Abstract
A particle-grid air quality modeling approach that can incorporate chemistry is proposed as an alternative to the conventional PDE-grid air quality modeling. The particle trajectory model can accurately describe advection of air pollutants without introducing artificial diffusion, generating negative concentrations or distorting the concentration distributions. It also accurately describes the dispersion of emissions from point sources and is capable of retaining subgrid-scale information. Inhomogeneous turbulence necessitates use of a small timestep, say, 10 s to describe vertical dispersion of particles in convective conditions. A timestep as large as 200 s can be used to simulate horizontal dispersion. A time-splitting scheme can be used to couple the horizontal and vertical dispersion in a 3D simulation, and about 2000–3000 particles per cell of size 5 km × 5 km × 50 m is sufficient to yield a highly accurate simulation of 3D dispersion. Use of an hourly-averaged concentration further reduces the demand of particle per cell to 500.
The particle-grid method is applied to a system of ten reacting chemical species in a two-dimensioned rotating flow field with and without diffusion. A chemistry grid within which reactions are assumed to take place can be decoupled from the grid describing the flow field. Two types of chemistry grids are used to describe the chemical reactions: a fixed coarse grid and a moving (the advection case) or stationary (the advection plus diffusion case) fine grid. Two particle-number densities are also used: 256 and 576 particles per fixed coarse grid cell. The species mass redistributed back to the particle after each reaction step is assumed to be proportioned to the species mass in the particle before the reaction. The simulation results are very accurate, especially in the advection-chemistry case. Accuracy improves with the use of a fine grid. A higher particle-number density also reduces the concentration fluctuation in the cases involving diffusion.
We also show by examples that chemistry can lead to significantly different results from numerical methods for the diffusion equation (let alone the advection equation) which otherwise yield almost identical solutions. The absence of this difficulty in the particle-grid method further enhances its attractiveness.
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References
D.P. CHOCK, A comparison of numerical methods for solving the advection equation—III, Atmospheric Environment, 25A (1991), pp. 853–871.
G.T. CSANADY, Turbulent Diffusion in the Environment, D. Reidel, Dordrecht, Holland, 1973, p. 8.
A. DRUILHET, J.P. FRANGI, D. GUEDALIA and J. FONTAN, Experimental studies of the turbulence structure parameters of the convective boundary layer, J. Climate and Appl. Met., 22 (1983), pp. 594–608.
F.A. GIFFORD, The time-scale of atmospheric diffusion considered in relation to the universal diffusion function, f1, Atmospheric Environment, 21 (1987), pp. 1315–1320.
S.R. HANNA, Lagrangian and Eulerian time-scale relations in the daytime boundary layer, J. Appl. Met., 20 (1981), pp. 242–249.
B.B. HICKS, Behavior of turbulence statistics in the convective boundary layer, J. Climate and Appl. Met., 24 (1985), pp. 607–614.
O. HOV, Z. ZLATEV, R. BERKOWICZ, A. ELIASSEN and L.P. PRAHM, Comparison of numerical techniques for use in air pollution models with nonlinear chemical reactions, Atmospheric Environment, 23 (1989), pp. 967–983.
B.J. LEGG and M.R. RAUPACH, Markov-chain simulation of particle dispersion in inhomogeneous flows: the mean drift velocity induced by a gradient in Eulerian velocity variance, Boundary-Layer Meteorol, 24 (1982), pp. 3–13.
D.H. LENSCHOW, J.C. WYNGAARD and W.T. PENNELL, Mean-field and secondmoment budgets in abaroclinic, convective boundary layer, J. Atmos. Sci., 37 (1980), pp. 1313–1326.
W.W. LI AND R.N. MERONEY, Estimation of Lagrangian time scales from laboratory measurements of lateral dispersion, Atmospheric Environment, 18 (1984), pp. 1601–1611.
A.K. LUHAR and R.E. BRITTER, A random walk model for dispersion in inhomogeneous turbulence in a convective boundary layer, Atmospheric Environment, 23 (1989), pp. 1911–1924.
G.J. MCRAE, W.R. GOODIN AND J.H. SEINFELD, Numerical solution of the atmospheric diffusion equation for chemically reacting flows, J. Comp. Phys., 45 (1982), pp. 1–42.
NAG Fortran Library Manual, Mark 13, The Numerical Algorithms Group Limited, Oxford, U.K. (1989).
M.T. ODMAN AND A.G. RUSSELL, Multiscale modeling of pollutant transport and chemistry, J. Geophys. Res., 96 (1991), pp. 7363–7370.
S.D. REYNOLDS, P.M. ROTH and J.H. SEINFELD, Mathematical modeling of photochemical air pollution—I, Atmospheric Environment, 7 (1973), pp. 1033–1061.
B.L. SAWFORD, Generalized random forcing in random-walk turbulent dispersion models, Phys. Fluids, 29 (1986), pp. 3582–3585.
J.H. SEINFELD, Ozone air quality models. A critical review, JAPCA, 38 (1988), pp. 616–645.
D.J. THOMSON, Random walk modelling of diffusion in inhomogeneous turbulence, Q. J. Royal Meteor. Soc., 110 (1984), pp. 1107–1120.
D.J. THOMSON, Criteria for the selection of stochastic models of particle trajectories in turbulent flows, J. Fluid Mech., 180 (1987), pp. 529–556.
A.F.B. TOMPSON and D.E. DOUGHERTY, Particle-grid methods for reacting flows in porous media with application to Fisher’s equation, Appl. Math. Modeling, 16 (1992), pp. 374–383.
H. VAN DOP, F.T.M. NIEUWSTADT AND J.C.R. HUNT, Random walk models for particle displacements in inhomogeneous unsteady turbulent flows, Phys. Fluids, 28 (1985), pp. 1639–1653.
J.C. WEIL, A diagnosis of the asymmetry in top-down and bottom-up diffusion using a Lagrangian stochastic model, J. Atmos Sci., 47 (1990), pp. 501–515.
J.D. WILSON, G.W. THURTELL AND G.E. KIDD, Numerical simulation of particle trajectories in inhomogeneous turbulence, II: systems with variable turbulent velocity scale, Boundary-Layer Meteorol., 21 (1981), pp. 423–441.
J.D. WILSON, B.J. LEGG AND D.J. THOMSON, Calculation of particle trajectories in the presence of a gradient in turbulent-velocity variance, Boundary-Layer Meteorol., 27 (1983), pp. 163–169.
G.S. YOUNG, Turbulence structure of the convective boundary layer. Part I: variability of normalized turbulence statistics, J. Atmos. Sci., 45 (1988), pp. 719–726.
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The authors would like to thank Prof. Jean Bahr of University of Wisconsin for bringing the paper of Tompson and Dougherty [20] to their attention.
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© 1996 Springer-Verlag New York, Inc.
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Chock, D.P., Winkler, S.L. (1996). A Particle-Grid Air Quality Modeling Approach. In: Wheeler, M.F. (eds) Environmental Studies. The IMA Volumes in Mathematics and its Applications, vol 79. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8492-2_4
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DOI: https://doi.org/10.1007/978-1-4613-8492-2_4
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