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

@@ -283,10 +283,10 @@ for the type of coordinate system.
         -   `I`: inflow – fluid is allowed to flow inwards through the
             corresponding domain boundary but not to flow outwards. This
             means for the perpendicular velocity component
-            *u*<sub>*o*</sub> =  ± sgn *u*<sub>*i*</sub> ⋅ *u*<sub>*i*</sub>
+            *u*<sub>*o*</sub>=± sgn*u*<sub>*i*</sub>⋅*u*<sub>*i*</sub>
             where the ’+’(’-’)-sign stands for a lower (upper) domain
             boundary. Zero derivative,
-            *u*<sub>*o*</sub> = *u*<sub>*i*</sub>, is assumed for other
+            *u*<sub>*o*</sub>=*u*<sub>*i*</sub>, is assumed for other
             cell-centroid quantities except the total energy density.
             The total energy density is set consistently under the
             assumption of a zero derivative for the thermal energy
@@ -298,21 +298,21 @@ for the type of coordinate system.
         -   `O`: outflow – fluid is allowed to flow outwards through the
             corresponding domain boundary but not to flow inwards. This
             means for the perpendicular velocity component
-            *u*<sub>*o*</sub> =  ∓ sgn *u*<sub>*i*</sub> ⋅ *u*<sub>*i*</sub>
+            *u*<sub>*o*</sub>=∓sgn *u*<sub>*i*</sub>⋅*u*<sub>*i*</sub>
             where the ’+’(’-’)-sign stands for a lower (upper) domain
             boundary. Other variables are likewise to I.
 
         -   `M`: mirror symmetry – reflecting conditions,
-            *u*<sub>*o*</sub> =  − *u*<sub>*i*</sub>, for the
+            *u*<sub>*o*</sub>=−*u*<sub>*i*</sub>, for the
             perpendicular components of velocity and magnetic field and
             zero derivative for the other variables.
 
         -   `A`: antimirror symmetry – same as M for non-magnetic
             variables. The magnetic field is forced to have dipole
             parity with respect to the domain boundary. This means
-            *u*<sub>*o*</sub> =  − *u*<sub>*i*</sub> for the parallel
+            *u*<sub>*o*</sub>=−*u*<sub>*i*</sub> for the parallel
             magnetic field components and
-            *u*<sub>*o*</sub> = *u*<sub>*i*</sub> for the perpendicular
+            *u*<sub>*o*</sub>=*u*<sub>*i*</sub> for the perpendicular
             magnetic field component.
 
         -   `R`: reflection-on-axis (only of relevance in cylindrical
@@ -320,13 +320,13 @@ for the type of coordinate system.
             `_C.bc[2]`,`_C.bc[3]`) – reflecting conditions at the
             geometric axis. Same as M except for the azimutal magnetic
             field component for which
-            *u*<sub>*o*</sub> =  − *u*<sub>*i*</sub>.
+            *u*<sub>*o*</sub>=−*u*<sub>*i*</sub>.
 
         -   `C`: reflection-at-center (only of relevance in spherical
             geometry for `_C.bc[0]`) – reflecting conditions at the
             coordinate origin. Same as M except for the non-radial
             magnetic field components for which
-            *u*<sub>*o*</sub> =  − *u*<sub>*i*</sub>.
+            *u*<sub>*o*</sub>=−*u*<sub>*i*</sub>.
 
         -   `P`: periodicity – periodic conditions for all variables.
 
@@ -364,7 +364,7 @@ for the type of coordinate system.
 
     -   `_C.imr` (≤`MAXLEVEL`): maximal requested refinement level in a
         user-defined initially refined mesh (cf.
-        [here](3.2-User-interfaces#user-defined-initial/restricted-mesh)).
+        [here](3.2-User-interfaces#user-defined-initial/restricted-mesh-refinement)).
         `_C.imr` cannot be larger than the macro `MAXLEVEL` defined in
         the header file `nirvanaUser.h`.