<s>
The	O
answers	O
delivered	O
are	O
,	O
however	O
,	O
usually	O
qualitatively	O
different	O
since	O
dynamical	O
and	O
geometric	O
similitude	O
are	O
difficult	O
to	O
enforce	O
simultaneously	O
between	O
the	O
lab	O
experiment	O
and	O
the	O
prototype	B-Application
.	O
</s>
<s>
The	O
central	O
process	O
in	O
CFD	O
is	O
the	O
process	O
of	O
discretization	B-Algorithm
,	O
i.e.	O
</s>
<s>
Errors	O
creep	O
in	O
during	O
the	O
discretization	B-Algorithm
process	O
.	O
</s>
<s>
Various	O
discretization	B-Algorithm
schemes	O
have	O
been	O
developed	O
to	O
cope	O
with	O
a	O
variety	O
of	O
issues	O
.	O
</s>
<s>
The	O
most	O
notable	O
for	O
our	O
purposes	O
are	O
:	O
finite	B-Algorithm
difference	I-Algorithm
methods	I-Algorithm
,	O
finite	O
volume	O
methods	O
,	O
finite	B-Application
element	I-Application
methods	I-Application
,	O
and	O
spectral	B-Algorithm
methods	I-Algorithm
.	O
</s>
<s>
Most	O
FDM	B-Algorithm
used	O
in	O
practice	O
are	O
at	O
least	O
second	O
order	O
accurate	O
except	O
in	O
very	O
special	O
circumstances	O
.	O
</s>
<s>
Finite	B-Algorithm
Difference	I-Algorithm
method	I-Algorithm
is	O
still	O
the	O
most	O
popular	O
numerical	O
method	O
for	O
solution	O
of	O
PDEs	O
because	O
of	O
their	O
simplicity	O
,	O
efficiency	O
and	O
low	O
computational	O
cost	O
.	O
</s>
<s>
The	O
finite	B-Application
element	I-Application
method	I-Application
was	O
designed	O
to	O
deal	O
with	O
problem	O
with	O
complicated	O
computational	O
regions	O
.	O
</s>
<s>
The	O
discretization	B-Algorithm
step	O
proceeds	O
by	O
dividing	O
the	O
computational	O
domain	O
into	O
elements	O
of	O
triangular	O
or	O
rectangular	O
shape	O
.	O
</s>
<s>
The	O
CFD	O
community	O
adopted	O
the	O
FEM	B-Application
in	O
the	O
1980s	O
when	O
reliable	O
methods	O
for	O
dealing	O
with	O
advection	O
dominated	O
problems	O
were	O
devised	O
.	O
</s>
<s>
Both	O
finite	B-Application
element	I-Application
and	O
finite	B-Algorithm
difference	I-Algorithm
methods	I-Algorithm
are	O
low	O
order	O
methods	O
,	O
usually	O
of	O
2nd4th	O
order	O
,	O
and	O
have	O
local	O
approximation	O
property	O
.	O
</s>
<s>
In	O
contrast	O
,	O
spectral	B-Algorithm
method	I-Algorithm
have	O
global	O
approximation	O
property	O
.	O
</s>
<s>
Spectral	B-Algorithm
methods	I-Algorithm
are	O
mostly	O
used	O
in	O
the	O
computations	O
of	O
homogeneous	O
turbulence	O
,	O
and	O
require	O
relatively	O
simple	O
geometries	O
.	O
</s>
<s>
Atmospheric	O
model	O
have	O
also	O
adopted	O
spectral	B-Algorithm
methods	I-Algorithm
because	O
of	O
their	O
convergence	O
properties	O
and	O
the	O
regular	O
spherical	O
shape	O
of	O
their	O
computational	O
domain	O
.	O
</s>
<s>
The	O
CPU	B-Device
time	O
to	O
solve	O
the	O
system	O
of	O
equations	O
differs	O
substantially	O
from	O
method	O
to	O
method	O
.	O
</s>
<s>
Finite	O
differences	O
are	O
usually	O
the	O
cheapest	O
on	O
a	O
per	O
grid	O
point	O
basis	O
followed	O
by	O
the	O
finite	B-Application
element	I-Application
method	I-Application
and	O
spectral	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
Spectral	B-Algorithm
methods	I-Algorithm
deliver	O
more	O
accuracy	O
on	O
a	O
per	O
grid	O
point	O
basis	O
than	O
either	O
FEM	B-Application
or	O
FDM	B-Algorithm
.	O
</s>
