Field Model of Street Canyon : Theoretical Description Part 1

A general proecological urban road traffic control idea for the street canyon is proposed with emphasis placed on development of advanced continuum field gasdynamical (hydrodynamical) control model of the street canyon. The continuum field model of optimal control of street canyon is studied. The mathematical physics' approach (Eu-lerian approach) to vehicular movement, to pollutants' emission, and to pollutants' dynamics is used. The rigorous mathematical model is presented, using gasdynamical (hydrodynamical) theory for both air constituents and vehicles, including many types of vehicles and many types of pollutant (exhaust gases) emitted from vehicles. The six optimal control problems are formulated. 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 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 of noninteracting, Newtonian, viscous fluid (perfect or ideal gases). The complete model incorporates as variables the following fields: density of the mixture, mass concentrations of constituents of the mixture, velocity of mixture, temperature of mixture, pressure of mixture, intrinsic (internal) energy of mixture, densities of vehicles, and velocities of vehicles. The 1