3-NIRVANA-user-guide/3.2-User-interfaces.md

@@ -168,7 +168,7 @@ possible values or a numeric range.
 
     -   `_C.freq_ana`: interval in units of timesteps at which the user
         interface function `analysisUser()` is called for user-specific
-        analysis tasks (cf. [Data analysis](3.3-Output-data#data-analysis)).
+        analysis tasks (cf. [Data analysis](3.5-Data-analysis)).
 
     -   `_C.freq_walltime`: interval in seconds at which the special
         snapshot `NIRLAST.#` (cf. [Snapshot files](3.3-Output-data#snapshot-files)) is
@@ -297,14 +297,14 @@ possible values or a numeric range.
             $u_o=u_i$ for the perpendicular magnetic field component.
 
         -   `R`: reflection-on-axis (only of relevance in cylindrical
-            geometry at the $y$-lower boundary (at $R=0$) or in
-            spherical geometry at the $y$-lower/upper boundaries (at
-            $\theta=0,\pi$)) -- reflecting conditions at the geometric
+            geometry at the $y$-lower boundary at $R=0$ or in
+            spherical geometry at the $y$-lower/upper boundaries at
+            $\theta =0,\pi $) -- reflecting conditions at the geometric
             axis. Same as M except for the azimutal magnetic field
             component for which $u_o=-u_i$.
 
         -   `C`: reflection-at-center (only of relevance in spherical
-            geometry at the $x$-lower boundary (at $r=0$)) -- reflecting
+            geometry at the $x$-lower boundary at $r=0$) -- reflecting
             conditions at the coordinate center. Same as M except for
             the non-radial magnetic field components for which
             $u_o=-u_i$.
@@ -316,9 +316,9 @@ possible values or a numeric range.
             (pseudo-vacuum condition) for the magnetic field.
 
         -   `F`: free boundary (only of relevance in cylindrical
-            geometry at the $y$-lower boundary (at $R=0$) or in
-            spherical geometry at the $y$-lower/upper boundaries (at
-            $\theta=0,\pi$) and $x$-lower boundary (at $r=0$)) --
+            geometry at the $y$-lower boundary at $R=0$ or in
+            spherical geometry at the $y$-lower/upper boundaries at
+            $\theta =0,\pi$ and $x$-lower boundary at $r=0$) --
             'natural' boundary condition at the geometric axis. Boundary
             values are not set explictely but are implicitly given by
             $\pi$-shifted values. Note that when a `F`-type boundary
@@ -400,13 +400,13 @@ possible values or a numeric range.
         value `_C.amr_exp>1` (`_C.amr_exp<1`) means that mesh refinement
         becomes progressively more difficult (easier) with increasing
         refinement level compared to the standard linear dependence
-        (`_C.amr_exp=1`) (cf. [AMR](#adaptive-mesh-refinement)).
+        (`_C.amr_exp=1`) (cf. [AMR](3.1-Code-basics#adaptive-mesh-refinement)).
 
 -   `05` (`_C.amr_Jeans`, `_C.amr_exp`, `_C.amr_Field`)
 
     -   `_C.amr_Jeans` (typical value: $0.2$): threshold in the
         Jeans-length-based mesh refinement criterion (cf.
-        [AMR](#adaptive-mesh-refinement)). The value `_C.amr_Jeans`
+        [AMR](3.1-Code-basics#adaptive-mesh-refinement)). The value `_C.amr_Jeans`
         defines the fraction of local Jeans length to be resolved by one
         grid cell. A zero or negative value means that the
         Jeans-length-based criterion is disabled.
@@ -426,7 +426,7 @@ possible values or a numeric range.
 
     -   `_C.amr_Field` (typical value: $0.2$): threshold in the
         Field-length-based mesh refinement criterion (cf.
-        [AMR](#adaptive-mesh-refinement)). The value `_C.amr_Field`
+        [AMR](3.1-Code-basics#adaptive-mesh-refinement)). The value `_C.amr_Field`
         defines the fraction of the local Field length to be resolved by
         one grid cell. A zero or negative value means that the
         Field-length-based criterion is disabled.
@@ -603,7 +603,7 @@ possible values or a numeric range.
         given by the parameter `_C.diffusion_coeff` described below. U
         enables Ohmic diffusion with a user-defined magnetic diffusion
         coefficient as coded in the user interface function
-        **diffusionCoeffUser()**. (cf. [Ohmic
+        `diffusionCoeffUser()`. (cf. [Ohmic
         diffusion](#ohmic-diffusion)). N disables Ohmic diffusion.
 
     -   `_C.diffusion_coeff`: constant magnetic diffusion coefficient.
@@ -646,7 +646,7 @@ possible values or a numeric range.
         coefficient given by the parameter `_C.APdiffusion_coeff`
         described below. U enables ambipolar diffusion with a
         user-defined anbipolar diffusion coefficient as coded in the
-        user interface function **APdiffusionCoeffUser()** (cf.
+        user interface function `APdiffusionCoeffUser()` (cf.
         [Ambipolar diffusion](#user-defined-coefficient-for-ambipolar-diffusion)).
         N disables ambipolar diffusion.
 
@@ -800,7 +800,7 @@ The module `configUser.c` serves as user interface for the definition of
 initial conditions (IC). To do this the user must program the function
 `configUser()` in the module. Defining IC means assigning values to
 primary physical variables on the mesh, that are
-$\{\varrho,\mathbf{m},e,\mathbf{B},C_\mc,n_\ms\}$ -- gas density,
+$\{\varrho,\mathbf{m},e,\mathbf{B},C_c,n_s\}$ -- gas density,
 momentum,total energy density, magnetic field, tracer
 ($c=0,{\tt\_C.tracer}-1$), species number densities
 ($s=0,{\tt\_C.species}-1$). The parameter `_C.tracer` (`_C.species`)
@@ -819,7 +819,7 @@ considered as primary variables and must be assigned by the user. The
 parameter `_C.testfields` denotes the number of testfields.
 
 **Important:** In case magnetic field splitting is enabled (cf. [Code
-features](#code-features)) the variable $\mathbf{B}$ represents the
+features](3.1-Code-basics#code-features)) the variable $\mathbf{B}$ represents the
 residual magnetic field, i.e., total field minus background field. In
 addition, $e$ represents the residual total energy density, i.e, has a
 magnetic energy density contribution solely from the residual magnetic
@@ -843,7 +843,7 @@ il=0,`_C.level`, and all its superblocks:
         }
 
 Please recall in this context the introduction to NIRVANA's [Mesh data
-structure](#mesh-data-structure).
+structure](3.1-Code-basics#mesh-data-structure).
 
 There are two types of mesh variables: cell-averaged variables and
 face-averaged variables. Cell-averaged variables are
@@ -944,7 +944,7 @@ divergence-free setup:
 
 **(I)** Explicit computation of cell-face-averaged magnetic field
 components by exact integration of given analytical expressions. For a
-grid cell (,,) on superblock `g` the discretized components would then
+grid cell (ix,iy,iz) on superblock `g` the discretized components would then
 read 
 $$\mathtt{g->bx[iz][iy][ix]}=\frac{1}{\delta \mathcal{A}_x}\int
 \limits_\mathtt{g->y[iy]}^\mathtt{g->y[iy+1]}
@@ -957,8 +957,8 @@ $$\mathtt{g->bz[iz][iy][ix]}=\frac{1}{\delta \mathcal{A}_z}\int
 \int\limits_\mathtt{g->y[iy]}^\mathtt{g->y[iy+1]} B_z(x,y,\mathtt{g->z[iz]})h_ydxdy$$
 where the numerical expressions for the cell faces are:
 
-| cell face            | expression                               |
-|:---------------------|:-----------------------------------------|
+| 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`                       |
@@ -982,21 +982,21 @@ integral form of $\mathbf{B}=\nabla\times \mathbf{A}$:
 where the difference operators $\Delta_{ix}$, $\Delta_{iy}$ and
 $\Delta_{iz}$ are given by
 
-$\Delta_{ix}X=X(\mathtt{ix+1,iy,iz})-X(\mathtt{ix,iy,iz})$,
+$\Delta_{ix}X=X(\mathtt{iz,iy,ix+1})-X(\mathtt{iz,iy,ix})$,
 
-$\Delta_{iy}X=X(\mathtt{ix,iy+1,iz})-X(\mathtt{ix,iy,iz})$,
+$\Delta_{iy}X=X(\mathtt{iz,iy+1,ix})-X(\mathtt{iz,iy,ix})$,
 
-$\Delta_{iz}X=X(\mathtt{ix,iy,iz+1})-X(\mathtt{ix,iy,iz})$
+$\Delta_{iz}X=X(\mathtt{iz,iy,ix+1})-X(\mathtt{iz,iy,ix})$
 
 and $(\hat{A}_x,\hat{A}_y,\hat{A}_z)$ are the cell-edge integrals
 
-$$\hat{A}_x(\mathtt{ix,iy,iz})=\int\limits_\mathtt{g->x[ix]}^\mathtt{g->x[ix+1]}
+$$\hat{A}_x(\mathtt{iz,iy,ix})=\int\limits_\mathtt{g->x[ix]}^\mathtt{g->x[ix+1]}
 A_x(x,\mathtt{g->y[iy]},\mathtt{g->z[iz]})dx$$
 
-$$\hat{A}_y(\mathtt{ix,iy,iz})=\int\limits_\mathtt{g->y[iy]}^\mathtt{g->y[iy+1]}
+$$\hat{A}_y(\mathtt{iz,iy,ix})=\int\limits_\mathtt{g->y[iy]}^\mathtt{g->y[iy+1]}
 A_y(\mathtt{g->x[ix]},y,\mathtt{g->z[iz]})dy$$
 
-$$\hat{A}_z(\mathtt{ix,iy,iz})=\int\limits_\mathtt{g->z[iz]}^\mathtt{g->z[iz+1]}
+$$\hat{A}_z(\mathtt{iz,iy,ix})=\int\limits_\mathtt{g->z[iz]}^\mathtt{g->z[iz+1]}
 A_z(\mathtt{g->x[ix]},\mathtt{g->y[iy]},z)dz$$
 
 The $\hat{A}$'s are usually easier to compute than the face-averaged
@@ -1025,7 +1025,7 @@ for two problems: the Orszag-Tang vortex problem (example 1) and a
 shock-cloud interaction problem (example 2).
 
 **Example 1** (taken from `/nirvana/testproblems/MHD/problem2`; cf.
-[@Z04])
+\[[Z04](#references)\])
 
 IC for the Orszag-Tang vortex problem simulated in a doubly-periodic
 square domain of length $L$ (given by `_C.up[0]-_C.lo[0]`):