<s>
Numerical	B-Algorithm
diffusion	I-Algorithm
is	O
a	O
difficulty	O
with	O
computer	B-Application
simulations	I-Application
of	O
continua	O
(	O
such	O
as	O
fluids	O
)	O
wherein	O
the	O
simulated	O
medium	O
exhibits	O
a	O
higher	O
diffusivity	O
than	O
the	O
true	O
medium	O
.	O
</s>
<s>
This	O
phenomenon	O
can	O
be	O
particularly	O
egregious	O
when	O
the	O
system	O
should	O
not	O
be	O
diffusive	O
at	O
all	O
,	O
for	O
example	O
an	O
ideal	O
fluid	O
acquiring	O
some	O
spurious	O
viscosity	O
in	O
a	O
numerical	B-Application
model	I-Application
.	O
</s>
<s>
In	O
Eulerian	B-Algorithm
simulations	I-Algorithm
,	O
time	O
and	O
space	O
are	O
divided	O
into	O
a	O
discrete	O
grid	O
and	O
the	O
continuous	O
differential	O
equations	O
of	O
motion	O
(	O
such	O
as	O
the	O
Navier	O
–	O
Stokes	O
equation	O
)	O
are	O
discretized	B-Algorithm
into	O
finite-difference	B-Algorithm
equations	I-Algorithm
.	O
</s>
<s>
The	O
amount	O
and	O
character	O
of	O
the	O
difference	O
depends	O
on	O
the	O
system	O
being	O
simulated	O
and	O
the	O
type	O
of	O
discretization	B-Algorithm
that	O
is	O
used	O
.	O
</s>
<s>
Most	O
fluid	O
dynamics	O
or	O
magnetohydrodynamic	O
simulations	O
seek	O
to	O
reduce	O
numerical	B-Algorithm
diffusion	I-Algorithm
to	O
the	O
minimum	O
possible	O
,	O
to	O
achieve	O
high	O
fidelity	O
—	O
but	O
under	O
certain	O
circumstances	O
diffusion	O
is	O
added	O
deliberately	O
into	O
the	O
system	O
to	O
avoid	O
singularities	O
.	O
</s>
<s>
Higher	O
order	O
numerical	O
methods	O
(	O
including	O
spectral	O
methods	O
)	O
tend	O
to	O
have	O
less	O
numerical	B-Algorithm
diffusion	I-Algorithm
than	O
low	O
order	O
methods	O
.	O
</s>
<s>
As	O
an	O
example	O
of	O
numerical	B-Algorithm
diffusion	I-Algorithm
,	O
consider	O
an	O
Eulerian	O
simulation	O
using	O
an	O
explicit	O
time-advance	O
of	O
a	O
drop	O
of	O
green	O
dye	O
diffusing	O
through	O
water	O
.	O
</s>
<s>
When	O
numerical	B-Algorithm
diffusion	I-Algorithm
applies	O
to	O
the	O
components	O
of	O
the	O
momentum	B-Algorithm
vector	O
,	O
it	O
is	O
called	O
numerical	O
viscosity	O
;	O
when	O
it	O
applies	O
to	O
a	O
magnetic	O
field	O
,	O
it	O
is	O
called	O
numerical	B-Algorithm
resistivity	I-Algorithm
.	O
</s>
<s>
These	O
inaccuracies	O
between	O
single	O
phases	O
are	O
based	O
on	O
numerical	B-Algorithm
diffusion	I-Algorithm
and	O
can	O
be	O
decreased	O
by	O
mesh	B-Algorithm
refining	O
.	O
</s>
