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

@@ -916,7 +916,7 @@ Here is an example of looping over the active region of a superblock:
 The tracer array index, `ic`, runs from 0 to `_C.tracer`-1 whereas the
 species array index, `is`, runs from 0 to `_C.species`-1. Tracer
 variables are assumed dimensionless and it are usually defined in the
-range $[0,1]$. The mesh of the superblock is indexed by
+range [0,1]. The mesh of the superblock is indexed by
 (`ix`,`iy`,`iz`).
 
 **Important:** The species number densities must be consistently defined
@@ -1110,7 +1110,7 @@ The macro `SPQR(a,b,c)` defined in header file `nirvana.h` shortcuts the
 algebraic expression $a^2+b^2+c^2$.
 
 **Example 2** (taken from `/nirvana/testproblems/MHD/problem17`; cf.
-[@Z05])
+[Z05](#references))
 
 IC for the shock-cloud interaction problem simulated in a 3D Cartesian
 box given by $(x,y,z)\in [-1/2,1/2]^3$:
@@ -1118,7 +1118,7 @@ $$(\varrho,p,v_x,v_y,v_z,B_x,B_y,B_z)=\left\{\begin{array}{ll}
 (3.86859,167.345,0,0,0,0,2.1826182,-2.1826182) & x<0.1\\
 (1,1,-11.2536,0,0,0,0.56418958,0.56418958) & x\ge 0.1
 \end{array}\right.$$ At ${\mathbf x}=(0.3,0,0)$ a spherical clump with
-radius $0.15$ and density of $10$ is embedded and co-moving with its
+radius 0.15 and density of 10 is embedded and co-moving with its
 surrounding flow under the assumption of pressure equilibrium. The
 adiabatic index $\gamma =5/3$ and magnetic permeability $\mu=1$. The
 grid is initially refined with 3 refinement levels, `_C.level`=3, in the
@@ -1254,8 +1254,8 @@ boundary.
 
 #### User-defined BC
 
-When U specified BC at the corresponding domain boundary are assumed
-user-defined. In that case the code calls user-programmable functions in
+With letter U boundary conditions at the corresponding domain boundary 
+is assumed user-specified. In that case the code calls user-programmable functions in
 the following modules:
 
 | module        | function      | BC for                                                                     |
@@ -1282,7 +1282,7 @@ formalism is enabled (cf. [Specification of main simulation
 parameters](#specification-of-main-simulation-parameters)).
 
 Boundary values have to be assigned in ghost cells running from to
-`g->ixs`-1 ( to `g->iys`-1, to `g->izs`-1) in $x$($y$,$z$)-direction at
+`g->ixs`-1 ( to `g->iys`-1, to `g->izs`-1) in x(y,z)-direction at
 the lower domain boundary. At upper domain boundaries the index range
 depends on the type of variable as listed in the following table:
 
@@ -1305,7 +1305,7 @@ is adopted to transform MHD BC types into BC types for $\Phi$:
 |            M,A,R |     | von-Neumann                            |
 |            I,O,D |     | Dirichlet                              |
 |                F |     | not supported                          |
-|                U |     | user-defined *Φ* (function `phiUser()` |
+|                U |     | user-defined *Φ* (function `phiUser()`)|
 
 In case of von-Neumann conditions (M,A,R) the gradient of potential
 vanishes normal to the corresponding domain boundary, i.e.,