All Figures

$\begin{figure} \par\includegraphics[width=8cm,clip]{5371f1.ps} \end{figure}$ Figure 1: Amplitude ( upper panel) and phase velocity ( lower panel) of the circularly polarized Alfvén wave as a function of time. The full lines display result using a Roe solver whereas the dotted lines show results obtained with a Lax-Friedrich solver. The resolutions are from top to bottom, 100, 30 and 10 grid points per wavelength.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5371f2.ps} \end{figure}$ Figure 2: Solution to the MHD shock tube showing the density as a function of x, obtained with RAMSES when $\alpha =\pi$ . The code uses 400 grid points in that case and the Roe Riemann solver.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5371f3.ps} \end{figure}$ Figure 3: Zoom on the region in which the compound wave develops when $\alpha =3$ . Black curves are obtained on a uniform grid. From top to bottom (at $x \sim -0.24$ ), they correspond to 800, 1200, 1600, 2000, 3000, 5000, 10 000 and 20 000 grid points respectively. The red curve was calculated after switching on the AMR scheme and using a similar CPU time as for the 20 000 grid points curve. Its maximum resolution is equivalent to using about 10⁶ cells on a uniform grid and show a dramatic improvement toward the regular solution.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5371f4.ps} \end{figure}$ Figure 4: Complete solution of the MHD shock tube when $\alpha =3$ , with the AMR scheme turned on. The solid line is a plot of the density as a function of position while the dashed line (whose scale is given on the right axis) illustrates the level of refinement the code uses for each cell.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5371f5.ps} \end{figure}$ Figure 5: Time history of the magnetic energy in the magnetic loop advection test. The different curves are obtained using the Roe Riemann solver ( solid line) and the Lax-Friedrich solver ( dashed line).
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{5371f6.ps} \end{figure}$ Figure 6: Snapshot of the density at time t=0.5 resulting from the Orszag-Tang test. The grid is uniform and composed of 512² cells. The result is computed using the Roe Riemann solver and the C-MUSCL predictive step.
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In the text

$\begin{figure} \par\includegraphics[width=4.2cm,clip]{5371f7.ps}\hspace*{3mm} \i... ...f14.ps}\hspace*{3mm} \includegraphics[width=4.2cm,clip]{5371f15.ps} \end{figure}$ Figure 7: Time evolution of the magnetic field lines during the current sheet test. The calculation was performed on a uniform grid composed of 256² cells, using the Roe solver and the MonCen slope limiter. From top left to bottom right, the snapshots corresponds successively to times t=0,0.5,1,1.5,2,2.5,3, 3.5 and 4. The entire figure can be compared to Fig. 12 of Gardiner & Stone (2005a).
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In the text

$\begin{figure} \par\includegraphics[width=10cm,clip]{5371f16.ps} \end{figure}$ Figure 8: This figure compares the magnetic field lines obtained at time t=2 for high-resolution runs ( bottom) and low-resolution runs ( top), as well as for the Roe solver ( right) and the local Lax-Friedrich solver ( left). Both low and high-resolution runs were performed using the AMR scheme: $l_{\rm min}=5$ for the former and $l_{\rm min}=10$ for the latter. The refinement strategy is detailed in the text.
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In the text

$\begin{figure} \par\includegraphics[width=15.4cm,clip]{5371f17.ps} \end{figure}$ Figure 9: This figure shows a zoom on the bottom left magnetic island for the high-resolution run with the Roe solver at time t=3. On the left, only octs boundaries are plotted to clarify the visualization of the AMR grid. On the right, a grey scale image of the thermal pressure is shown, with strong transverse shock-waves clearly visible as sharp discontinuities.
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In the text

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5371f18.ps} \end{figure}$ Figure 10: Structure of the flow in the (x,z) plane after 60 orbits. The arrows shows the poloidal velocity field overplotted on gray scale contours of the y-component of the magnetic field. Because of the growth of the MRI, the entire flow has become turbulent.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{5371f19.ps} \end{figure}$ Figure 11: Time history of the volume averaged Maxwell stress tensor normalized by pressure, obtained in the shearing box model. The solid line was computed using RAMSES and the dashed line was calculated using ZEUS. Both models use exactly the same set of parameters. Both shows sustained MHD turbulence and a similar amount of angular momentum transport.
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In the text

$\begin{figure} \par\includegraphics[width=7cm,clip]{5371f20.ps}\par\vspace*{2mm}... ...1.ps}\par\vspace*{2mm} \includegraphics[width=7cm,clip]{5371f22.ps} \end{figure}$ Figure 12: Three timesteps illustrating the hydrodynamical collapse.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=7cm,clip]{5371f23.ps}\hspace{4mm... ...1f25.ps}\hspace{4mm} \includegraphics[width=7cm,clip]{5371f26.ps} } \end{figure}$ Figure 13: Two timesteps illustrating the magnetized collapse. The upper panels display the equatorial density and velocity field whereas bottom panels displays the density in x-z plane. The calculation is performed with the Lax-Friedrich solver.
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In the text

$\begin{figure} \par\mbox{\includegraphics[width=7cm,clip]{5371f27.ps}\hspace{4mm... ...f29.ps}\hspace{4mm} \includegraphics[width=7cm,clip]{5371f30.ps} }\end{figure}$ Figure 14: Same as Fig. 13 except that the calculation has been carried out with the Roe solver.
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In the text

$\begin{figure} \par\includegraphics[width=8cm,clip]{5371f1.ps} \end{figure}$	Figure 1: Amplitude ( upper panel) and phase velocity ( lower panel) of the circularly polarized Alfvén wave as a function of time. The full lines display result using a Roe solver whereas the dotted lines show results obtained with a Lax-Friedrich solver. The resolutions are from top to bottom, 100, 30 and 10 grid points per wavelength.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5371f2.ps} \end{figure}$	Figure 2: Solution to the MHD shock tube showing the density as a function of x, obtained with RAMSES when $\alpha =\pi$ . The code uses 400 grid points in that case and the Roe Riemann solver.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5371f4.ps} \end{figure}$	Figure 4: Complete solution of the MHD shock tube when $\alpha =3$ , with the AMR scheme turned on. The solid line is a plot of the density as a function of position while the dashed line (whose scale is given on the right axis) illustrates the level of refinement the code uses for each cell.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5371f5.ps} \end{figure}$	Figure 5: Time history of the magnetic energy in the magnetic loop advection test. The different curves are obtained using the Roe Riemann solver ( solid line) and the Lax-Friedrich solver ( dashed line).
Open with DEXTER

$\begin{figure} \par\includegraphics[width=6cm,clip]{5371f6.ps} \end{figure}$	Figure 6: Snapshot of the density at time t=0.5 resulting from the Orszag-Tang test. The grid is uniform and composed of 512² cells. The result is computed using the Roe Riemann solver and the C-MUSCL predictive step.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=15.4cm,clip]{5371f17.ps} \end{figure}$	Figure 9: This figure shows a zoom on the bottom left magnetic island for the high-resolution run with the Roe solver at time t=3. On the left, only octs boundaries are plotted to clarify the visualization of the AMR grid. On the right, a grey scale image of the thermal pressure is shown, with strong transverse shock-waves clearly visible as sharp discontinuities.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7.6cm,clip]{5371f18.ps} \end{figure}$	Figure 10: Structure of the flow in the (x,z) plane after 60 orbits. The arrows shows the poloidal velocity field overplotted on gray scale contours of the y-component of the magnetic field. Because of the growth of the MRI, the entire flow has become turbulent.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=8cm,clip]{5371f19.ps} \end{figure}$	Figure 11: Time history of the volume averaged Maxwell stress tensor normalized by pressure, obtained in the shearing box model. The solid line was computed using RAMSES and the dashed line was calculated using ZEUS. Both models use exactly the same set of parameters. Both shows sustained MHD turbulence and a similar amount of angular momentum transport.
Open with DEXTER

$\begin{figure} \par\includegraphics[width=7cm,clip]{5371f20.ps}\par\vspace{2mm}... ...1.ps}\par\vspace{2mm} \includegraphics[width=7cm,clip]{5371f22.ps} \end{figure}$	Figure 12: Three timesteps illustrating the hydrodynamical collapse.
Open with DEXTER

$\begin{figure} \par\mbox{\includegraphics[width=7cm,clip]{5371f23.ps}\hspace{4mm... ...1f25.ps}\hspace{4mm} \includegraphics[width=7cm,clip]{5371f26.ps} } \end{figure}$	Figure 13: Two timesteps illustrating the magnetized collapse. The upper panels display the equatorial density and velocity field whereas bottom panels displays the density in x-z plane. The calculation is performed with the Lax-Friedrich solver.
Open with DEXTER

$\begin{figure} \par\mbox{\includegraphics[width=7cm,clip]{5371f27.ps}\hspace{4mm... ...f29.ps}\hspace{4mm} \includegraphics[width=7cm,clip]{5371f30.ps} }\end{figure}$	Figure 14: Same as Fig. 13 except that the calculation has been carried out with the Roe solver.
Open with DEXTER