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

@@ -1097,7 +1097,8 @@ algebraic expression $a^2+b^2+c^2$.
 IC for the shock-cloud interaction problem simulated in a 3D Cartesian
 box given by (x,y,z)=[-1/2,1/2]<sup>3</sup>:
 
-![ic_example2](uploads/e31ebefeb64b91e0ef74d839ebac4de8/ic_example2.png){width=500px}
+![ic_example2](uploads/e31ebefeb64b91e0ef74d839ebac4de8/ic_example2.png){width=7:w
+00px}
 
 At **x**=(0.3,0,0) a spherical clump with
 radius 0.15 and density of 10 is embedded and co-moving with its
@@ -1279,9 +1280,8 @@ depends on the type of variable as listed in the following table:
 
 BC for the gravitational potential *Φ* cannot be explicitely set
 except when specifying U in `nirvana.par`. Otherwise, the following rule
-is adopted to transform MHD BC types into BC types for $\Phi$:
+is adopted to transform MHD BC types into BC types for *Φ*:
 
-*Φ*
 | selected BC type |  ⇒  | BC type for *Φ*                        |
 |------------------|:----|:---------------------------------------|
 |                P |     | P (periodicity)                        |
@@ -1304,7 +1304,7 @@ function `phiUser()` expecting a user-defined gravitational potential.
 possible. The solver only supports triple-periodic BC when periodic.
 
 When using the screening mass approach for cylindrical/spherical
-problems with $2\pi$ 2*π*-periodicity BC are computed to discretization error
+problems with 2*π*-periodicity BC are computed to discretization error
 accuracy by the gravity solver itself. In this case above rules do not
 apply and any specified BC are ignored.
 
@@ -1319,22 +1319,21 @@ respectively.
 
 Fluid viscosity enters the momentum equation and energy equation via the
 viscous stress tensor $\tau$ given by
+viscous stress tensor *τ* given by
 
-$$\tau=\nu \left[\nabla\mathbf{v}+(\nabla\mathbf{v})^\top
--2/3(\nabla\cdot\mathbf{v})\mathrm{I}\right]$$
+*τ* = *ν*\[∇**v**+(∇**v**)<sup>⊤</sup>−2/3(∇⋅**v**)*I*\]
 
-where $\nu$ in units
-\[$\mathtt{kg}\cdot\mathtt{m}^{-1}\cdot\mathtt{s}^{-1}$\] is the
-*dynamic* viscosity coefficient, $\mathbf{v}$ the fluid velocity and
-$\mathrm{I}$ the identity operator.
+where *ν* in units \[kg⋅m<sup>−1</sup>⋅s<sup>−1</sup>\] is the
+*dynamic* viscosity coefficient, **v** the fluid velocity and *I* the
+identity operator.
 
-**Important:** The viscosity coefficient $\nu$ here should not be
-confused with the kinetic viscosity coefficient,
-$\nu_{\mathrm{kinetic}}$ with unit \[m$^2\cdot$s$^{-1}$\], which is
-related to the dynamic coefficient by
-$\nu=\varrho\nu_{\mathrm{kinetic}}$.
+**Important:** The viscosity coefficient *ν*
+here should not be confused with the kinetic viscosity coefficient,
+*ν*<sub>*kinetic*</sub> with unit \[m<sup>2</sup>⋅s<sup>−1</sup>\], 
+which is related to the dynamic coefficient by
+*ν* = 𝜚*ν*<sub>*kinetic*</sub>.
 
-A user-defined coefficient, $\nu$, has to be assigned in module
+A user-defined coefficient, *ν*, has to be assigned in module
 `viscosityUser.c` in the function
 
       viscosityCoeffUser(g,vis);