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Update 3.1 Code basics
authored
Jan 08, 2021
by
Udo Ziegler
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3-NIRVANA-user-guide/3.1-Code-basics.md
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@@ -380,7 +380,7 @@ lower cell node. Besides cell-nodal coordinates cell-centroid
coordinates locating the center of cell volume and face-centroid
coordinates locating the center of cell faces are of importance. Their
definition for cylindrical- and spherical geometry is given in the table
below where
*Δ*
<sub>
`i`
*x*
</sub>
(
*Δ*
<sub>
`i`
*y*
</sub>
) denotes the
below where
*Δ*
<sub>
`i
x
`
</sub>
(
*Δ*
<sub>
`i
y
`
</sub>
) denotes the
difference of a quantity evaluated at
`ix`
+1 (
`iy`
+1) and
`ix`
(
`iy`
).
Formal half-index subscripts mean that a quantity is to be evaluated at
the geometric cell center. Corresponding coordinates are called
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@@ -388,10 +388,10 @@ cell-centered.
| location |
`g->`
| definition: cylindrical | definition: spherical |
|:------------------------------|:-------------|:--------------------------------------------------------------------------------|:--------------------------------------------------------------------------------|
| cell-centroid x |
`xc[ix]`
|
*z*
<sub>
`i`
*x*
+ 1/2
</sub>
| 3
*Δ*
<sub>
`i`
*x*
</sub>
*r*
<sup>
4
</sup>
/(4
*Δ*
<sub>
`i`
*x*
</sub>
*r*
<sup>
3
</sup>
) |
| cell-centroid y |
`yc[iy]`
| 2
*Δ*
<sub>
`i`
*y*
</sub>
*R*
<sup>
3
</sup>
/(3
*Δ*
<sub>
`i`
*y*
</sub>
*R*
<sup>
2
</sup>
) |
*Δ*
<sub>
`i`
*y*
</sub>
(
*θ*
cos
*θ*
− sin
*θ*
)/
*Δ*
<sub>
`i`
*y*
</sub>
cos
*θ*
|
|
*xy*
/
*xz*
-face-centroid x |
`xf[ix]`
|
*z*
<sub>
`i
`
*x*
+
1/2
</sub>
| 2
*Δ*
<sub>
`i`
*x*
</sub>
*r*
<sup>
3
</sup>
/(3
*Δ*
<sub>
`i`
*x*
</sub>
*r*
<sup>
2
</sup>
) |
|
*yx*
-face-centroid y | (≡)
`yc[iy]`
| 2
*Δ*
<sub>
`i`
*y*
</sub>
*R*
<sup>
3
</sup>
/(3
*Δ*
<sub>
`i`
*y*
</sub>
*R*
<sup>
2
</sup>
) |
*Δ*
<sub>
`i`
*y*
</sub>
(
*θ*
cos
*θ*
− sin
*θ*
)/
*Δ*
<sub>
`i`
*y*
</sub>
cos
*θ*
|
| cell-centroid x |
`xc[ix]`
|
*z*
<sub>
`i
x
`
+ 1/2
</sub>
| 3
*Δ*
<sub>
`i
x
`
</sub>
*r*
<sup>
4
</sup>
/(4
*Δ*
<sub>
`i
x
`
</sub>
*r*
<sup>
3
</sup>
) |
| cell-centroid y |
`yc[iy]`
| 2
*Δ*
<sub>
`i
y
`
</sub>
*R*
<sup>
3
</sup>
/(3
*Δ*
<sub>
`i
y
`
</sub>
*R*
<sup>
2
</sup>
) |
*Δ*
<sub>
`i
y
`
</sub>
(
*θ*
cos
*θ*
− sin
*θ*
)/
*Δ*
<sub>
`i
y
`
</sub>
cos
*θ*
|
|
*xy*
/
*xz*
-face-centroid x |
`xf[ix]`
|
*z*
<sub>
`i
x`
+
1/2
</sub>
| 2
*Δ*
<sub>
`i
x
`
</sub>
*r*
<sup>
3
</sup>
/(3
*Δ*
<sub>
`i
x
`
</sub>
*r*
<sup>
2
</sup>
) |
|
*yx*
-face-centroid y | (≡)
`yc[iy]`
| 2
*Δ*
<sub>
`i
y
`
</sub>
*R*
<sup>
3
</sup>
/(3
*Δ*
<sub>
`i
y
`
</sub>
*R*
<sup>
2
</sup>
) |
*Δ*
<sub>
`i
y
`
</sub>
(
*θ*
cos
*θ*
− sin
*θ*
)/
*Δ*
<sub>
`i
y
`
</sub>
cos
*θ*
|
*
Note 5: Other cell/face-centroid coordinates not listed in the table
are identical to their cell/face-centered coordinates.
*
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