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

@@ -944,7 +944,7 @@ divergence-free setup:
 \(1\) computation of cell-face-averaged magnetic field components via
 exact integration of the analytical expressions. The so discretized
 field is per se cell-wise divergence-free. For a grid cell
-(`ix`,`iy`,`iz`) on superblock `g` this means
+(`ix`,`iy`,`iz`) on superblock `g` the discritized components read
 
 ![ic_b](uploads/411b3e817fec94afa0a2861772697e71/ic_b.png)  
 The numerical expressions for the cell face contents are:
@@ -1289,7 +1289,7 @@ physics guide
 non-periodic BC. The combination of periodic BC at one domain boundary
 with non-periodic BC at another domain boundary is not supported.*
 
-### User-defined coefficients for dissipative processes
+## User-defined coefficients for dissipative processes
 
 The modules `viscosityCoeffUser.c`, `conductionCoeffUser.c` and
 `diffusionCoeffUser.c` serve as templates for a user-defined coefficient
@@ -1423,7 +1423,7 @@ User-defined Ohmic diffusion is enabled by appropriate choice in the
 parameter interface `nirvana.par` under the category
 `PHYSICS SPECIFICATIONS` (code parameter: `_C.diffusion`).
 
-### User-defined coefficient for ambipolar diffusion
+## User-defined coefficient for ambipolar diffusion
 
 The module `APdiffusionCoeffUser.c` serves as template for a
 user-defined ambipolar diffusion coefficient. Ambipolar diffusion enters
@@ -1467,11 +1467,11 @@ User-defined ambipolar diffusion is enabled by appropriate choice in the
 parameter interface `nirvana.par` under the category
 `PHYSICS SPECIFICATIONS` (code parameter: `_C.APdiffusion`).
 
-### User-defined body force
+## User-defined body force
 
 The module `forceUser.c` serves as template for coding a user-defined
 *specific* body force **f** (force per mass in units
-*N* ⋅ *k**g*<sup> − 1</sup>). The body force then enters the momentum
+N⋅kg<sup>−1</sup>). The body force then enters the momentum
 equation and energy equation as source term.
 
 In the call of `forceUser()` the function arguments are the superblock
@@ -1506,17 +1506,17 @@ The body force is enabled by specification in the parameter interface
 `nirvana.par` under the category `PHYSICS SPECIFICATIONS` (code
 parameter: `_C.force`).
 
-### User-defined cooling/heating function
+## User-defined cooling/heating function
 
 The modules `sourceCoolingUser.c` and `sourceHeatingUser.c` serve as
 templates for coding a user-defined cooling function,
-*L*<sub>*c**o**o**l*</sub> ≤ 0, and heating function,
-*L*<sub>*h**e**a**t*</sub> ≥ 0, respectively. Both functions are allowed
+*L*<sub>*cool*</sub> ≤ 0, and heating function,
+*L*<sub>*heat*</sub> ≥ 0, respectively. Both functions are allowed
 to depend on temperature *T* and density 𝜚. The net heatloss, i.e. the
 sum
-*L*<sub>*c**o**o**l*</sub>(*T*, 𝜚) + *L*<sub>*h**e**a**t*</sub>(*T*, 𝜚)
+*L*<sub>*cool*</sub>(*T*, 𝜚) + *L*<sub>*heat*</sub>(*T*, 𝜚)
 of both functions, enters as a source term in the energy equation.
-*L*<sub>*c**o**o**l*</sub> and *L*<sub>*h**e**a**t*</sub> are measured
+*L*<sub>*cool*</sub> and *L*<sub>*heat*</sub> are measured
 in units *J* ⋅ *s*<sup> − 1</sup> ⋅ *m*<sup> − 3</sup>.
 
 In the call of `sourceCoolingUser()` (`sourceHeatingUser()`) the
@@ -1529,12 +1529,12 @@ the pointer `deriv` to the derivatives flag and the 2-element vector
       f=sourceHeatingUser(T,rho,deriv,dfh);
 
 The user must define the return value
-`f` = *L*<sub>*c**o**o**l*</sub>(`T``,` `r``h``o`)
-(*L*<sub>*h**e**a**t*</sub>(`T``,` `r``h``o`)) in `sourceCoolingUser.c`
+`f` = *L*<sub>*cool*</sub>(`T``,` `rho`)
+(*L*<sub>*heat*</sub>(`T``,` `rho`)) in `sourceCoolingUser.c`
 (`sourceHeatingUser.c`). The `deriv`-flag is thought to indicate the
 calling function whether a user provides the derivatives of
-*L*<sub>*c**o**o**l*</sub>(*T*, 𝜚) and
-*L*<sub>*h**e**a**t*</sub>(*T*, 𝜚) with respect to *T* and 𝜚 himself.
+*L*<sub>*cool*</sub>(*T*, 𝜚) and
+*L*<sub>*heat*</sub>(*T*, 𝜚) with respect to *T* and 𝜚 himself.
 The `deriv`-flag is preset to `NO` when entering the code function. If
 the user sets
 
@@ -1542,9 +1542,9 @@ the user sets
 
 the derivatives must be stored by the user in the 2-element vector `dfc`
 (`dfh`) with `dfc[0]` (`dfh[0]`) storing the derivative
-∂*L*<sub>*c**o**o**l*</sub>/∂*T* (∂*L*<sub>*h**e**a**t*</sub>/∂*T*) and
+∂*L*<sub>*cool*</sub>/∂*T* (∂*L*<sub>*heat*</sub>/∂*T*) and
 `dfc[1]` (`dfh[1]`) storing the derivative
-∂*L*<sub>*c**o**o**l*</sub>/∂𝜚 (∂*L*<sub>*h**e**a**t*</sub>/∂𝜚).
+∂*L*<sub>*cool*</sub>/∂𝜚 (∂*L*<sub>*heat*</sub>/∂𝜚).
 Otherwise derivatives are automatically computed by a finite difference
 approximation.
 
@@ -1559,7 +1559,7 @@ User-defined cooling/heating is enabled by appropriate choice in the
 parameter interface `nirvana.par` under the category
 `PHYSICS SPECIFICATIONS` (code parameter: `_C.heatloss`).
 
-### User-defined equation of state
+## User-defined equation of state
 
 #### Analytic EOS
 
@@ -1724,7 +1724,7 @@ A tabulated EOS is enabled by appropriate choice in the parameter
 interface `nirvana.par` under category `PHYSICS SPECIFICATIONS` (code
 paramter: `_C.eos`).
 
-### User-defined initial/restricted mesh refinement
+## User-defined initial/restricted mesh refinement
 
 For certain problems it may be advantageous to start a simulation with a
 pre-refined mesh in some parts of the computational domain or to retrict
@@ -1835,7 +1835,7 @@ the requested refinement control parameter.
 An example can be found in the testproblem
 `/nirvana/testproblems/GRAVITY/problem3`.
 
-### Specification of NCCM parameters
+## Specification of NCCM parameters
 
 The parameter file `NCCM.par` serves as user interface to the
 multi-species framework/NCCM. `NCCM.par` is grouped into the category
@@ -1987,7 +1987,7 @@ A thermal process is activated (deactivated) by specifying the value Y
 (N). Every text in a line following the ’`>`’-character is ignored by
 the parser and serves for comments.
 
-### User-controllable macros
+## User-controllable macros
 
 Besides the parameters collected in the user interfaces `nirvana.par`
 and `NCCM.par` there are a number of further parameters which can be