All Figures

$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg01.eps} \end{figure}$ Figure 1: Snapshots of the logarithm of the rest mass density of models C2-0, C2-1/20, C2-1 and C2-10/3 at $t \sim 126~r_{\rm b}/c$ .
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In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg02.eps} \end{figure}$ Figure 2: Same as Fig. 1 but showing snapshots of the Lorentz factor and the flow field.
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In the text

$\begin{figure} \par\includegraphics[width=11.5cm,clip]{2520fg03.eps} \end{figure}$ Figure 3: Snapshots of the magnetization parameter $\beta$ ( upper two panels) and the toroidal field component $B^\phi$ ( lower two panels) of the two most strongly magnetized models of series C2 at $t \sim 126~r_{\rm b}/c$ .
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In the text

$\begin{figure} \par\includegraphics[width=11.5cm,clip]{2520fg04.eps} \end{figure}$ Figure 4: Snapshots of the logarithm of the pressure for all the models having a toroidal field with $\bar\beta = 10/3$ . The overlaid vector field shows the structure of the currents ( $\nabla\times \vec{B} / \vert\nabla\times \vec{B}\vert$ ).
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In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg05.eps} \end{figure}$ Figure 5: Snapshots of the poloidal field model C2-pol-1 at $t \sim 126~r_{\rm b}/c$ . From top to bottom: rest mass density, Lorentz factor with flow field, logarithm of the modulus of the magnetic field with field lines superimposed, and magnetization parameter $\beta$ . The magnetic field lines shown in the third panel are placed randomly, but weighted with the local field strength, such that on average their density reflects the field strength in the plane where the integration is started ( $z=50~r_{\rm b}$ ).
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In the text

$\begin{figure} \par\begin{tabular}{ccc} \includegraphics[angle=0, scale=0.31]{2... ... \includegraphics[angle=0, scale=0.31]{2520f06f.eps} \end{tabular} \end{figure}$ Figure 6: Average thermal pressure $\langle p\rangle \equiv \sum_{z_k=1}^{z_k=n_z} p(r_i,z_k) / n_z$ measured in code units ( top row) and average of the radial component of the net force $\langle F_r\rangle \equiv \sum_{z_k=1}^{z_k=n_z} [-\nabla p(r_i,z_k) + (\nabla \times B) \times B]_r / n_z$ ( bottom row) versus radius for the models of all series. The snapshots are computed at $t \approx 126~r_{\rm b}/c$ , $\approx$ $80~r_{\rm b}/c$ and $\approx$ $249~r_{\rm b}/c$ for series C2, B1 and C1 ( from left to right), respectively. For models with zero magnetic field and with poloidal fields, the net force is almost zero, and hence the corresponding lines show almost no variation (around zero) at the scale used in the plots in the bottom row.
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In the text

$\begin{figure} \par\includegraphics[angle=90, scale=1.0]{2520f07a.eps} \includeg... ...]{2520f07b.eps} \includegraphics[angle=90, scale=1.0]{2520f07c.eps} \end{figure}$ Figure 7: Motion of the head of the jet for all computed models. The solid lines correspond to the 1D velocity estimate given by Eq. (47).
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In the text

$\begin{figure} \par\includegraphics[angle=90, scale=1.0]{2520f08a.eps} \includeg... ...]{2520f08b.eps} \includegraphics[angle=90, scale=1.0]{2520f08c.eps} \end{figure}$ Figure 8: Temporal change of the cylindric aspect ratio $A_{\rm c}$ for all models.
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In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg09.eps} \end{figure}$ Figure 9: Snapshots of the logarithm of the rest mass density of models B1-0, B1-1/20, B1-1 and B1-10/3 at $t \sim 80~r_{\rm b}/c$ . For model B1-1/20 the jet is about to leave the computational grid because of its large propagation speed.
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In the text

$\begin{figure} \par\includegraphics[width=11.2cm,clip]{2520fg10.eps} \end{figure}$ Figure 10: Same as Fig. 9 but showing snapshots of the Lorentz factor and the flow field.
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In the text

$\begin{figure} \par\includegraphics[width=11.2cm,clip]{2520fg11.eps} \end{figure}$ Figure 11: Snapshots of the magnetization parameter $\beta$ ( upper two panels) and the toroidal field component $B^\phi$ ( lower two panels) of the two most strongly magnetized models of series B1 at $t \sim 80~r_{\rm b}/c$ .
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In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg12.eps} \end{figure}$ Figure 12: Snapshots of the poloidal field model B1-pol-1 at $t \sim 80~r_{\rm b}/c$ . From top to bottom: rest mass density, Lorentz factor with flow field, logarithm of the modulus of the magnetic field with field lines superimposed, and $\beta$ . The magnetic field lines shown in the third panel are placed randomly, but weighted with the local field strength such that on average their density reflects the field strength in the plane where the integration is started ( $z=50~r_{\rm b}$ ).
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In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg13.eps} \end{figure}$ Figure 13: Snapshots of the logarithm of the rest mass density of the models C1-0, C1-1 and C1-10/3 at $t \sim249~r_{\rm b}/c$ .
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In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg14.eps} \end{figure}$ Figure 14: Same as Fig. 13 but showing snapshots of the Lorentz factor and the flow pattern.
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In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg15.eps} \end{figure}$ Figure 15: Snapshots of the magnetization parameter $\beta$ ( upper two panels) and the toroidal field component $B^\phi$ ( lower two panels) of the two most strongly magnetized models of series C1 at $t \sim249~r_{\rm b}/c$ .
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In the text

$\begin{figure} \par\includegraphics[width=10.9cm,clip]{2520fg16.eps} \end{figure}$ Figure 16: Snapshots of the poloidal field model C1-pol-1 at $t \sim249~r_{\rm b}/c$ . From top to bottom: rest mass density, Lorentz factor with flow field, logarithm of the modulus of the magnetic field with field lines superimposed, and magnetization parameter $\beta$ . The magnetic field lines shown in the third panel are placed randomly, but weighted with the local field strength, such that on average their density reflects the field strength in the plane where the integration is started ( $z=50~r_{\rm b}$ ).
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In the text

$\begin{figure} \par\includegraphics[width=13.5cm,clip]{2520fg17.eps} \end{figure}$ Figure B.1: Third 1D test problem. Blast wave test with large initial pressure difference. The black crosses are the results obtained with PPM interpolation, the grey dots those computed with PLM interpolation.

In the text

$\begin{figure} \par\includegraphics[width=14cm,clip]{2520fg18.eps} \end{figure}$ Figure B.2: Fourth 1D test problem. Shock reflection test. The black crosses are the results obtained with PPM interpolation, the grey dots those computed with PLM interpolation.

In the text

$\begin{figure} \par\includegraphics[width=13cm,clip]{2520fg19.eps} \end{figure}$ Figure B.3: Cylindrical explosion test with PLM reconstruction.

In the text

$\begin{figure} \par\includegraphics[angle=90,width=8.7cm,clip]{2520f20a.eps}\vsp... ...{5.3mm} \includegraphics[angle=90,width=8.7cm,clip]{2520f20b.eps} \end{figure}$ Figure B.4: Plot along x=0 of the thermal pressure of the cylindrical explosion test. The top panel shows the results for the original grid of 200 by 200 zones, while the bottom panel is the result of the same test on a grid of 800 by 800 zones. The black crosses are obtained with PPM interpolation, the grey dots with PLM interpolation.

In the text

$\begin{figure} \par\includegraphics[width=8.7cm,clip]{2520fg21.eps} \end{figure}$ Figure B.5: Convergence test for the propagation of circularly polarized waves in 2D. The relative L₁ errors (Eq. B.1) are shown in logarithmic scale (solid line) as a function of the resolution per dimension (N=N_x=N_y). The PLM reconstruction has been used. As a reference, the perfect second order convergence slope is also shown (dashed line).

In the text

$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg01.eps} \end{figure}$	Figure 1: Snapshots of the logarithm of the rest mass density of models C2-0, C2-1/20, C2-1 and C2-10/3 at $t \sim 126~r_{\rm b}/c$ .
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$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg02.eps} \end{figure}$	Figure 2: Same as Fig. 1 but showing snapshots of the Lorentz factor and the flow field.
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$\begin{figure} \par\includegraphics[width=11.5cm,clip]{2520fg03.eps} \end{figure}$	Figure 3: Snapshots of the magnetization parameter $\beta$ ( upper two panels) and the toroidal field component $B^\phi$ ( lower two panels) of the two most strongly magnetized models of series C2 at $t \sim 126~r_{\rm b}/c$ .
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$\begin{figure} \par\includegraphics[width=11.5cm,clip]{2520fg04.eps} \end{figure}$	Figure 4: Snapshots of the logarithm of the pressure for all the models having a toroidal field with $\bar\beta = 10/3$ . The overlaid vector field shows the structure of the currents ( $\nabla\times \vec{B} / \vert\nabla\times \vec{B}\vert$ ).
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$\begin{figure} \par\includegraphics[angle=90, scale=1.0]{2520f07a.eps} \includeg... ...]{2520f07b.eps} \includegraphics[angle=90, scale=1.0]{2520f07c.eps} \end{figure}$	Figure 7: Motion of the head of the jet for all computed models. The solid lines correspond to the 1D velocity estimate given by Eq. (47).
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$\begin{figure} \par\includegraphics[angle=90, scale=1.0]{2520f08a.eps} \includeg... ...]{2520f08b.eps} \includegraphics[angle=90, scale=1.0]{2520f08c.eps} \end{figure}$	Figure 8: Temporal change of the cylindric aspect ratio $A_{\rm c}$ for all models.
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$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg09.eps} \end{figure}$	Figure 9: Snapshots of the logarithm of the rest mass density of models B1-0, B1-1/20, B1-1 and B1-10/3 at $t \sim 80~r_{\rm b}/c$ . For model B1-1/20 the jet is about to leave the computational grid because of its large propagation speed.
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$\begin{figure} \par\includegraphics[width=11.2cm,clip]{2520fg10.eps} \end{figure}$	Figure 10: Same as Fig. 9 but showing snapshots of the Lorentz factor and the flow field.
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$\begin{figure} \par\includegraphics[width=11.2cm,clip]{2520fg11.eps} \end{figure}$	Figure 11: Snapshots of the magnetization parameter $\beta$ ( upper two panels) and the toroidal field component $B^\phi$ ( lower two panels) of the two most strongly magnetized models of series B1 at $t \sim 80~r_{\rm b}/c$ .
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$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg13.eps} \end{figure}$	Figure 13: Snapshots of the logarithm of the rest mass density of the models C1-0, C1-1 and C1-10/3 at $t \sim249~r_{\rm b}/c$ .
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$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg14.eps} \end{figure}$	Figure 14: Same as Fig. 13 but showing snapshots of the Lorentz factor and the flow pattern.
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$\begin{figure} \par\includegraphics[width=11cm,clip]{2520fg15.eps} \end{figure}$	Figure 15: Snapshots of the magnetization parameter $\beta$ ( upper two panels) and the toroidal field component $B^\phi$ ( lower two panels) of the two most strongly magnetized models of series C1 at $t \sim249~r_{\rm b}/c$ .
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