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Continuum Field Model of Street Canyon Theoretical Description Part I
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Continuum Field Model of Street Canyon: Theoretical Description
Part 1
Maciej M. Duras ?
Institute of Physics, Cracow University of Technology, ulica Podchora?z?ych 1, PL-30-084
Cracow, Poland
? Email: mduras @ riad.usk.pk.edu.pl
Engng. Trans. 48, 415-432 (2000).
Abstract
A general proecological urban road traffic control idea for the street canyon is pro-
posed 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 NOx). 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,
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