Transport Phenomena in the Urban Street Canyon

1 Abstract A generic proecological traffic control model for the urban street canyon is proposed by development of advanced continuum field hydrodynamical control model of the street canyon. The model of optimal control of street canyon dynamics is also investigated. The mathematical physics' approach (Eulerian approach) to vehicular movement, to pollutants' emission, and to pollutants' dynamics is used. The rigorous mathematical model is presented, using hydrodynamical theory for both air constituents and vehicles, including many types of vehicles and many types of pollutants emitted from vehicles. The six proposed optimal mon-ocriterial control problems consist of minimization of functionals of the total travel time, of global emissions of pollutants, and of global concentrations of pollutants, both in the studied street canyon, and in its two nearest neighbour substitute canyons, respectively. The six optimization problems are solved numerically. Generic traffic control issues are inferred. The discretization method, comparison with experiment, mathematical issues, and programming issues are discussed. 2 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 equations with nonzero right-hand sides (sources), and of boundary and of initial problem. The pollutants, oxygen, and the remaining gaseous constituents of air, are treated as mixture 1