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

@@ -969,9 +969,9 @@ where (*Â*<sub>*x*</sub>, *Â*<sub>*y*</sub>, *Â*<sub>*z*</sub>) denote
 the path integrals
 ![ic_A](uploads/d7670a3203d0f3a1e2a9a759e69e2e77/ic_A.png)  
 over corresponding cell edges. The difference operator
-*Δ*<sub>`i`*y*</sub>, for instance, is given by
+*Δ*<sub>`iy`</sub>, for instance, is given by
 
-*Δ*<sub>`iy`</sub>*Â*<sub>*x*</sub> = *Â*<sub>*x*</sub>(`ix`,`iy`+1,` `iz`) − *Â*<sub>*x*</sub>(`ix`,`iy`,`iz`)
+*Δ*<sub>`iy`</sub>*Â*<sub>*x*</sub> = *Â*<sub>*x*</sub>(`ix`,`iy`+1,`iz`) − *Â*<sub>*x*</sub>(`ix`,`iy`,`iz`)
 
 and similarly for others. If the *Â*’s are *unambiguously* computed (or
 approximated) on coinciding cell edges in the grid hierarchy, the
@@ -1011,15 +1011,15 @@ domain of length *L* (given by `_C.up[0]-_C.lo[0]`):
 
 𝜚 = 𝜚<sub>0</sub>
 
-**m** = 𝜚<sub>0</sub>(−sin(2*π*  *y*/*L*),sin(2*π*  *x*/*L*),0)
+**m** = 𝜚<sub>0</sub>(−sin(2*π* *y*/*L*),sin(2*π* *x*/*L*),0)
 
-**B** = *B*<sub>0</sub>(−sin(2*π*  *y*/*L*),sin(4*π*  *x*/*L*),0)
+**B** = *B*<sub>0</sub>(−sin(2*π* *y*/*L*),sin(4*π* *x*/*L*),0)
 
-*e* = *p*<sub>0</sub>/(*γ* − 1) + **m**<sup>2</sup>/(2𝜚) + **B**<sup>2</sup>/(2*μ*)
+*e* = *p*<sub>0</sub>/(*γ*−1) + **m**<sup>2</sup>/(2𝜚) + **B**<sup>2</sup>/(2*μ*)
 
-where 𝜚<sub>0</sub> = 2.77778, *p*<sub>0</sub> = 5/3 and
-*B*<sub>0</sub> = 1. The adiabatic index *γ* = 5/3 and the magnetic
-permeability *μ* = 1.
+where 𝜚<sub>0</sub>=2.77778, *p*<sub>0</sub>=5/3 and
+*B*<sub>0</sub>=1. The adiabatic index *γ*=5/3 and the magnetic
+permeability *μ*=1.
 
     void configUser(GRD **gm)
     /**
@@ -1092,10 +1092,7 @@ expression *a*<sup>2</sup> + *b*<sup>2</sup> + *c*<sup>2</sup>.
 
 IC for the shock-cloud interaction problem simulated in a Cartesian box
 given by (*x*, *y*, *z*) ∈ \[ − 1/2, 1/2\]<sup>3</sup>:
-$$(\\varrho,p,v\_x,v\_y,v\_z,B\_x,B\_y,B\_z)=\\left\\{\\begin{array}{ll}
-(3.86859,167.345,0,0,0,0,2.1826182,-2.1826182) & x&lt;0.1\\\\
-(1,1,-11.2536,0,0,0,0.56418958,0.56418958) & x\\ge 0.1
-\\end{array}\\right.$$
+![ic_example2](uploads/e31ebefeb64b91e0ef74d839ebac4de8/ic_example2.png)  
 At **x** = (0.3, 0, 0) a spherical clump with 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 *γ* = 5/3 and
@@ -1201,7 +1198,7 @@ magnetic permeability *μ* = 1.
     return;
     }
 
-### Defining boundary conditions
+## Defining boundary conditions
 
 A superblock `g` includes up to 3 ghost cells per side per coordinate
 direction beyond its active region. The number of ghost cells depends on