<s>
In	O
applied	O
mathematics	O
,	O
the	O
central	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
is	O
a	O
finite	B-Algorithm
difference	I-Algorithm
method	I-Algorithm
that	O
optimizes	O
the	O
approximation	O
for	O
the	O
differential	O
operator	O
in	O
the	O
central	O
node	O
of	O
the	O
considered	O
patch	O
and	O
provides	O
numerical	O
solutions	O
to	O
differential	O
equations	O
.	O
</s>
<s>
The	O
right	O
side	O
of	O
the	O
convection-diffusion	O
equation	O
,	O
which	O
basically	O
highlights	O
the	O
diffusion	O
terms	O
,	O
can	O
be	O
represented	O
using	O
central	B-Algorithm
difference	I-Algorithm
approximation	I-Algorithm
.	O
</s>
<s>
In	O
a	O
central	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
,	O
we	O
try	O
linear	O
interpolation	O
to	O
compute	O
cell	O
face	O
values	O
for	O
convection	O
terms	O
.	O
</s>
<s>
Conservation	O
is	O
ensured	O
in	O
central	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
since	O
overall	O
flux	O
balance	O
is	O
obtained	O
by	O
summing	O
the	O
net	O
flux	O
through	O
each	O
control	O
volume	O
taking	O
into	O
account	O
the	O
boundary	O
fluxes	O
for	O
the	O
control	O
volumes	O
around	O
nodes	O
1	O
and	O
4	O
.	O
</s>
<s>
Central	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
satisfies	O
first	O
condition	O
of	O
boundedness	B-Algorithm
.	O
</s>
<s>
Another	O
essential	O
requirement	O
for	O
boundedness	B-Algorithm
is	O
that	O
all	O
coefficients	O
of	O
the	O
discretised	O
equations	O
should	O
have	O
the	O
same	O
sign	O
(	O
usually	O
all	O
positive	O
)	O
.	O
</s>
<s>
But	O
central	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
does	O
not	O
possess	O
transportiveness	O
at	O
higher	O
pe	O
since	O
Φ	O
at	O
a	O
point	O
is	O
average	O
of	O
neighbouring	O
nodes	O
for	O
all	O
Pe	O
.	O
</s>
<s>
The	O
Taylor	O
series	O
truncation	O
error	O
of	O
the	O
central	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
is	O
second	O
order	O
.	O
</s>
<s>
Central	B-Algorithm
differencing	I-Algorithm
scheme	I-Algorithm
will	O
be	O
accurate	O
only	O
if	O
Pe	O
<	O
2	O
.	O
</s>
<s>
Leads	O
to	O
oscillations	B-Algorithm
in	O
the	O
solution	O
or	O
divergence	O
if	O
the	O
local	O
Peclet	O
number	O
is	O
larger	O
than	O
2	O
.	O
</s>
