<s>
The	O
upwind	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
is	O
a	O
method	O
used	O
in	O
numerical	O
methods	O
in	O
computational	O
fluid	O
dynamics	O
for	O
convection	O
–	O
diffusion	O
problems	O
.	O
</s>
<s>
By	O
taking	O
into	O
account	O
the	O
direction	O
of	O
the	O
flow	O
,	O
the	O
upwind	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
overcomes	O
that	O
inability	O
of	O
the	O
central	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
.	O
</s>
<s>
For	O
a	O
Peclet	O
number	O
of	O
lower	O
value	O
( |Pe|	O
<	O
2	O
)	O
,	O
diffusion	O
is	O
dominant	O
and	O
for	O
this	O
the	O
central	B-Algorithm
difference	I-Algorithm
scheme	I-Algorithm
is	O
used	O
.	O
</s>
<s>
For	O
other	O
values	O
of	O
the	O
Peclet	O
number	O
,	O
the	O
upwind	B-Algorithm
scheme	I-Algorithm
is	O
used	O
for	O
convection-dominated	O
flows	O
with	O
Peclet	O
number	O
( |Pe|	O
>2	O
)	O
.	O
</s>
<s>
Corresponding	O
upwind	B-Algorithm
scheme	I-Algorithm
equation	O
:	O
</s>
<s>
Corresponding	O
upwind	B-Algorithm
scheme	I-Algorithm
equation	O
:	O
</s>
<s>
Solution	O
in	O
the	O
central	B-Algorithm
difference	I-Algorithm
scheme	I-Algorithm
fails	O
to	O
converge	B-Algorithm
for	O
Peclet	O
number	O
greater	O
than	O
2	O
which	O
can	O
be	O
overcome	O
by	O
using	O
an	O
upwind	B-Algorithm
scheme	I-Algorithm
to	O
give	O
a	O
reasonable	O
result	O
.	O
</s>
<s>
Therefore	O
the	O
upwind	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
is	O
applicable	O
for	O
Pe>2	O
for	O
positive	O
flow	O
and	O
Pe	O
<	O
2	O
for	O
negative	O
flow	O
.	O
</s>
<s>
The	O
upwind	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
formulation	O
is	O
conservative	O
.	O
</s>
<s>
As	O
the	O
coefficients	O
of	O
the	O
discretised	B-Algorithm
equation	O
are	O
always	O
positive	O
hence	O
satisfying	O
the	O
requirements	O
for	O
boundedness	O
and	O
also	O
the	O
coefficient	O
matrix	O
is	O
diagonally	O
dominant	O
therefore	O
no	O
irregularities	O
occur	O
in	O
the	O
solution	O
.	O
</s>
<s>
Distribution	O
of	O
transported	O
properties	O
become	O
marked	O
giving	O
diffusion-like	O
appearance	O
,	O
called	O
as	O
the	O
false	B-Algorithm
diffusion	I-Algorithm
.	O
</s>
<s>
Refinement	O
of	O
grid	O
serves	O
in	O
overcoming	O
the	O
issue	O
of	O
false	B-Algorithm
diffusion	I-Algorithm
.	O
</s>
<s>
With	O
decrease	O
in	O
the	O
grid	O
size	O
,	O
false	B-Algorithm
diffusion	I-Algorithm
decrease	O
thus	O
increasing	O
the	O
accuracy	O
.	O
</s>
