2. ENVIRONMENTAL ChEMISTRy & TEChNOLOGy 2.1. Lectures

Chem. Listy, 102, s265–s1311 (2008) Environmental Chemistry & Technology
( x,
+ N , k)
= 0.
C j
( x,
−N , k)
= 0.
C j
C
( x,
j,
N ) = 0.
+ k
( ∞)
Dz
C(
x,
j,
0)
=
C(
x,
j,
2)
.
2∆z(
v −W
) + D
z
( ∞)
(7b)
(7c)
(7d)
(7e)
For integration of the system of ODEs (7) the 4 th order
Runge-Kutta method was chosen. It has sufficient accuracy
as is shown in the next chapter.
Results
As was mentioned above equation (3) supposes one point
source that has constant strength. It means that the amount of
pollutant is constant during time. The wind flows along x axis
with constant speed and the ground is flat everywhere. In our
experiments, all diffusion coefficients were constant in every
space points during time, for simplicity.
now everything is defined to solve our model of
PDE (3) with boundary conditions (3a–e). The experiment
has been done with following coefficient setting. The diffusion
coefficients has been set like that: D y = 0.23 m 2 s –1 ,
D z = 0.23 m 2 s –1 which is the parameter of ammonia, other
coefficients has been: v = 2 m s –1 , W = 3 m s –1 , u x = 2 m s –1 ,
Q = 0.1 kg s –1 and H = 1.5 m.
The space discretization has been chosen as follows:
N i = 600, N j = 50, N k = 50, Δx = 0.005 m, Δy = 0.05 m and
Δz = 0.05 m. In this case the assumed space 3 m × 2.5 m × 2.5 m
has been discretized into 1,500,000 points in which the equations
have been calculated.
V i s u a l i z a t i o n
We made simple program/tool for solving given A-DE
and for the visualization of the results with possibility of
comparison the analytical and the obtained numerical soluti-
Fig. 1. xy plane cut in zero depth, which means that the ground
pollutant dispersion is shown. The wind flows from left to right
s388
ons. The program has possibility to make the cuts through the
perpendicular grid in XY, XZ and YZ planes in any depth and
the appropriate grid points can be plotted.
Fig. 1. and Fig. 2. show the XY and XZ cuts for our
above-defined experiment. The level of gray (the lighter the
more concentrated) expresses the amount of concentration of
pollutant at each point - the most concentrated means approximately
0.5% of source concentration.
Fig. 2. xZ plane cut in depth of 25 of overall depth 50 which
means that the cut in depth of point source is shown. The wind
flows from left to right
Scales of axes (x is horizontal, y is vertical) in figures
above are these:
• Fig. 1.: x axis: m, y axis: m
• Fig. 2.: x axis: m, y axis: m
The three-dimension (3D) visualization is another way
to represent the calculated data in space. It has many advantages
and gives to the user tool for fast investigation of the
result. Many methods of gas or fluid visualization were developed
however not all are suitable for our purpose. We can
mention the stream ribbons, stream surfaces, particle traces,
vector fields etc. 7 .
Fig. 3. 3D visualization of pollutant dispersion in the atmosphere.
The white color points show the highest concentration of
pollutant, the black color points show its low concentration