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version 4.2
authored
Oct 29, 2025
by
Udo Ziegler
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3-NIRVANA-user-guide/3.2-User-interfaces.md
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@@ -947,9 +947,9 @@ divergence-free setup:
components by exact integration of given analytical expressions. For a
grid cell (ix,iy,iz) on superblock
`g`
the discretized components would then
read
$$
\m
athtt{
g->bx
[
iz
][
iy
]
[ix]
}
=
\f
rac{1}{
\d
elta
\m
athcal{A}_x}
\i
nt
`
g->bx[iz][iy][ix]
`
$
=
\f
rac{1}{
\d
elta
\m
athcal{A}_x}
\i
nt
\l
imits_
\m
athtt{g->y[iy]}^
\m
athtt{g->y[iy+1]}
\i
nt
\l
imits_
\m
athtt{g->z[iz]}^
\m
athtt{g->z[iz+1]} B_x(
\m
athtt{g->x[ix]},y,z)h_yh_zdydz$
$
\i
nt
\l
imits_
\m
athtt{g->z[iz]}^
\m
athtt{g->z[iz+1]} B_x(
\m
athtt{g->x[ix]},y,z)h_yh_zdydz$
$$
\m
athtt{g->by
[
iz
][
iy
]
[ix]}=
\f
rac{1}{
\d
elta
\m
athcal{A}_y}
\i
nt
\l
imits_
\m
athtt{g->x[ix]}^
\m
athtt{g->x[ix+1]}
\i
nt
\l
imits_
\m
athtt{g->z[iz]}^
\m
athtt{g->z[iz+1]} B_y(x,
\m
athtt{g->y[iy]},z)h_zdxdz$$
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@@ -971,7 +971,7 @@ integration over cell faces turns out to be too complicated.
The face-averaged magnetic field components are then obtained from the
integral form of $
\m
athbf{B}=
\n
abla
\t
imes
\m
athbf{A}$:
$
\m
athtt{
g->bx
[
iz
][
iy
]
[ix]
}
=
\l
eft[h_y
\D
elta_{iy} (h_{zy}
\h
at{A}_z)
`
g->bx[iz][iy][ix]
`
$
=
\l
eft[h_y
\D
elta_{iy} (h_{zy}
\h
at{A}_z)
-h_y
\D
elta_{iz}
\h
at{A}_y
\r
ight]/
\d
elta
\m
athcal{A}_x$
`g->by[iz][iy][ix]`
$=
\l
eft[
\D
elta_{iz}
\h
at{A}_x
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