<s>
The	O
extended	B-Algorithm
discrete	I-Algorithm
element	I-Algorithm
method	I-Algorithm
(	O
XDEM	B-Algorithm
)	O
is	O
a	O
numerical	O
technique	O
that	O
extends	O
the	O
dynamics	O
of	O
granular	O
material	O
or	O
particles	O
as	O
described	O
through	O
the	O
classical	O
discrete	B-Algorithm
element	I-Algorithm
method	I-Algorithm
(	O
DEM	O
)	O
(	O
Cundall	O
and	O
Allen	O
)	O
by	O
additional	O
properties	O
such	O
as	O
the	O
thermodynamic	O
state	O
,	O
stress/strain	O
or	O
electro-magnetic	O
field	O
for	O
each	O
particle	O
.	O
</s>
<s>
Contrary	O
to	O
a	O
continuum	O
mechanics	O
concept	O
,	O
the	O
XDEM	B-Algorithm
aims	O
at	O
resolving	O
the	O
particulate	O
phase	O
with	O
its	O
various	O
processes	O
attached	O
to	O
the	O
particles	O
.	O
</s>
<s>
While	O
the	O
discrete	B-Algorithm
element	I-Algorithm
method	I-Algorithm
predicts	O
position	O
and	O
orientation	O
in	O
space	O
and	O
time	O
for	O
each	O
particle	O
,	O
the	O
extended	B-Algorithm
discrete	I-Algorithm
element	I-Algorithm
method	I-Algorithm
additionally	O
estimates	O
properties	O
such	O
as	O
internal	O
temperature	O
and/or	O
species	O
distribution	O
or	O
mechanical	O
impact	O
with	O
structures	O
.	O
</s>
<s>
and	O
early	O
1960s	O
by	O
Rahman	O
may	O
be	O
regarded	O
as	O
a	O
first	O
step	O
toward	O
the	O
extended	B-Algorithm
discrete	I-Algorithm
element	I-Algorithm
method	I-Algorithm
,	O
although	O
the	O
forces	O
due	O
to	O
collisions	O
between	O
particles	O
were	O
replaced	O
by	O
energy	O
potentials	O
e.g.	O
</s>
<s>
It	O
has	O
seen	O
a	O
mayor	O
development	O
in	O
last	O
two	O
decades	O
and	O
describes	O
motion	O
of	O
the	O
solid	O
phase	O
by	O
the	O
Discrete	B-Algorithm
Element	I-Algorithm
Method	I-Algorithm
(	O
DEM	O
)	O
on	O
an	O
individual	O
particle	O
scale	O
and	O
the	O
remaining	O
phases	O
are	O
treated	O
by	O
the	O
Navier-Stokes	O
equations	O
.	O
</s>
<s>
The	O
theoretical	O
foundation	O
for	O
the	O
XDEM	B-Algorithm
was	O
developed	O
in	O
1999	O
by	O
Peters	O
,	O
who	O
described	O
incineration	O
of	O
a	O
wooden	O
moving	O
bed	O
on	O
a	O
forward	O
acting	O
grate	O
.	O
</s>
<s>
Numerical	O
simulation	O
of	O
fluid	O
injection	O
into	O
a	O
gaseous	O
environment	O
nowadays	O
is	O
adopted	O
by	O
a	O
large	O
number	O
of	O
CFD-codes	O
such	O
as	O
Simcenter	B-Algorithm
STAR-CCM	I-Algorithm
+	I-Algorithm
,	O
Ansys	B-Application
and	O
AVL-Fire	O
.	O
</s>
<s>
XDEM	B-Algorithm
provides	O
a	O
solution	O
for	O
some	O
of	O
those	O
engineering	O
applications	O
.	O
</s>
<s>
However	O
,	O
there	O
exist	O
scenarios	O
for	O
which	O
it	O
is	O
difficult	O
to	O
arrange	O
the	O
coefficients	O
of	O
combined	O
differential	O
equations	O
in	O
one	O
matrix	B-Architecture
.	O
</s>
<s>
Within	O
the	O
staggered	O
concept	O
of	O
XDEM	B-Algorithm
,	O
continuous	O
fields	O
are	O
described	O
by	O
the	O
solution	O
the	O
respective	O
continuous	O
(	O
conservation	O
)	O
equations	O
.	O
</s>
<s>
Major	O
conservation	O
principles	O
with	O
their	O
equations	O
and	O
variables	O
to	O
be	O
solved	O
for	O
and	O
that	O
are	O
employed	O
to	O
an	O
individual	O
particle	O
within	O
XDEM	B-Algorithm
are	O
listed	O
in	O
the	O
following	O
table	O
.	O
</s>
<s>
Initially	O
,	O
such	O
studies	O
were	O
limited	O
to	O
simple	O
flow	O
configurations	O
as	O
pointed	O
out	O
by	O
Hoomans	O
,	O
however	O
,	O
Chu	O
and	O
Yu	O
demonstrated	O
that	O
the	O
method	O
could	O
be	O
applied	O
to	O
a	O
complex	O
flow	O
configuration	O
consisting	O
of	O
a	O
fluidized	O
bed	O
,	O
conveyor	O
belt	O
and	O
a	O
cyclone	B-Device
.	O
</s>
<s>
modelled	O
the	O
complex	O
flow	O
of	O
air	O
,	O
water	O
,	O
coal	O
and	O
magnetite	O
particles	O
of	O
different	O
sizes	O
in	O
a	O
dense	O
medium	O
cyclone	B-Device
(	O
DMC	O
)	O
.	O
</s>
<s>
Further	O
applications	O
of	O
XDEM	B-Algorithm
include	O
thermal	O
conversion	O
of	O
biomass	O
on	O
a	O
backward	O
and	O
forward	O
acting	O
grate	O
.	O
</s>
