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fix_lb_pc.cpp
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rLAMMPS lammps
fix_lb_pc.cpp
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/* ----------------------------------------------------------------------
LAMMPS - Large-scale Atomic/Molecular Massively Parallel Simulator
http://lammps.sandia.gov, Sandia National Laboratories
Steve Plimpton, sjplimp@sandia.gov
Copyright (2003) Sandia Corporation. Under the terms of Contract
DE-AC04-94AL85000 with Sandia Corporation, the U.S. Government retains
certain rights in this software. This software is distributed under
the GNU General Public License.
See the README file in the top-level LAMMPS directory.
------------------------------------------------------------------------- */
/* ----------------------------------------------------------------------
Contributing authors: Frances Mackay, Santtu Ollila, Colin Denniston (UWO)
------------------------------------------------------------------------- */
#include "math.h"
#include "stdio.h"
#include "string.h"
#include "fix_lb_pc.h"
#include "atom.h"
#include "force.h"
#include "update.h"
#include "respa.h"
#include "error.h"
#include "memory.h"
#include "comm.h"
#include "domain.h"
#include "fix_lb_fluid.h"
#include "modify.h"
#include "mpi.h"
#include "group.h"
using
namespace
LAMMPS_NS
;
using
namespace
FixConst
;
/* ---------------------------------------------------------------------- */
FixLbPC
::
FixLbPC
(
LAMMPS
*
lmp
,
int
narg
,
char
**
arg
)
:
Fix
(
lmp
,
narg
,
arg
)
{
if
(
narg
<
3
)
error
->
all
(
FLERR
,
"Illegal fix lb/pc command"
);
time_integrate
=
1
;
// perform initial allocation of atom-based array
// register with Atom class
force_old
=
NULL
;
up
=
NULL
;
up_old
=
NULL
;
grow_arrays
(
atom
->
nmax
);
atom
->
add_callback
(
0
);
Gamma_MD
=
new
double
[
atom
->
ntypes
+
1
];
int
groupbit_lb_fluid
=
0
;
for
(
int
ifix
=
0
;
ifix
<
modify
->
nfix
;
ifix
++
)
if
(
strcmp
(
modify
->
fix
[
ifix
]
->
style
,
"lb/fluid"
)
==
0
){
fix_lb_fluid
=
(
FixLbFluid
*
)
modify
->
fix
[
ifix
];
groupbit_lb_fluid
=
group
->
bitmask
[
modify
->
fix
[
ifix
]
->
igroup
];
}
if
(
groupbit_lb_fluid
==
0
)
error
->
all
(
FLERR
,
"the lb/fluid fix must also be used if using the lb/pc fix"
);
int
*
mask
=
atom
->
mask
;
int
nlocal
=
atom
->
nlocal
;
int
print_warning
=
0
;
for
(
int
j
=
0
;
j
<
nlocal
;
j
++
){
if
((
mask
[
j
]
&
groupbit
)
&&
!
(
mask
[
j
]
&
groupbit_lb_fluid
))
error
->
one
(
FLERR
,
"can only use the lb/pc fix for an atom if also using the lb/fluid fix for that atom"
);
}
}
/* ---------------------------------------------------------------------- */
FixLbPC
::~
FixLbPC
()
{
atom
->
delete_callback
(
id
,
0
);
memory
->
destroy
(
force_old
);
memory
->
destroy
(
up
);
memory
->
destroy
(
up_old
);
delete
[]
Gamma_MD
;
}
/* ---------------------------------------------------------------------- */
int
FixLbPC
::
setmask
()
{
int
mask
=
0
;
mask
|=
INITIAL_INTEGRATE
;
mask
|=
FINAL_INTEGRATE
;
return
mask
;
}
/* ---------------------------------------------------------------------- */
void
FixLbPC
::
init
()
{
double
*
Gamma
=
fix_lb_fluid
->
Gamma
;
double
dm_lb
=
fix_lb_fluid
->
dm_lb
;
double
dt_lb
=
fix_lb_fluid
->
dt_lb
;
MPI_Comm_rank
(
world
,
&
me
);
dtv
=
update
->
dt
;
dtf
=
update
->
dt
*
force
->
ftm2v
;
for
(
int
i
=
0
;
i
<=
atom
->
ntypes
;
i
++
)
Gamma_MD
[
i
]
=
Gamma
[
i
]
*
dm_lb
/
dt_lb
;
}
/* ---------------------------------------------------------------------- */
void
FixLbPC
::
initial_integrate
(
int
vflag
)
{
double
dtfm
;
double
**
x
=
atom
->
x
;
double
dx
[
3
];
double
**
v
=
atom
->
v
;
double
**
f
=
atom
->
f
;
double
*
mass
=
atom
->
mass
;
double
*
rmass
=
atom
->
rmass
;
int
*
type
=
atom
->
type
;
int
*
mask
=
atom
->
mask
;
int
nlocal
=
atom
->
nlocal
;
if
(
igroup
==
atom
->
firstgroup
)
nlocal
=
atom
->
nfirst
;
compute_up
();
for
(
int
i
=
0
;
i
<
nlocal
;
i
++
){
up_old
[
i
][
0
]
=
up
[
i
][
0
];
up_old
[
i
][
1
]
=
up
[
i
][
1
];
up_old
[
i
][
2
]
=
up
[
i
][
2
];
force_old
[
i
][
0
]
=
f
[
i
][
0
];
force_old
[
i
][
1
]
=
f
[
i
][
1
];
force_old
[
i
][
2
]
=
f
[
i
][
2
];
}
if
(
rmass
){
for
(
int
i
=
0
;
i
<
nlocal
;
i
++
)
{
if
(
mask
[
i
]
&
groupbit
)
{
dtfm
=
dtf
/
rmass
[
i
];
expminusdttimesgamma
=
exp
(
-
dtv
*
Gamma_MD
[
type
[
i
]]
/
rmass
[
i
]);
dx
[
0
]
=
dtv
*
v
[
i
][
0
]
+
0.5
*
(
f
[
i
][
0
]
*
force
->
ftm2v
-
Gamma_MD
[
type
[
i
]]
*
(
v
[
i
][
0
]
-
up
[
i
][
0
]))
*
dtv
*
dtv
/
rmass
[
i
];
dx
[
1
]
=
dtv
*
v
[
i
][
1
]
+
0.5
*
(
f
[
i
][
1
]
*
force
->
ftm2v
-
Gamma_MD
[
type
[
i
]]
*
(
v
[
i
][
1
]
-
up
[
i
][
1
]))
*
dtv
*
dtv
/
rmass
[
i
];
dx
[
2
]
=
dtv
*
v
[
i
][
2
]
+
0.5
*
(
f
[
i
][
2
]
*
force
->
ftm2v
-
Gamma_MD
[
type
[
i
]]
*
(
v
[
i
][
2
]
-
up
[
i
][
2
]))
*
dtv
*
dtv
/
rmass
[
i
];
x
[
i
][
0
]
+=
dx
[
0
];
x
[
i
][
1
]
+=
dx
[
1
];
x
[
i
][
2
]
+=
dx
[
2
];
// Approximation for v
if
(
Gamma_MD
[
type
[
i
]]
==
0.0
){
v
[
i
][
0
]
+=
f
[
i
][
0
]
*
dtfm
;
v
[
i
][
1
]
+=
f
[
i
][
1
]
*
dtfm
;
v
[
i
][
2
]
+=
f
[
i
][
2
]
*
dtfm
;
}
else
{
v
[
i
][
0
]
=
(
v
[
i
][
0
]
-
up
[
i
][
0
]
-
f
[
i
][
0
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]])
*
expminusdttimesgamma
+
f
[
i
][
0
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
0
];
v
[
i
][
1
]
=
(
v
[
i
][
1
]
-
up
[
i
][
1
]
-
f
[
i
][
1
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]])
*
expminusdttimesgamma
+
f
[
i
][
1
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
1
];
v
[
i
][
2
]
=
(
v
[
i
][
2
]
-
up
[
i
][
2
]
-
f
[
i
][
2
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]])
*
expminusdttimesgamma
+
f
[
i
][
2
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
2
];
}
}
}
}
else
{
// this does NOT take varying masses into account
for
(
int
i
=
0
;
i
<
nlocal
;
i
++
)
{
if
(
mask
[
i
]
&
groupbit
)
{
dtfm
=
dtf
/
mass
[
type
[
i
]];
expminusdttimesgamma
=
exp
(
-
dtv
*
Gamma_MD
[
type
[
i
]]
/
mass
[
type
[
i
]]);
dx
[
0
]
=
dtv
*
v
[
i
][
0
]
+
0.5
*
(
f
[
i
][
0
]
*
force
->
ftm2v
-
Gamma_MD
[
type
[
i
]]
*
(
v
[
i
][
0
]
-
up
[
i
][
0
]))
*
dtv
*
dtv
/
mass
[
type
[
i
]];
dx
[
1
]
=
dtv
*
v
[
i
][
1
]
+
0.5
*
(
f
[
i
][
1
]
*
force
->
ftm2v
-
Gamma_MD
[
type
[
i
]]
*
(
v
[
i
][
1
]
-
up
[
i
][
1
]))
*
dtv
*
dtv
/
mass
[
type
[
i
]];
dx
[
2
]
=
dtv
*
v
[
i
][
2
]
+
0.5
*
(
f
[
i
][
2
]
*
force
->
ftm2v
-
Gamma_MD
[
type
[
i
]]
*
(
v
[
i
][
2
]
-
up
[
i
][
2
]))
*
dtv
*
dtv
/
mass
[
type
[
i
]];
x
[
i
][
0
]
+=
dx
[
0
];
x
[
i
][
1
]
+=
dx
[
1
];
x
[
i
][
2
]
+=
dx
[
2
];
// Approximation for v
if
(
Gamma_MD
[
type
[
i
]]
==
0.0
){
v
[
i
][
0
]
+=
f
[
i
][
0
]
*
dtfm
;
v
[
i
][
1
]
+=
f
[
i
][
1
]
*
dtfm
;
v
[
i
][
2
]
+=
f
[
i
][
2
]
*
dtfm
;
}
else
{
v
[
i
][
0
]
=
(
v
[
i
][
0
]
-
up
[
i
][
0
]
-
f
[
i
][
0
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]])
*
expminusdttimesgamma
+
f
[
i
][
0
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
0
];
v
[
i
][
1
]
=
(
v
[
i
][
1
]
-
up
[
i
][
1
]
-
f
[
i
][
1
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]])
*
expminusdttimesgamma
+
f
[
i
][
1
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
1
];
v
[
i
][
2
]
=
(
v
[
i
][
2
]
-
up
[
i
][
2
]
-
f
[
i
][
2
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]])
*
expminusdttimesgamma
+
f
[
i
][
2
]
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
2
];
}
}
}
}
}
/* ---------------------------------------------------------------------- */
void
FixLbPC
::
final_integrate
()
{
double
dtfm
;
double
**
v
=
atom
->
v
;
double
**
f
=
atom
->
f
;
double
*
mass
=
atom
->
mass
;
double
*
rmass
=
atom
->
rmass
;
int
*
type
=
atom
->
type
;
int
*
mask
=
atom
->
mask
;
int
nlocal
=
atom
->
nlocal
;
if
(
igroup
==
atom
->
firstgroup
)
nlocal
=
atom
->
nfirst
;
compute_up
();
if
(
rmass
){
for
(
int
i
=
0
;
i
<
nlocal
;
i
++
)
{
if
(
mask
[
i
]
&
groupbit
)
{
dtfm
=
dtf
/
rmass
[
i
];
expminusdttimesgamma
=
exp
(
-
dtv
*
Gamma_MD
[
type
[
i
]]
/
rmass
[
i
]);
DMDcoeff
=
(
dtv
-
rmass
[
i
]
*
(
1.0
-
expminusdttimesgamma
)
/
Gamma_MD
[
type
[
i
]]);
if
(
Gamma_MD
[
type
[
i
]]
==
0.0
){
v
[
i
][
0
]
+=
0.5
*
(
f
[
i
][
0
]
-
force_old
[
i
][
0
])
*
dtfm
;
v
[
i
][
1
]
+=
0.5
*
(
f
[
i
][
1
]
-
force_old
[
i
][
1
])
*
dtfm
;
v
[
i
][
2
]
+=
0.5
*
(
f
[
i
][
2
]
-
force_old
[
i
][
2
])
*
dtfm
;
}
else
{
v
[
i
][
0
]
+=
DMDcoeff
*
((
f
[
i
][
0
]
-
force_old
[
i
][
0
])
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
0
]
-
up_old
[
i
][
0
])
/
dtv
;
v
[
i
][
1
]
+=
DMDcoeff
*
((
f
[
i
][
1
]
-
force_old
[
i
][
1
])
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
1
]
-
up_old
[
i
][
1
])
/
dtv
;
v
[
i
][
2
]
+=
DMDcoeff
*
((
f
[
i
][
2
]
-
force_old
[
i
][
2
])
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
2
]
-
up_old
[
i
][
2
])
/
dtv
;
}
}
}
}
else
{
// this does NOT take varying masses into account
for
(
int
i
=
0
;
i
<
nlocal
;
i
++
)
{
if
(
mask
[
i
]
&
groupbit
)
{
dtfm
=
dtf
/
mass
[
type
[
i
]];
expminusdttimesgamma
=
exp
(
-
dtv
*
Gamma_MD
[
type
[
i
]]
/
mass
[
type
[
i
]]);
DMDcoeff
=
(
dtv
-
mass
[
type
[
i
]]
*
(
1.0
-
expminusdttimesgamma
)
/
Gamma_MD
[
type
[
i
]]);
if
(
Gamma_MD
[
type
[
i
]]
==
0.0
){
v
[
i
][
0
]
+=
0.5
*
(
f
[
i
][
0
]
-
force_old
[
i
][
0
])
*
dtfm
;
v
[
i
][
1
]
+=
0.5
*
(
f
[
i
][
1
]
-
force_old
[
i
][
1
])
*
dtfm
;
v
[
i
][
2
]
+=
0.5
*
(
f
[
i
][
2
]
-
force_old
[
i
][
2
])
*
dtfm
;
}
else
{
v
[
i
][
0
]
+=
DMDcoeff
*
((
f
[
i
][
0
]
-
force_old
[
i
][
0
])
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
0
]
-
up_old
[
i
][
0
])
/
dtv
;
v
[
i
][
1
]
+=
DMDcoeff
*
((
f
[
i
][
1
]
-
force_old
[
i
][
1
])
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
1
]
-
up_old
[
i
][
1
])
/
dtv
;
v
[
i
][
2
]
+=
DMDcoeff
*
((
f
[
i
][
2
]
-
force_old
[
i
][
2
])
*
force
->
ftm2v
/
Gamma_MD
[
type
[
i
]]
+
up
[
i
][
2
]
-
up_old
[
i
][
2
])
/
dtv
;
}
}
}
}
}
/* ----------------------------------------------------------------------
allocate atom-based array
------------------------------------------------------------------------- */
void
FixLbPC
::
grow_arrays
(
int
nmax
)
{
memory
->
grow
(
force_old
,
nmax
,
3
,
"FixLbPC:force_old"
);
memory
->
grow
(
up_old
,
nmax
,
3
,
"FixLbPC:up_old"
);
memory
->
grow
(
up
,
nmax
,
3
,
"FixLbPC:up"
);
}
/* ----------------------------------------------------------------------
copy values within local atom-based array
------------------------------------------------------------------------- */
void
FixLbPC
::
copy_arrays
(
int
i
,
int
j
,
int
delflag
)
{
force_old
[
j
][
0
]
=
force_old
[
i
][
0
];
force_old
[
j
][
1
]
=
force_old
[
i
][
1
];
force_old
[
j
][
2
]
=
force_old
[
i
][
2
];
up_old
[
j
][
0
]
=
up_old
[
i
][
0
];
up_old
[
j
][
1
]
=
up_old
[
i
][
1
];
up_old
[
j
][
2
]
=
up_old
[
i
][
2
];
up
[
j
][
0
]
=
up
[
i
][
0
];
up
[
j
][
1
]
=
up
[
i
][
1
];
up
[
j
][
2
]
=
up
[
i
][
2
];
}
/* ----------------------------------------------------------------------
pack values in local atom-based array for exchange with another proc
------------------------------------------------------------------------- */
int
FixLbPC
::
pack_exchange
(
int
i
,
double
*
buf
)
{
buf
[
0
]
=
force_old
[
i
][
0
];
buf
[
1
]
=
force_old
[
i
][
1
];
buf
[
2
]
=
force_old
[
i
][
2
];
buf
[
3
]
=
up_old
[
i
][
0
];
buf
[
4
]
=
up_old
[
i
][
1
];
buf
[
5
]
=
up_old
[
i
][
2
];
buf
[
6
]
=
up
[
i
][
0
];
buf
[
7
]
=
up
[
i
][
1
];
buf
[
8
]
=
up
[
i
][
2
];
return
9
;
}
/* ----------------------------------------------------------------------
unpack values in local atom-based array from exchange with another proc
------------------------------------------------------------------------- */
int
FixLbPC
::
unpack_exchange
(
int
nlocal
,
double
*
buf
)
{
force_old
[
nlocal
][
0
]
=
buf
[
0
];
force_old
[
nlocal
][
1
]
=
buf
[
1
];
force_old
[
nlocal
][
2
]
=
buf
[
2
];
up_old
[
nlocal
][
0
]
=
buf
[
3
];
up_old
[
nlocal
][
1
]
=
buf
[
4
];
up_old
[
nlocal
][
2
]
=
buf
[
5
];
up
[
nlocal
][
0
]
=
buf
[
6
];
up
[
nlocal
][
1
]
=
buf
[
7
];
up
[
nlocal
][
2
]
=
buf
[
8
];
return
9
;
}
/* ---------------------------------------------------------------------- */
void
FixLbPC
::
compute_up
(
void
)
{
int
*
mask
=
atom
->
mask
;
int
nlocal
=
atom
->
nlocal
;
double
**
x
=
atom
->
x
;
int
i
,
k
;
int
ix
,
iy
,
iz
;
int
ixp
,
iyp
,
izp
;
double
dx1
,
dy1
,
dz1
;
int
isten
,
ii
,
jj
,
kk
;
double
r
,
rsq
,
weightx
,
weighty
,
weightz
;
double
****
u_lb
=
fix_lb_fluid
->
u_lb
;
int
subNbx
=
fix_lb_fluid
->
subNbx
;
int
subNby
=
fix_lb_fluid
->
subNby
;
int
subNbz
=
fix_lb_fluid
->
subNbz
;
double
dx_lb
=
fix_lb_fluid
->
dx_lb
;
double
dt_lb
=
fix_lb_fluid
->
dt_lb
;
double
FfP
[
64
];
int
trilinear_stencil
=
fix_lb_fluid
->
trilinear_stencil
;
for
(
i
=
0
;
i
<
nlocal
;
i
++
){
if
(
mask
[
i
]
&
groupbit
){
//Calculate nearest leftmost grid point.
//Since array indices from 1 to subNb-2 correspond to the
// local subprocessor domain (not indices from 0), use the
// ceiling value.
ix
=
(
int
)
ceil
((
x
[
i
][
0
]
-
domain
->
sublo
[
0
])
/
dx_lb
);
iy
=
(
int
)
ceil
((
x
[
i
][
1
]
-
domain
->
sublo
[
1
])
/
dx_lb
);
iz
=
(
int
)
ceil
((
x
[
i
][
2
]
-
domain
->
sublo
[
2
])
/
dx_lb
);
//Calculate distances to the nearest points.
dx1
=
x
[
i
][
0
]
-
(
domain
->
sublo
[
0
]
+
(
ix
-
1
)
*
dx_lb
);
dy1
=
x
[
i
][
1
]
-
(
domain
->
sublo
[
1
]
+
(
iy
-
1
)
*
dx_lb
);
dz1
=
x
[
i
][
2
]
-
(
domain
->
sublo
[
2
]
+
(
iz
-
1
)
*
dx_lb
);
// Need to convert these to lattice units:
dx1
=
dx1
/
dx_lb
;
dy1
=
dy1
/
dx_lb
;
dz1
=
dz1
/
dx_lb
;
up
[
i
][
0
]
=
0.0
;
up
[
i
][
1
]
=
0.0
;
up
[
i
][
2
]
=
0.0
;
if
(
trilinear_stencil
==
0
){
isten
=
0
;
for
(
ii
=-
1
;
ii
<
3
;
ii
++
){
rsq
=
(
-
dx1
+
ii
)
*
(
-
dx1
+
ii
);
if
(
rsq
>=
4
)
weightx
=
0.0
;
else
{
r
=
sqrt
(
rsq
);
if
(
rsq
>
1
){
weightx
=
(
5.0
-
2.0
*
r
-
sqrt
(
-
7.0
+
12.0
*
r
-
4.0
*
rsq
))
/
8.
;
}
else
{
weightx
=
(
3.0
-
2.0
*
r
+
sqrt
(
1.0
+
4.0
*
r
-
4.0
*
rsq
))
/
8.
;
}
}
for
(
jj
=-
1
;
jj
<
3
;
jj
++
){
rsq
=
(
-
dy1
+
jj
)
*
(
-
dy1
+
jj
);
if
(
rsq
>=
4
)
weighty
=
0.0
;
else
{
r
=
sqrt
(
rsq
);
if
(
rsq
>
1
){
weighty
=
(
5.0
-
2.0
*
r
-
sqrt
(
-
7.0
+
12.0
*
r
-
4.0
*
rsq
))
/
8.
;
}
else
{
weighty
=
(
3.0
-
2.0
*
r
+
sqrt
(
1.0
+
4.0
*
r
-
4.0
*
rsq
))
/
8.
;
}
}
for
(
kk
=-
1
;
kk
<
3
;
kk
++
){
rsq
=
(
-
dz1
+
kk
)
*
(
-
dz1
+
kk
);
if
(
rsq
>=
4
)
weightz
=
0.0
;
else
{
r
=
sqrt
(
rsq
);
if
(
rsq
>
1
){
weightz
=
(
5.0
-
2.0
*
r
-
sqrt
(
-
7.0
+
12.0
*
r
-
4.0
*
rsq
))
/
8.
;
}
else
{
weightz
=
(
3.0
-
2.0
*
r
+
sqrt
(
1.0
+
4.0
*
r
-
4.0
*
rsq
))
/
8.
;
}
}
ixp
=
ix
+
ii
;
iyp
=
iy
+
jj
;
izp
=
iz
+
kk
;
if
(
ixp
==-
1
)
ixp
=
subNbx
+
2
;
if
(
iyp
==-
1
)
iyp
=
subNby
+
2
;
if
(
izp
==-
1
)
izp
=
subNbz
+
2
;
FfP
[
isten
]
=
weightx
*
weighty
*
weightz
;
// interpolated velocity based on delta function.
for
(
k
=
0
;
k
<
3
;
k
++
){
up
[
i
][
k
]
+=
u_lb
[
ixp
][
iyp
][
izp
][
k
]
*
FfP
[
isten
];
}
}
}
}
}
else
{
FfP
[
0
]
=
(
1.
-
dx1
)
*
(
1.
-
dy1
)
*
(
1.
-
dz1
);
FfP
[
1
]
=
(
1.
-
dx1
)
*
(
1.
-
dy1
)
*
dz1
;
FfP
[
2
]
=
(
1.
-
dx1
)
*
dy1
*
(
1.
-
dz1
);
FfP
[
3
]
=
(
1.
-
dx1
)
*
dy1
*
dz1
;
FfP
[
4
]
=
dx1
*
(
1.
-
dy1
)
*
(
1.
-
dz1
);
FfP
[
5
]
=
dx1
*
(
1.
-
dy1
)
*
dz1
;
FfP
[
6
]
=
dx1
*
dy1
*
(
1.
-
dz1
);
FfP
[
7
]
=
dx1
*
dy1
*
dz1
;
ixp
=
(
ix
+
1
);
iyp
=
(
iy
+
1
);
izp
=
(
iz
+
1
);
for
(
k
=
0
;
k
<
3
;
k
++
)
{
// tri-linearly interpolated velocity at node
up
[
i
][
k
]
=
u_lb
[
ix
][
iy
][
iz
][
k
]
*
FfP
[
0
]
+
u_lb
[
ix
][
iy
][
izp
][
k
]
*
FfP
[
1
]
+
u_lb
[
ix
][
iyp
][
iz
][
k
]
*
FfP
[
2
]
+
u_lb
[
ix
][
iyp
][
izp
][
k
]
*
FfP
[
3
]
+
u_lb
[
ixp
][
iy
][
iz
][
k
]
*
FfP
[
4
]
+
u_lb
[
ixp
][
iy
][
izp
][
k
]
*
FfP
[
5
]
+
u_lb
[
ixp
][
iyp
][
iz
][
k
]
*
FfP
[
6
]
+
u_lb
[
ixp
][
iyp
][
izp
][
k
]
*
FfP
[
7
];
}
}
for
(
k
=
0
;
k
<
3
;
k
++
)
up
[
i
][
k
]
=
up
[
i
][
k
]
*
dx_lb
/
dt_lb
;
}
}
}
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