3 J ul 2 00 3 Hydrodynamical Approach to Vehicular Flow in the Urban Street Canyon

The vehicular flow in the urban street canyon is considered. The classical field description is used in the modelling of the vehicular movement and of gaseous mixture in generic urban street canyon. The dynamical variables include vehicular densities, velocities, and emissivities: of pollutants, heat and exhaust gases, as well as standard mixture components' variables: densities, velocities, temperature, pressures. The local balances' equations predict the dynamics of the complex system. The automatic control of the vehicular flow is attained by the sets of coordinated traffic lights. The automatic control is aimed at minimization of traffic ecological costs by the application of variational calculus (Lagrange's and Bolz's problems). The theoretical description is accompanied by numerical examples of computer fluid dynamics based on real traffic data. 1 Description of the model. In the present article we develop a continuum field model of the street canyon. In the next article we will deal with numerical examples [1]. The vehicular flow in the canyon is multilane bidirectional one-level rectilinear, and it is considered with two coordinated signalized junctions [2, 3, 4]. The vehicles belong to different vehicular classes: passenger cars, and trucks. Emissions from the vehicles are based on technical measurements and many types of pollutants are considered (carbon monoxide CO, hydrocarbons HC, nitrogen oxides NO x). The vehicular dynamics is based on a hydrodynamical approach [5]. The governing equations are the continuity equation for the number of vehicles, and Greenshields' equilibrium speed-density u-k model [6]. The model of dynamics of pollutants is also hydrodynamical. The model consists of a set of mutually interconnected nonlinear, three-dimensional, time-dependent, partial differential 1