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