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

@@ -94,7 +94,7 @@ clusters based on the Message Passing Interface (MPI). The underlying
 concepts of parallelism and load balancing are described in some more
 detail .
 
-#### Adaptive mesh refinement
+#### Adaptive mesh simulations
 
 NIRVANA features the possibility of multi-scale simulations by applying
 the technique of Adaptive Mesh Refinement (AMR). AMR works in all
@@ -388,7 +388,7 @@ cell-centered.
 
 | location                      | `g->`        | definition: cylindrical                                                         | definition: spherical                                                           |
 |:------------------------------|:-------------|:--------------------------------------------------------------------------------|:--------------------------------------------------------------------------------|
-| 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>)   |
+| 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>)   |
 | 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*      |
 | *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>) |
 | *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*      |
@@ -399,7 +399,7 @@ are identical to their cell/face-centered coordinates.*
 *Note 6: In Cartesian geometry all cell/face-centroid coordinates are
 identical to their cell/face-centered counterparts.*
 
-### Adaptive mesh refinement
+## Adaptive mesh refinement
 
 The mesh refinement algorithm relies on the oct-tree data structure
 `_G0` (of type `*GRD`) which represents a hierarchy of nested generic
@@ -487,7 +487,7 @@ criteria which are
     user-specific threshold with the reciprocal value giving the minimum
     number of grid cells the Field length should be resolved.
 
-### Parallelism and load balancing
+## Parallelism and load balancing
 
 The NIRVANA code is parallelized making use of the MPI library. The code
 infrastructure provides routines for mesh partitioning in order to