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

@@ -974,7 +974,7 @@ integral form of $\mathbf{B}=\nabla\times \mathbf{A}$:
 where the difference operators *Δ*<sub>ix</sub>, *Δ*<sub>iy</sub> 
 and *Δ*<sub>iz</sub> are given by
 
-*Δ*<sub>ix</sub>X=X(ix,iy,iz+1)-X(ix,iy,iz)
+*Δ*<sub>ix</sub>X=X(ix+1,iy,iz)-X(ix,iy,iz)
 
 *Δ*<sub>iy</sub>X=X(ix,iy+1,iz)-X(ix,iy,iz)
 
@@ -1011,10 +1011,19 @@ 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.
-\[[Z04](#references)\])
+[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]`):
+square 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)  
+**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*)
+
+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.
 
 $\varrho = \varrho_0$