*** 20th Anniversary: 2003 to 2023 ***


by Marek
(Warsaw, Poland)

Mass Transport Equation

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:
(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 -


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.

Comments for Vanadis

Average Rating starstarstarstarstar

Click here to add your own comments

Vanadis user instruction - english version
by: Marek

I have uploaded short Vanadis demo manual in english in file vanadis_eng.txt.

Vanadis model history
by: Marek

Hi guys,
Model was designed in 1998 for my PhD.

Click here to add your own comments

Join in and write your own page! It's easy to do. How? Simply click here to return to Hi-Tech Idea.

ADD TO OTHER SOCIAL BOOKMARKS: add to Del.icio.usDel.icio.us add to DiggDiggadd to SpurlSpurl

Do you have concerns about air pollution in your area??

Perhaps modelling air pollution will provide the answers to your question.

That is what I do on a full-time basis.  Find out if it is necessary for your project.

Have your Say...

on the StuffintheAir         facebook page

Other topics listed in these guides:

The Stuff in the Air Site Map


See the newsletter chronicle. 

Thank you to my research and writing assistants, ChatGPT and WordTune, as well as Wombo for the images.