Chemistry Reference
In-Depth Information
10
15
10
14
10
13
10
12
10
11
NH
3
HCN
CH
3
CH
4
C
2
H
2
C
2
H
4
C
2
H
6
FIGURE 9.4
Calculated (gray bars) and measured (white bars) particle densities in H
2
-Ar-
N
2
-CH
4
plasma.
are called fully implicit or backward time and θ
0.5 gives the Crank-Nicolson
difference scheme, which is second-order accurate in time [8].
Depending on the plasma conditions considered, the operator
W
can be rep-
resented in zero, one, two, or even three spatial dimensions. In the 0D case,
globally averaged properties of the plasma are obtained. In particular, the plasma-
chemical reaction mechanisms are often analyzed on the basis of such global models.
The solution of the resulting equation system for the plasma-chemical kinetics is
challenging because the different species generally evolve on very different time
scales. Several software packages have been developed to integrate these stiff sys-
tems of ordinary differential equations, for example, Chemkin [9], Facsimile [10],
and Odepack [11]. As an example of plasma chemistry modeling using Facsim-
ile, Figure 9.4 shows the particle densities of several compounds in H
2
-Ar-N
2
-CH
4
microwave plasmas with a gas mixture of 73% hydrogen, 10.8% argon, 9% nitro-
gen, and 7.2% methane under static conditions in comparison with experimental
data [12].
For the solution in one or more spatial dimensions, the methods most commonly
applied to model gas discharge plasmas are the finite difference method (FDM) and
the finite element method (FEM) (see, e.g., [13-15] and references therein). The finite
volume method (FVM) has been applied, for example, to modeling of HID lamps
and microdischarge devices [16-18] and has become very popular for the analysis of
problems of computational fluid dynamics.
In the finite difference method, the solution domain is divided into a discrete set of
grid points
=
x
[19]. The first and second
derivatives of
W
at any grid point are approximated by suitable finite difference
counterparts including function values at neighboring points. Explicit time-stepping
methods are in general the easiest to implement but are restricted on the time step by
the Courant-Friedrichs-Levy (CFL) condition [20].
x
i
with a distance
x
i
for each coordinate of
