4/98
SED2D-WES Version 4.3 Beta
x=
primary flow direction, m
v=
flow velocity in y - direction, m/sec
y=
direction perpendicular to x , m
effective diffusion coefficient in x-direction, m2/sec
Dx =
effective diffusion coefficient in y-direction, m2/sec
Dy =
α1 =
a coefficient for the source term, 1/sec
α2 =
This equation is then cast into the finite element form using quadratic shape functions, N ,
C
$+
$
$
$
$
Nj
Nj
NE
NL
C
C
C
- α1 C
∑ ∫∫ N j Q + u
+v
+
dxdy + ∑ ∫ N j qs dζ = 0
(2)
Dx
Dy
i
ne =1 Dne
y
x
y
x
x
y
i =1 ζ
where
NE =
total number of elements
N=
the quadratic shape functions
( C t) + α2 for the transient problem
$
Q=
$
C=
the approximate concentration in an element as evaluated from shape functions and nodal point
values of C
NL =
total number of boundary segments
ζ =
the local coordinate
qs =
flux from source on boundary i
i
The transient equation is expressed as
8
WORKING DRAFT
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