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Nektar
Nektar
Commits
723bddaf
Commit
723bddaf
authored
Dec 04, 2016
by
Spencer Sherwin
Browse files
Updated with details of moving body outflow modifications
parent
9b42e311
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7
docs/refs.bib
docs/refs.bib
+9
0
docs/userguide/solvers/incompressiblens.tex
docs/userguide/solvers/incompressiblens.tex
+35
7
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docs/refs.bib
View file @
723bddaf
...
...
@@ 451,3 +451,12 @@ year={2011}
publisher
=
{Springer London}
}
@Article
{
BaPlGrSh16
,
author
=
{Bao, Y. and Palacios, R. and Graham, M. and Sherwin, S.J. }
,
title
=
{Generalized “thick” strip modelling for vortexinduced vibration of long flexible cylinders}
,
journal
=
{J. Comp. Phys}
,
year
=
{2016}
,
volume
=
{321}
,
pages
=
{10791097}
,
}
docs/userguide/solvers/incompressiblens.tex
View file @
723bddaf
...
...
@@ 210,12 +210,13 @@ $p=0$ which can be specified as
However when energetic vortices pass through an outflow region one can
experience instabilities as identified by the work of Dong, Karnidakis
and Chryssostomidis
\cite
{
DoKa14
}
. In this
work one impose a pressure
Dirichlet outflow condition of the form
and Chryssostomidis
\cite
{
DoKa14
}
. In this
paper they suggest to
impose a pressure
Dirichlet outflow condition of the form
\begin{equation}
p
^{
n+1
}
=
\nu
\nabla\mathbf
{
u
}^{
*,n+1
}
\cdot
\mathbf
{
n
}

\frac
{
1
}{
2
}
\mid
\mathbf
{
u
}^{
*,n+1
}
\mid
^
2 S
_
o(
\mathbf
{
n
}
\cdot
\mathbf
{
u
}^{
*,n+1
}
)
\mathbf
{
f
}_
b
^{
n+1
}
\cdot
\mathbf
{
n
}
\mid
\mathbf
{
u
}^{
*,n+1
}
\mid
^
2 S
_
o(
\mathbf
{
n
}
\cdot
\mathbf
{
u
}^{
*,n+1
}
)+
\mathbf
{
f
}_
b
^{
n+1
}
\cdot
\mathbf
{
n
}
\end{equation}
with a step function defined by
$
S
_
o
(
n
\cdot
...
...
@@ 225,13 +226,19 @@ is a nondimensional positive constant chosen to be sufficiently
small.
$
\mathbf
{
f
}_
b
$
is the forcing term in this case the analytical
conditions can be given but if these are not known explicitly, it is
set to zero, i.e.
$
\mathbf
{
f
}_
b
=
0
$
. (see the test
KovaFlow
\_
m8
\_
short
\_
HOBC.xml for a nonzero example). For the
velocity component one can specify
KovaFlow
\_
m8
\_
short
\_
HOBC.xml for a nonzero example). Note that in
the paper
\cite
{
DoKa14
}
they define this term as the negative of what
is shown here so that it could be use used to impose a default
pressure values. This does however mean that the forcing term is
imposed through the velocity components
$
u,v
$
by specifying the entry
\inltt
{
VALUE
}
(An example can be found in
ChanFlow
\_
m3
\_
VCSWeakPress
\_
ConOBC.xml). For the velocity component
one can specify
\begin{equation}
\nabla\mathbf
{
u
}^{
n+1
}
\cdot\mathbf
{
n
}
=
\frac
{
1
}{
\nu
}
\Bigl
[p
^{
n+1
}
\mathbf
{
n
}
+
\frac
{
1
}{
2
}
\mid
\mathbf
{
u
}^{
*,n+1
}
\mid
^
2 S
_
o(
\mathbf
{
n
}
\cdot
\mathbf
{
u
}^{
*,n+1
}
)
\nu
(
\nabla\cdot\mathbf
{
u
}^{
*,n+1
}
)
\mathbf
{
n
}
+
\mathbf
{
f
}_
b
^{
n+1
}
\Bigr
]
\mathbf
{
u
}^{
*,n+1
}
)
\nu
(
\nabla\cdot\mathbf
{
u
}^{
*,n+1
}
)
\mathbf
{
n
}

\mathbf
{
f
}_
b
^{
n+1
}
\Bigr
]
\end{equation}
This condition can be enforced using the
\inltt
{
USERDEFINEDTYPE
}
``HOutflow'', i.e.
...
...
@@ 245,7 +252,28 @@ This condition can be enforced using the \inltt{USERDEFINEDTYPE} ``HOutflow'', i
</BOUNDARYCONDITIONS>
\end{lstlisting}
Dong has more also suggested convective like outflow conditions in
\cite
{
Dong15
}
which can be enforced through a Robin type specification of the form
Note that in the moving body work of Bao et al.
\cite
{
BaPlGrSh16
}
some care must be made to identify when the flow over the boundary is
incoming or outgoing and so a modification of the term
\[
\frac
{
1
}{
2
}
\mid
\mathbf
{
u
}^{
*
,n
+
1
}
\mid
^
2
S
_
o
(
\mathbf
{
n
}
\cdot
\mathbf
{
u
}^{
*
,n
+
1
}
)
\]
is replaced with
\[
\frac
{
1
}{
2
}
\left
(
(
\theta
+
\alpha
_
2
)
\mid
\mathbf
{
u
}^{
*
,n
+
1
}
\mid
^
2
+
(
1

\theta
+
\alpha
_
1
)
(
\mathbf
{
u
}^{
*
,n
+
1
}
\cdot
\mathbf
{
n
}
)
\mathbf
{
u
}^{
*
,n
+
1
}
\right
)
S
_
o
(
\mathbf
{
n
}
\cdot
\mathbf
{
u
}^{
*
,n
+
1
}
)
\]
where the default values are given by
$
\theta
=
1
,
\alpha
_
1
=
0
,
\alpha
_
2
=
0
$
and these values can be set through the parameters
\inltt
{
OutflowBC
\_
theta
}
,
\inltt
{
OutflowBC
\_
alpha1
}
and
\inltt
{
OutflowBC
\_
alpha2
}
.
Dong has also suggested convective like outflow conditions in
\cite
{
Dong15
}
which can be enforced through a Robin type specification
of the form
\begin{equation}
\frac
{
\partial
\mathbf
{
u
}^{
n+1
}}{
\partial
n
}
+
\frac
{
\gamma
_
0 D
_
0
}{
\Delta
t
}
\mathbf
{
u
}^{
n+1
}
=
\frac
{
1
}{
\nu
}
\Bigl
[
\mathbf
{
f
}^{
n+1
}
+
\mathbf
{
E
}
(
\mathbf
{
n
}
,
\mathbf
{
u
}^{
*,n+1
}
) + p
^{
n+1
}
\mathbf
{
n
}

\nu
(
\nabla\cdot
\mathbf
{
u
}^{
*,n+1
}
)
\mathbf
{
n
}
...
...
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