Atmospheric diffusion equation solutions

D. Solutions of the Steady-State Atmospheric Diffusion Equation. 286... 

The object of this section is to derive the Gaussian equations of the previous section as solutions to the atmospheric diffusion equation. Such a relationship has already been demonstrated in Section IV,B for the case of no boundaries. We extend that consideration now to boundaries. We recall that constant eddy diffusivities were assumed in Section IV,B. 

Sklarew, R. C., A. J. Fabrick, and J. E. Prager. A Particle-in-Oll Method for Numerical Solution of the Atmospheric Diffusion Equation, and Applications to Air Pollution Problems. Final Report 3SR-844. Vol. 1. (Prepared for the Environmental Protection Agency under Contract 68-02-(X)06) La Jolla, Calif. Systems, Science and Software, 1971. 173 pp. 

McRae J.G., W. R. Goodin, and J. H. Seinfeld (1982) Numerical solution of atmospheric diffusion equation for chemically reactings flows, J. Comput. Phys., 45. 

SOLUTION OF THE ATMOSPHERIC DIFFUSION EQUATION FOR AN INSTANTANEOUS SOURCE... 

Derivation of the Gaussian Plume Equation as a Solution of the Atmospheric Diffusion Equation... 

We saw that by assuming constant eddy diffusivities Kxx. Kyy, and K77, the solution of the atmospheric diffusion equation has a Gaussian form. Thus it should be possible to obtain (18.88) or (18.89) as a solution of an appropriate form of the atmospheric diffusion equation. More importantly, because of the ease in specifying different physical situations in the boundary conditions for the atmospheric diffusion equation, we want to include those situations that we were unable to handle easily in Section 18.9.1, namely, the existence of an inversion layer at height H and partial absorption at the surface. Readers not concerned with the details of this solution may skip directly to Section 18.9.3. 

SOLUTIONS OF THE STEADY-STATE ATMOSPHERIC DIFFUSION EQUATION 873... 

Lin, J. S., and Hildemann, L. M. (1996) Analytical solutions of the atmospheric diffusion equation with multiple sources and height-dependent wind speed and eddy diffusivities, Atmos. Environ. 30, 239-254. 

The solution of the full atmospheric diffusion equation requires the specification of the initial concentration field of all species ... 

Order of operator application is another issue. McRae et al. (1982a) recommended using a symmetric operator splitting scheme for the solution of the atmospheric diffusion equation. They used the scheme... 

We begin in this section to obtain solutions for atmospheric diffusion problems. Let us consider, as we did in the previous section, an instantaneous point source of strength 5 at the origin in an infinite fluid with a velocity u in the x direction. We desire to solve the atmospheric diffusion equation, (17.11), in this situation. Let us assume, for lack of anything bet-... 

Having demonstrated that exact solution for the mean concentrations (c, (x, t j) even of inert species in a turbulent fluid is not possible in general by either the Eulerian or Lagrangian approaches, we now consider what assumptions and approximations can be invoked to obtain practical descriptions of atmospheric diffusion. In Section 18.4 we shall proceed from the two basic equations for (c,), (18.4) and (18.8), to obtain the equations commonly used for atmospheric diffusion. A particularly important aspect is the delineation of the assumptions and limitations inherent in each description. 

In Equation 12.3, D is normally assumed to be independent of both penetrant concentration and polymer relaxations at low concentration, and x is the thickness of the membrane. This is especially true for gases such as oxygen (O2), carbon dioxide (CO2) at atmospheric pressure, and some organic compounds. Many theories have been proposed and many models have been developed to describe diffusion in polymers a detailed description of these models can be found elsewhere [7]. The diffusion processes through the membrane can generally be considered unidirectional and perpendicular to the flat surface, and solutions to the diffusion equations are obtained from the boundary conditions where the Henry s or Langmuir-Henry s law is applied. 

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