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

@@ -156,8 +156,7 @@ possible values or a numeric range.
         physical evolution time `_C.time_max` is reached the simulation
         stops ahead of schedule.
 
--   `03` (`_C.freq_log`, `_C.freq_nir`, `_C.freq_ana`,
-    `_C.freq_walltime`)
+-   `03` (`_C.freq_log`, `_C.freq_nir`, `_C.freq_ana`, `_C.freq_walltime`)
 
     -   `_C.freq_log`: interval in units of timesteps at which the
         NIRVANA log file `nirvana.log` and monitoring file `nirvana.mon`
@@ -181,8 +180,10 @@ possible values or a numeric range.
 
 -   `01` (`_C.geometry`, `_C.omega[0-2]`)
 
-    -   `_C.geometry` ({CART,CYL,SPH}): choice of coordinate system
-        where CART=Cartesian, CYL=cylindrical and SPH=spherical.
+    -   `_C.geometry` ({CART,CYL,SPH}): choice of coordinate system where
+        - CART: Cartesian
+        - CYL: cylindrical
+        - SPH: spherical
 
     -   `_C.omega[0-2]`: components of the angular velocity vector of a
         rotating frame of reference with respect to the inertial frame
@@ -202,32 +203,32 @@ possible values or a numeric range.
 
 -   `01` (`_C.lo[0]`, `_C.up[0]`, `_C.dim[0]`)
 
-    -   `_C.lo[0]`,\_C.up\[0\]: lower,upper $x$-coordinate of the
+    -   `_C.lo[0]`,\_C.up\[0\]: lower,upper **x**-coordinate of the
         computational domain.
 
     -   `_C.dim[0]`: number of *base-level* grid points in
-        $x$-direction. `_C.dim[0]` must be an integral factor of 4, and
+        **x**-direction. `_C.dim[0]` must be an integral factor of 4, and
         excludes ghost cells which are automatically added by the code.
 
 -   `02` (`_C.lo[1]`, `_C.up[1]`, `_C.dim[1]`)
 
-    -   `_C.lo[1]`,`_C.up[1]`: lower,upper $y$-coordinate of the
+    -   `_C.lo[1]`,`_C.up[1]`: lower,upper **y**-coordinate of the
         computational domain. In case of spherical geometry
         ($y\equiv \theta$) `_C.lo[1]`,`_C.up[1]` have to be specified in
         units of $\pi$.
 
     -   `_C.dim[1]`: number of *base-level* grid points in
-        $y$-direction. `_C.dim[1]` must be a multiple factor of 4.
+        **y**-direction. `_C.dim[1]` must be a multiple factor of 4.
 
 -   `03` (`_C.lo[2]`, `_C.up[2]`, `_C.dim[2]`)
 
-    -   `_C.lo[2]`,`_C.up[2]`: lower,upper $z$-coordinate of the
+    -   `_C.lo[2]`,`_C.up[2]`: lower,upper **z**-coordinate of the
         computational domain. In case of cylindrical- or spherical
         geometry ($z\equiv \phi$) `_C.lo[2]`,`_C.up[2]` have to be
         specified in units of $\pi$.
 
     -   `_C.dim[2]`: number of *base-level* grid points in
-        $z$-direction. `_C.dim[2]` must be a multiple factor of 4. If
+        **z**-direction. `_C.dim[2]` must be a multiple factor of 4. If
         `_C.dim[2]`=0 the simulation is assumed 2D, i.e., axisymmetric
         in case of cylindrical- or spherical coordinates.
 
@@ -241,7 +242,7 @@ possible values or a numeric range.
         SFC-decomposition is automatically used instead.
 
     -   `_C.bnx`,`_C.bny`,`_C.bnz`: number of domain subdivisions in
-        $x,y,z$-direction in case \_C.partitioning_type=BLOCK. Numbers
+        **x,y,z**-direction in case \_C.partitioning_type=BLOCK. Numbers
         must be chosen such that the grid dimension of subdomains is a
         multiple factor of 4 in each coordinate direction. Moreover, the
         total number of subdomains must equal the number of MPI threads,
@@ -341,14 +342,14 @@ possible values or a numeric range.
 
 -   `01` (`_C.imr`, `_C.amr`)
 
-    -   `_C.imr` ($\le$`MAXLEVEL`): maximum refinement level for an
+    -   `_C.imr` (<=`MAXLEVEL`): maximum refinement level for an
         initially refined mesh by the user (cf. [User-defined initial
         mesh refinement and refinement
         control](#user-defined-initial-mesh-refinement-and-refinement-control)).
         `_C.imr` cannot be larger than the macro `MAXLEVEL` defined in
         the header file `nirvanaUser.h`.
 
-    -   `_C.amr` ($\le$`MAXLEVEL`): allowed maximum mesh refinement
+    -   `_C.amr` (<=`MAXLEVEL`): allowed maximum mesh refinement
         level in a AMR simulations. `_C.amr` cannot be larger than the
         macro `MAXLEVEL` defined in the header file `nirvanaUser.h`.
 
@@ -411,14 +412,13 @@ possible values or a numeric range.
         grid cell. A zero or negative value means that the
         Jeans-length-based criterion is disabled.
 
-    -   `_C.amr_dJeans` ($\ge 0$): tuning parameter for the
+    -   `_C.amr_dJeans` (>=0): tuning parameter for the
         Jeans-length-based mesh refinement criterion allowing a
         systematic reduction of the Jeans threshold with increasing
-        refinement level $l$ according to the expression
-        `_C.amr_Jeans` $-l*$ `_C.amr_dJeans`
-        i.e., the local
+        refinement level l according to the expression
+        `_C.amr_Jeans`-l*`_C.amr_dJeans` i.e., the local
         Jeans length becomes gradually higher resolved with increasing
-        $l$. `_C.amr_dJeans` must be positiv. 
+        l. `_C.amr_dJeans` must be positiv.
 
         **Important**: `_C.amr_dJeans` must be chosen with care such
         that the actual Jeans threshold never becomes too small or
@@ -497,7 +497,7 @@ possible values or a numeric range.
             numerical technique (equiv. to genuinely 2D-HLL in the
             current implementation).
 
-    -   `_C.mhd_courant` (typical value: $<0.5$): CFL number in the
+    -   `_C.mhd_courant` (typical value: <0.5): CFL number in the
         MHD timestep.
 
 -   `02` (`_C.viscosity_solver`, `_C.viscosity_courant`)
@@ -512,7 +512,7 @@ possible values or a numeric range.
             Coupling to MHD integrator is via Strang-type splitting.
 
     -   `_C.viscosity_courant`: CFL-like number in the fluid viscosity
-        timestep. A typical value in case of STD is $<0.4$. Values much
+        timestep. A typical value in case of STD is <0.4. Values much
         larger than 1 are possible in the case of RKL.
 
 -   `03` (`_C.diffusion_solver`, `_C.diffusion_courant`)
@@ -529,13 +529,13 @@ possible values or a numeric range.
 
 -   `06` (`_C.heatloss_max_change`)
 
-    -   `_C.heatloss_max_change` (typical value: $<0.1$): allowed
+    -   `_C.heatloss_max_change` (typical value: <0.1): allowed
         maximal relative change in the temperature due to the heatloss
         source term.
 
 -   `07` (`_C.reactions_max_changeX`, `_C.reactions_max_changeT`)
 
-    -   `_C.reactions_max_changeX` (typical value: $<0.1$): allowed
+    -   `_C.reactions_max_changeX` (typical value: <0.1): allowed
         maximal relative change of species number densities (or total
         number density) in the time integration of the chemo-thermal
         rate equations.
@@ -546,7 +546,7 @@ possible values or a numeric range.
         number density (`SXN`=1 uses individual number densities;
         `SXN`=0 uses the total number density).
 
-    -   `_C.reactions_max_changeT` (typical value: $<0.1$): allowed
+    -   `_C.reactions_max_changeT` (typical value: <0.1): allowed
         maximal relative change in the temperature in the time
         integration of the chemo-thermal rate equations.
 
@@ -635,7 +635,7 @@ possible values or a numeric range.
         perpendicular to the magnetic field (meaningless in isotropic
         conduction).
 
-    -   `_C.conduction_coeff_sat` (typical value: $0.3$): $\Psi$ is the
+    -   `_C.conduction_coeff_sat` (typical value: 0.3): $\Psi$ is the
         parameter in the saturation heat flux model of \[[CM77](#references)\] (cf.
         [physics
         guide](https://gitlab.aip.de/ziegler/NIRVANA/-/tree/master/doc/pdf/PhysicsGuide.pdf)).
@@ -675,7 +675,7 @@ possible values or a numeric range.
         **Important:** Disabling the energy equation is not compatible
         with the use of an adiabatic EOS, for instance.
 
-    -   `_C.energy_dual_sw` ($[0,1]$; typical value: $0.01$): threshold
+    -   `_C.energy_dual_sw` (\[0,1\]; typical value: <=0.01): threshold
         value for the thermal-to-total energy density ratio in the dual
         energy formalism (when `_C.energy`=DUAL).