by Marek
(Warsaw, Poland)

Mass Transport Equation

3D unsteady state Eulerian type model with convection.

There is the equation that was solved (description is in polish :)

This model was developed using Finite Element Method (Galerkin scheme with up-winding technique, Fortran source code).

In the sample results I have attached, there are two sources of pollution, a high building on a way of smoke. Wind has changed after second chimney was turned on. Results are presented on two normal surfaces.

Sample results:
http://pl.wikipedia.org/wiki/Modelowanie_dyspersji_odorant%C3%B3w
(at the bottom of the page)

Barry's Response - The text, when translated into English, reads:

## Model spread of pollutants in the atmosphere

The model belongs to the group of the of Euler models of the first order. Solution mass transport equation using finite element method in 3D unsteady convection system.

For the relevant mass transport equation, see image above. The equation variables represent:

x,y,z - Coordinates
t - Time
S - Concentration
Qv - Volumetric emissions
P - Pollution Decay Rate
Kx,Ky,Kz - turbulent diffusion coefficients in x, y, z
vx,vy,vz - wind velocity components

The page then presents results of the calculations in the plane parallel to the earth, the first graph in each time step, and in a plane perpendicular to the surface. An instruction to view pollution concentration distribution with chimney "behind the backs" is included. Therefore, there are two graphics shown for each time step.

The time steps range from 100 seconds to 1800 seconds (15 minutes). Follow the first link above to see the model output presented graphically with comments. The Wikipedia page shown in the second link has these graphics presented in an animated frame. Here are the comments included with the still frames presented in the first link:

100 seconds - Times are given for after the time of "0", when the release occurs at the chimney. After 100 s something is already seen on the surface of the earth. For the cross-sectional area view of the modeled stream, pollution has not become apparent yet.

300 seconds - It avoids fumigation of a tall building located in the plume's way

1200 seconds - A second chimney (contaminant source) is added and the wind direction changes.

1800 seconds - After this time the solution becomes static, assuming equilibrium (dS/dt = 0).

The title of this document reads:

Engineering calculations -

DESIGN, STRENGTH , VIBRATION , BORDER CAPACITY

These model results appear to be quite reasonable for a plume dispersion simulation. There is no name provided for the model used, as it would have been custom designed for this particular study, and the code is not provided. This makes sense since the work that went into it is potentially proprietary.

Finally, near the top of the web page is a list of links to forum entries, all of which are in Polish as well.

Average Rating

 Rating Vanadis user instruction - english version by: Marek Hi, I have uploaded short Vanadis demo manual in english in file vanadis_eng.txt. Regards, Marek

 Rating Vanadis model history by: Marek Hi guys, Model was designed in 1998 for my PhD. Marek

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