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Update 3.2 User interfaces
authored
Jan 09, 2021
by
Udo Ziegler
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3-NIRVANA-user-guide/3.2-User-interfaces.md
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@@ -820,7 +820,7 @@ for the type of coordinate system.
freely selectable parameter but computed selfconsistently from
the ionisation structure.*
##
#
Defining initial conditions
## Defining initial conditions
The user interface
`configUser.c`
serves to define IC for a problem.
Defining IC means assigning values to primary physical variables,
...
...
@@ -842,8 +842,8 @@ considered primary.
The mesh is represented by the master mesh pointer
`gm`
which is the
only argument passed to function
`configUser()`
. The problem-relevant
variables have to be assigned for each superblock
`g`
in
`gm`
. Recall
the explanations about the
\
[
mesh data
structure
\
]
(3.1-Code-basics
\#
mesh-data-structure).
the explanations about the
[
mesh data
structure
](
3.1-Code-basics\#mesh-data-structure
)
.
There are two types of primary variables: cell-averaged variables and
face-averaged variables. Cell-averaged variables are
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@@ -911,7 +911,7 @@ like the mass density it can be assigned at the same place. The tracer
array index,
`ic`
, runs from 0 to
`_C.tracer`
-1 where the code parameter
`_C.tracer`
gives the number of tracers
*N*
<sub>
*c*
</sub>
. Tracer
variables are dimensionless and are usually defined in the range
\[
0,
1
\]
.
\[
0,1
\]
.
Similary, species number densities,
*n*
<sub>
*s*
</sub>
, are cell-averaged
quantities. The species array index,
`is`
, runs from 0 to
`_C.species`
-1
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@@ -946,6 +946,7 @@ exact integration of the analytical expressions. The so discretized
field is per se cell-wise divergence-free. For a grid cell
(
`ix`
,
`iy`
,
`iz`
) on superblock
`g`
this means
$$
\\
mathtt{g-
>
bx
\[
iz
\]\[
iy
\]\[
ix
\]
}=
\\
frac{1}{
\\
delta
\\
,
\\
!
\\
mathcal{A}
\_
x}
\\
int
\\
limits
\_\\
mathtt{g-
>
y\[iy\]}^\\mathtt{g-
>
y
\[
iy+1
\]
}
\\
int
\\
limits
\_\\
mathtt{g-
>
z\[iz\]}^\\mathtt{g-
>
z
\[
iz+1
\]
} B
\_
x(
\\
mathtt{g-
>
x
\[
ix
\]
},y,z)h
\_
yh
\_
zdydz$$
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...
@@ -962,19 +963,19 @@ The numerical expressions for the cell face contents are:
| cell face | expression |
|:---------------------|:-----------------------------------------|
|
*δ*
𝒜
<sub>
*x*
</sub>
|
`g->hyh[ix]*g->hyh[ix]*g->dvy[iy]*g->dz`
|
|
*δ*
𝒜
<sub>
*y*
</sub>
|
`g->dax[ix]*g->hzyh[iy]*g->dz`
|
|
*δ*
𝒜
<sub>
*z*
</sub>
|
`g->dax[ix]*g->dy`
|
|
*δ*
𝒜
<sub>
*x*
</sub>
|
`g->hyh[ix]*g->hyh[ix]*g->dvy[iy]*g->dz`
|
|
*δ*
𝒜
<sub>
*y*
</sub>
|
`g->dax[ix]*g->hzyh[iy]*g->dz`
|
|
*δ*
𝒜
<sub>
*z*
</sub>
|
`g->dax[ix]*g->dy`
|
\(
2
\)
use of the magnetic vector potential
**A**
, if known, with
**B**
= ∇ ×
**A**
. When discretized in integral form this gives for the
face-averaged magnetic field components
`g->bx[iz][iy][ix]`
=
\[
*h*
<sub>
*y*
</sub>
*Δ*
<sub>
`i`
*y*
</sub>
(
*h*
<sub>
*z**y*
</sub>
*Â*
<sub>
*z*
</sub>
)−
*h*
<sub>
*y*
</sub>
*Δ*
<sub>
`i`
*z*
</sub>
*Â*
<sub>
*y*
</sub>
\]
/
*δ*
𝒜
<sub>
*x*
</sub>
`g->bx[iz][iy][ix]`
=
\[
*h*
<sub>
*y*
</sub>
*Δ*
<sub>
`i`
*y*
</sub>
(
*h*
<sub>
*z**y*
</sub>
*Â*
<sub>
*z*
</sub>
)−
*h*
<sub>
*y*
</sub>
*Δ*
<sub>
`i`
*z*
</sub>
*Â*
<sub>
*y*
</sub>
\]
/
*δ*
𝒜
<sub>
*x*
</sub>
`g->by[iz][iy][ix]`
=
\[
*Δ*
<sub>
`i`
*z*
</sub>
*Â*
<sub>
*x*
</sub>
−
*h*
<sub>
*z**y*
</sub>
*Δ*
<sub>
`i`
*x*
</sub>
(
*h*
<sub>
*y*
</sub>
*Â*
<sub>
*z*
</sub>
)
\]
/
*δ*
𝒜
<sub>
*y*
</sub>
`g->by[iz][iy][ix]`
=
\[
*Δ*
<sub>
`i`
*z*
</sub>
*Â*
<sub>
*x*
</sub>
−
*h*
<sub>
*z**y*
</sub>
*Δ*
<sub>
`i`
*x*
</sub>
(
*h*
<sub>
*y*
</sub>
*Â*
<sub>
*z*
</sub>
)
\]
/
*δ*
𝒜
<sub>
*y*
</sub>
`g->bz[iz][iy][ix]`
=
\[
*Δ*
<sub>
`i`
*x*
</sub>
(
*h*
<sub>
*y*
</sub>
*Â*
<sub>
*y*
</sub>
)−
*Δ*
<sub>
`i`
*y*
</sub>
*Â*
<sub>
*x*
</sub>
\]
/
*δ*
𝒜
<sub>
*z*
</sub>
`g->bz[iz][iy][ix]`
=
\[
*Δ*
<sub>
`i`
*x*
</sub>
(
*h*
<sub>
*y*
</sub>
*Â*
<sub>
*y*
</sub>
)−
*Δ*
<sub>
`i`
*y*
</sub>
*Â*
<sub>
*x*
</sub>
\]
/
*δ*
𝒜
<sub>
*z*
</sub>
where (
*Â*
<sub>
*x*
</sub>
,
*Â*
<sub>
*y*
</sub>
,
*Â*
<sub>
*z*
</sub>
) denote
the path integrals
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