3-NIRVANA-user-guide/3.1-Code-basics.md

@@ -184,8 +184,8 @@ struct type `GRD`, i.e. `*GRD`. The `GRD` struct type is declared in the
 header file `nirvana.h` and contains all grid information (attributes,
 coordinates, variables arrays, etc.). Dereferencing `gm` to `gm[l]`,
 gives the first superblock in a linked list collecting all superblocks
-belonging to mesh refinement level `l`. `gm[l]`, like any superblock, is
-of `GRD` type, i.e., a pointer to struct `GRD`. The base level, `l`=0$,
+belonging to mesh refinement level $l$. `gm[l]`, like any superblock, is
+of `GRD` type, i.e., a pointer to struct `GRD`. The base level, $l=0$,
 spanning the computational domain starts with pointer `gm[0]`. In
 uniform grid simulations that is the only list existing. The superblocks
 of a refinement level $l$ are obtained by running through the
@@ -324,11 +324,11 @@ Elements V of struct `GRD`:
 
 | V (grid metrics)           | description                                                                                         |
 |:---------------------------|:----------------------------------------------------------------------------------------------------|
-| `dv[iy][ix]`               | volume *δ*  *V* ( = *δ*  *V*<sub>*x*</sub> ⋅ *δ*  *V*<sub>*y*</sub> ⋅ *δ*  *z*) of a numerical cell |
-| `dvx[ix]`                  | *x*-dependent part, *δ*  *V*<sub>*x*</sub>, of cell volume                                          |
-| `dvy[iy]`                  | *y*-dependent part, *δ*  *V*<sub>*y*</sub>, of cell volume                                          |
-| `dvyf[iy]`                 | *y*-dependent part, *δ*  *V*<sub>*y*</sub>, of cell volume at face-centroid coordinates             |
-| `dax[ix]`                  | vector storing                                                                                      |
+| `dv[iy][ix]`               | volume *δ* *V* ( = *δ* *V*<sub>*x*</sub> ⋅ *δ* *V*<sub>*y*</sub> ⋅ *δ* *z*) of a numerical cell |
+| `dvx[ix]`                  | *x*-dependent part, *δ* *V*<sub>*x*</sub>, of cell volume                                          |
+| `dvy[iy]`                  | *y*-dependent part, *δ* *V*<sub>*y*</sub>, of cell volume                                          |
+| `dvyf[iy]`                 | *y*-dependent part, *δ* *V*<sub>*y*</sub>, of cell volume at face-centroid coordinates             |
+| `dax[ix]`                  | *x*-dependent part of *xy*/*xz*-cell face surface                                                   |
 | `hy[ix]`                   | metric scale factor *h*<sub>*y*</sub>(*x*) at cell-nodal coordinates                                |
 | `hyh[ix]`                  | metric scale factor *h*<sub>*y*</sub>(*x*) at cell-center coordinates                               |
 | `hyc[ix]`                  | metric scale factor *h*<sub>*y*</sub>(*x*) at cell-centroid coordinates                             |
@@ -364,9 +364,9 @@ where (`g->x[ix]`,`g->y[iy]`,`g->z[iz]`) are the nodal coordinates of
 the lower cell corner. Cell-centroid coordinates locate the volume
 center of a cell and face-centroid coordinates locate the face centers
 of a cell. Their definition for cylindrical- and spherical geometry is
-given in the table below where $\D_\mix$ ($\D_\miy$) denotes the
-difference operator, $\D_\mix U=U_{{\tt ix}+1}-U_{\tt ix}$ and analog
-for $\D_\miy$. Half-index subscripts mean evaluation at the geometric
+given in the table below where $\Delta_{\tt ix}$ ($\Delta_{\tt iy}$) denotes the
+difference operator, $\Delta_{\tt ix} U=U_{{\tt ix}+1}-U_{\tt ix}$ and analog
+for $\Delta_{\tt iy}$. Half-index subscripts mean evaluation at the geometric
 center, i.e., at cell-centered coordinates. At certain cell locations
 centroid coordinates and centered coordinates coincide which, in
 general, is true in Cartesian geometry.