applied by the five participating laboratories are transient holographic gratings, annular and parallelepipedic thermogravitational columns, and vertical parallelepipedic columns with velocity amplitude determination by laser doppler velocimetry. The systems have also been studied in a annular thermogravitational column filled with a porous medium in the gap. There is a good agreement between the different experiments with deviations of the order of a few per cent in most cases (8.5% at most). The numerical values are tabulated in the paper