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

@@ -1318,7 +1318,6 @@ respectively.
 #### Fluid viscosity
 
 Fluid viscosity enters the momentum equation and energy equation via the
-viscous stress tensor $\tau$ given by
 viscous stress tensor *τ* given by
 
 *τ* = *ν*\[∇**v**+(∇**v**)<sup>⊤</sup>−2/3(∇⋅**v**)*I*\]
@@ -1362,23 +1361,21 @@ testproblem `/nirvana/testproblems/VISC/problem1`.
 #### Thermal conduction
 
 Thermal conduction enters the energy equation through a heat flux
-$\mathbf{F}_{\mathrm{C}}$. Generally, the presence of a magnetic field
+**F**<sub>*C*</sub>. Generally, the presence of a magnetic field
 introduces anisotropic effects with different transport properties along
-and across the magnetic field. $\mathbf{F}_\mathrm{C}$ is described by
+and across the magnetic field. **F**<sub>*C*</sub> is described by
 
-$$\mathbf{F}_\mathrm{C}=-\kappa_\parallel (\nabla T\cdot\mathbf{\hat{B}})\mathbf{\hat{B}}
--\kappa_\perp \left(\nabla T-(\nabla T\cdot\mathbf{\hat{B}})\mathbf{\hat{B}}\right)$$
+**F**<sub>*C*</sub> = −*κ*<sub>∥</sub>(∇*T*⋅**B̂**)**B̂**−*κ*<sub>⊥</sub>(∇*T*−(∇*T*⋅**B̂**)**B̂**)
 
-where $\kappa_\parallel$ and $\kappa_\perp$ is the thermal conduction
+where *κ*<sub>∥</sub> and *κ*<sub>⊥</sub> is the thermal conduction
 coefficient parallel and perpendicular to the magnetic field,
-respectively, and $\mathbf{\hat{B}}=\mathbf{B}/|\mathbf{B}|$ is the unit
-vector in the direction of the magnetic field. $\kappa_\parallel$ and
-$\kappa_\perp$ are measured in units
-J$\cdot$K$^{-1}\cdot$m$^{-1}\cdot$s$^{-1}$ (cf. [physics
-guide](https://gitlab.aip.de/ziegler/NIRVANA/-/tree/master/doc/pdf/PhysicsGuide.pdf)).
+respectively, and **B̂** = **B**/\|**B**\| is the unit vector in the
+direction of the magnetic field. *κ*<sub>∥</sub> and *κ*<sub>⊥</sub> are
+measured in units J⋅K<sup>−1</sup>⋅m<sup>−1</sup>⋅s<sup>−1</sup>
+(cf. [physics guide](https://gitlab.aip.de/ziegler/NIRVANA/-/tree/master/doc/pdf/PhysicsGuide.pdf)).
 
-User-defined coefficients, $\kappa_\parallel$ and $\kappa_\perp$, have
-to be assigned in module `conductionCoeffUser.c` in the function
+User-defined coefficients, *κ*<sub>∥</sub> and *κ*<sub>⊥</sub>,
+have to be assigned in module `conductionCoeffUser.c` in the function
 
       conductionCoeffUser(g,cond,cond_perp);
 
@@ -1403,8 +1400,8 @@ i.e., it should be defined at location
 (`g->xc[ix]`,`g->yc[iy]`,`g->zc[iz]`). In HD simulations and in MHD
 simulations with forced isotropy (when `COND_FORCE_ISO`=`YES` in
 `nirvanaUser.h`) only the `cond`-array has to be assigned with `cond`
-representing now the conduction coefficient $\kappa$ in the isotropic
-heat flux $\mathbf{F}_\mathrm{C}=-\kappa \nabla T$.
+representing now the conduction coefficient *κ* in the isotropic
+heat flux **F**<sub>*C*</sub> = −*κ*∇*T*.
 
 Thermal conduction with user-defined conduction coefficients is enabled
 by the appropriate choice of parameter `_C.conduction` in file