<s>
The	O
multiphase	B-Algorithm
particle-in-cell	I-Algorithm
method	I-Algorithm
(	O
MP-PIC	O
)	O
is	O
a	O
numerical	O
method	O
for	O
modeling	O
particle-fluid	O
and	O
particle-particle	O
interactions	O
in	O
a	O
computational	O
fluid	O
dynamics	O
(	O
CFD	O
)	O
calculation	O
.	O
</s>
<s>
The	O
MP-PIC	O
method	O
achieves	O
greater	O
stability	O
than	O
its	O
particle-in-cell	B-Algorithm
predecessor	O
by	O
simultaneously	O
treating	O
the	O
solid	O
particles	O
as	O
computational	O
particles	O
and	O
as	O
a	O
continuum	O
.	O
</s>
<s>
The	O
multiphase	O
particle-in-cell	B-Algorithm
(	O
MP-PIC	O
)	O
method	O
was	O
originally	O
developed	O
for	O
a	O
one-dimensional	O
case	O
in	O
the	O
mid-1990s	O
by	O
P.J.	O
</s>
<s>
The	O
multiphase	B-Algorithm
particle-in-cell	I-Algorithm
method	I-Algorithm
assumes	O
an	O
incompressible	O
fluid	O
phase	O
with	O
the	O
corresponding	O
continuity	O
equation	O
,	O
</s>
<s>
The	O
use	O
of	O
the	O
computational	O
particle	O
in	O
the	O
Multiphase	B-Algorithm
Particle-in-Cell	I-Algorithm
method	I-Algorithm
allows	O
a	O
full	O
particle	O
size	O
distribution	O
(	O
PSD	O
)	O
to	O
be	O
modeled	O
within	O
the	O
system	O
as	O
well	O
as	O
the	O
modeling	O
of	O
polydisperse	O
solids	O
.	O
</s>
<s>
Assuming	O
a	O
rectilinear	O
grid	O
consisting	O
of	O
rectangular	O
cuboid	B-General_Concept
cells	O
,	O
the	O
scalar	O
particle	O
properties	O
are	O
interpolated	O
to	O
the	O
cell	O
centers	O
while	O
the	O
vector	O
properties	O
are	O
interpolated	O
to	O
cell	O
faces	O
.	O
</s>
<s>
Reaction	O
kinetics	O
dependent	O
on	O
particle	O
density	O
,	O
surface	O
area	O
,	O
or	O
volume	O
can	O
be	O
included	O
as	O
well	O
for	O
applications	O
in	O
catalysis	O
,	O
gasification	O
,	O
or	O
solid	B-Algorithm
deposition	I-Algorithm
.	O
</s>
