Engineering Transactions, 48, 4, pp. 415–432, 2000

Continuum Field Model of Street Canyon: Theoretical Description. Part I

M.M. Duras
Cracow University of Technology

A general proecological urban road traffic control idea for the street canyon is proposed with emphasis placed on development of advanced continuum field gasdynamical (hydrodynamcal) control model of the street canyon. The continuum field model of optimal control of street canyon is studied. 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 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.
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M.M. DURAS, Continuum field model of street canyon: numerical examples. Part 2, Engng. Trans., 48, 4, 433–448, 2000.

M.M. DURAS, Road traffic control in street canyons, Ph. D. Thesis, University of Mining and Metallurgy, Cracow, August 1998, 1–363, 1998.

A. ADAMSKI and M.M. DURAS, Environmental traffic control issues in street canyons, Polish Journal of Environmental Studies, 6, 1, 13–20, 1997.

A. ADAMSKI and M.M. DURAS, Air pollution optimal traffic control issues in integrated street, Polish Journal of Environmental Studies, 8, 1, 7–17, 1999.

P.G. MICHALOPOULOS, D.E. BESKOS and J.-K. LIN, Analysis of interrupted traffic flow by finite difference methods, Transportation Research–B, 18B, 4/5, 409–421, 1984.

B.D. GREENSHIELDS, A study of traffic capacity, Proceedings of Highway Research Board, 14, 448–477, 1934.

A. CEMAL ERINGEN and G. A. MAUGIN, Electrodynamics of continua, Vol. I, Chapters 3, 5; Vol. II, Chapters 9, 10, Springer Verlag, New York 1990.

L.D. LANDAU, E.M. LIFSHITZ, Theoretical Physics: Hydrodynamics [in Russian], Chapters 2, 6, Nauka, Moscow 1986.

S.L. SOO, Fluid dynamics of multiphase systems, Series Titles: A Blaisdell Book in the Pure and Applied Sciences, Blaisdell Publishing Company, A Division of Ginn and Company, Chapters 6, 7, 8, Waltham: Massachusetts, Massachusetts, Toronto, London 1967.

Continuum Physics, A. CEMAL ERINGEN [Ed.], Contributors: A. Cemal Eringen and others, Academic Press, New York, San Francisco, London, 1971–1976, Vol. 1, Mathematics; Vol. 2, Continuum Mechanics of Single-Substance Bodies; Vol. 3, Mixtures and EM Field Theories; Vol. 4, Polar and Non-Local Field Theories; Vol. 1, Part 1; Vol. 3, Part 1; Vol. 4, Part 1.

A. CEMAL ERINGEN, Nonlinear theory of continuous media, McGraw–Hill Book Company, Inc., Chapters 2, 3, 4, 5, 7, New York, San Francisco, Toronto, London 1962.

H. LAMB, Hydrodynamics, Dover Publications, Chapter 1, New York 1945.

I.I. OL'KHOVSKIY, Course of theoretical mechanics for physicists [in Russian], Part 2, Moscow University Press, Moscow 1974.

G.A. MAUGIN, Continuum mechanics of electromagnetic solids, North–Holland Series in Applied Mathematics and Mechanics, Vol. 33, Chaper 2, North–Holland, Amsterdam, New York, Oxford, Tokyo 1988.

L.G. LOYTZYANSKIY, Mechanics of liquids and gases [in Russian], Chapters 1, 2, 3, 4, 8, 10, State Editorial of Technical–Theoretical Literature, Moscow 1958.

Computational Mechanics '88: Theory and Applications: Proceedings of the International Conference on Computational Engineering Science, April 10–14, 1988, Atlanta, Georgia, USA, S. N. ATLURI and G. YAGAWA [Eds.], Springer Verlag, Berlin, Heidelberg, New York, London, Paris, Tokyo, Volumes 1, 2, 1988, Vol. 1, Sessions 1, 7; Vol. 2, Sessions 33, 36, 38, 52, 53, 54, 55, 56, 58, 59.

E. BECKER, Gas dynamics [in German], B. G. TEUBNER, Chapters 1, 2, Stuttgart 1969.

L.I. SYEDOV, Mechanics of continuum medium [in Russian], Volumes 1, 2, 1970–1972, Vol. 1, Chapters 3, 4, 5, 7, Vol. 2, Chapter 8, Nauka, Moscow.

SHIH-PAI, Viscous flow theory, D. Van Nostrand Company, Inc., Toronto, Princeton, New Jersey, New York, London, Volumes 1, 2, 1956–1957, Vol. 1, Laminar Flow; Vol. 2, Turbulent Flow, Vol. 1, Chapters 1, 2, 3, 6.

T. OROVEANU, Mechanics of viscous fluids [in Romanian], Chapters 1, 2, 3, 4, Editorial of Academy of Popular Republic of Romania, Bucureşti 1967.

L.M. MILNE-THOMSON, Theoretical hydrodynamics, Chapter 3, The Macmillan Company, New York 1950.

Transport with chemical reactions, P. STROEVE and W. J. WARD [Eds.], AIChE Symposium Series, Vol. 77, Number 202, American Institute of Chemical Engineers, New York 1981.

M. BARRERE and R. PRUD'HOMME, Fundamental equations of the aerothermochemistry [in French], Masson et Compagnie, Éditeurs, Chapters 2, 3, 4, Paris 1973.

R.L. LIBOFF, Introduction to the theory of kinetic equations, Chapter 3, John Wiley and Sons, Inc., New York, London, Sydney, Toronto 1969.

G.A. BIRD, Molecular gas dynamics, Chapters 9, 11, 12, Clarendon Press, Oxford University Press, Oxford Engineering Science Series, Oxford 1976.

Z.G. SZABO, Advances in the kinetics of homogeneous gas reactions [in German], Chapter 2, 3, 4, 7, 8, Methuen and Company Ltd, London 1964.

Kinetic processes in gases and plasmas, Chapters 2, 3, 7, A. R. HOCHSTIM [Ed.], Academic Press, New York, London 1969. A Volume in the Reentry Physics Series,

J.F. CLARKE and M. McCHESNEY, Dynamics of relaxing gases, Chapter 2, Butterworths and Company Publishers, London, Boston 1975.

G.N. ABRAMOVICH, Applied gas dynamics [in Russian], Chapter 2, Nauka, Moscow 1969.

H. ROUSE, Elementary mechanics of fluids, Chapter 4, John Wiley and Sons, New York; Chapman and Hall Limited, Inc., 1946.

Lecture notes in physics, Vol. 31, Transport Phenomena, J. EHLERS, K. HEPP, H. A. WEIDENMULLER [Eds.], Sitges International School of Statistical Mechanics, 1974. Trans port phenomena: Sitges International School of Statistical Mechanics, June 1974, Sitges, Barcelona/Spain, G. KIRCZENOW and J. MARRO [Eds.], Springer Verlag, Berlin, Heidelberg, New York 1974.

Lecture notes in engineering, Vol. 18, C. A. BREBBIA and S. A. ORSZAG [Eds.], Numerical Simulation of Fluid Flow and Heat/Mass Transfer Processes; International PHOENICS Users Conference [1st: 1985: Dartford Campus of Thames Polytechnic], N. C. MARKATOS, D. G. TATCHELL, M. GROSS and N. RHODES [Eds.], Session 9, Springer Verlag, Berlin, Heidelberg, New York, Tokyo 1986.

W.M. ZAJACZKOWSKI, On nonstationary motion of a compressible barotropic viscous fluid bounded by a free surface, Dissertationes Mathematicae, Vol. CCCXXIV, Institute of Mathematics, Polish Academy of Sciences, Warsaw 1993.

S. PANCHEV, Random functions and turbulence [in Russian], Parts 2, 3, Hydrometeorological Editorial, Sankt Petersburg 1967.

C. JAKOB, Mathematical introduction to fluid mechanics [in French], Parts 2, 3, 4, Guthier-Villars Editeur-Imprimeur-Libraire, Paris.

T.N. ABRAMYENKO, Thermal diffusion in gases [in Russian], Chapters 1, 2, 3, 4, Science and Technics, Minsk 1982.

Combustion chemistry, W.C. GARDINER, Jr. [Ed.], Chapters 1, 2, 3, 5, 7, 8, Springer Verlag, New York, Berlin, Heidelberg, Tokyo 1984.

S. POSTRZEDNIK, Thermodynamics of flows [in Polish], Chapter 2, Selected Irreversible Flows and Molecular Flows, Silesian Technical University, University Lectures No. 1784, Gliwice 1993.

CHIA–SHUN YIH, Dynamics of nonhomogeneous fluids, Macmillan Series in Advanced Mathematics and Theoretical Physics, M. KAC, M. HALL, Jr., C.C. LIN, I. STAKGOLD, G.E. UHLENBECK, Editorial Board, Chapter 1, The Macmillan Company, New York, Collier-Macmillan Limited, London 1965.

S. CHAPMAN and T.G. COWLING, The mathematical theory of non–uniform gases, Chapters 2, 6, 9, 10, 12, 13, 14, 18, Cambridge University Press, Cambridge 1970.

H. ERBRINK, Turbulent diffusion from tall stacks, The Use of Advanced Boundary-Layer Meteorological Parameters in the Gaussian Dispersion Model "STACKS", Free University of Amsterdam Press, Ph. D. Thesis, Amsterdam 1995.

E. SZÜCS, Engineering models [in Hungarian], Chapters 3, 10, 11, Müszaki Könyvkiadó, Budapest 1972.

D. TELIONIS, Unsteady viscous flows, Springer Series in Computational Physics, Chapter 2, Springer Verlag, New York 1981.

Lecture notes in physics, Vol. 271, Nonlinear Hydrodynamic Modeling: a Mathematical Introduction, H.N. SHIRER [Ed.], Springer Verlag, Berlin, New York 1987.

J.A. BUTTON and R. WELLS, [In:] Lecture Notes in Physics, Vol. 271, Nonlinear Hydrodynamic Modeling: a Mathematical Introduction, H. N. SHIRER [Ed.], p. 444, Springer Verlag, Berlin, New York 1987.

V.V. KAFAROV, Fundamentals of mass transfer, Chapter 12, Mir, Moscow 1975.

Recent developments in theoretical and experimental fluid mechanics: Compressible and Incompressible Flows, U. MULLER, K. G. ROESNER, B. SCHMIDT and J. ZIEREP [Eds.], Springer Verlag, Berlin, New York 1979.

W. SCHÖNHAUER, H.-G. DAUBLER and G. GLOTZ, [In:] Recent Developments in Theoretical and Experimental Fluid Mechanics: Compressible and Incompressible Flows, U. MÜLLER, K. G. ROESNER, B. SCHMIDT and J. ZIEREP [Eds.], p. 257, Springer Verlag, Berlin, New York 1979.

A.D. KOVALYENKO, Principles of thermoelasticity [in Russian], Chapters 1, 2, 3, Naukova Dumka, Kiev 1970.

N.V. SALTANOV, Analytical hydromechanics [in Russian], Chapters 1, 2, 4, Naukova Dumka, Kiev 1984.

G.J. PRANGSMA, A.H. ALBERGA and J. J. M. BEENAKKER, Ultrasonic determination of the volume viscosity of N2, CO, CH4, and CD4 between 77 and 300 K, Physica, 64, 2, 278–288, 1973.

S. CHAPMAN and T.G. COWLING, The mathematical theory of non–uniform gases, Cambridge University Press, Cambridge 1970, Table No. 22, p. 263; Table No. 24, p. 266; Table No. 25, p. 267.

H.S. EGGLESTON, D. GAUDIOSO, N. GORISSEN, R. JOUMARD, R. C. RIJKEBOER, Z. SAMARAS and K.-H. ZIEROCK, CORINAIR Working Group on Emission Factors for Calculating 1990 Emissions from Road Traffic office for official Publications of the European Communities, ECSC-EEC-EAEC, Vol. 1, Brussels-Luxembourg, Brussels-Luxembourg 1993.

A. STURM, University of Graz Report, 1996 [private communication].

M. BRZEŻAŃSKI, Evaluation of transport emission of the amount on a chosen section of theroad network in Cracow [in Polish], KONMOT'98, Table 2, 1998.

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