| ... | ... | @@ -947,9 +947,9 @@ divergence-free setup: |
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components by exact integration of given analytical expressions. For a
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grid cell (ix,iy,iz) on superblock `g` the discretized components would then
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read
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$$\mathtt{g->bx[iz][iy][ix]}=\frac{1}{\delta \mathcal{A}_x}\int
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`g->bx[iz][iy][ix]`$=\frac{1}{\delta \mathcal{A}_x}\int
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\limits_\mathtt{g->y[iy]}^\mathtt{g->y[iy+1]}
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\int\limits_\mathtt{g->z[iz]}^\mathtt{g->z[iz+1]} B_x(\mathtt{g->x[ix]},y,z)h_yh_zdydz$$
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\int\limits_\mathtt{g->z[iz]}^\mathtt{g->z[iz+1]} B_x(\mathtt{g->x[ix]},y,z)h_yh_zdydz$
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$$\mathtt{g->by[iz][iy][ix]}=\frac{1}{\delta \mathcal{A}_y}\int
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\limits_\mathtt{g->x[ix]}^\mathtt{g->x[ix+1]}
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\int\limits_\mathtt{g->z[iz]}^\mathtt{g->z[iz+1]} B_y(x,\mathtt{g->y[iy]},z)h_zdxdz$$
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| ... | ... | @@ -971,7 +971,7 @@ integration over cell faces turns out to be too complicated. |
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The face-averaged magnetic field components are then obtained from the
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integral form of $\mathbf{B}=\nabla\times \mathbf{A}$:
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$\mathtt{g->bx[iz][iy][ix]}=\left[h_y\Delta_{iy} (h_{zy}\hat{A}_z)
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`g->bx[iz][iy][ix]`$=\left[h_y\Delta_{iy} (h_{zy}\hat{A}_z)
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-h_y\Delta_{iz} \hat{A}_y\right]/\delta \mathcal{A}_x$
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`g->by[iz][iy][ix]`$=\left[\Delta_{iz} \hat{A}_x
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| ... | ... | |