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$\begin{figure} \par\includegraphics[width=7.2cm,clip]{5486f1.eps}\end{figure}$ Figure 1: Eigenvalues of the Jacobian matrix normalized by c.
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In the text

$\begin{figure} \par\includegraphics[angle=90,width=7.6cm,clip]{5486f2.eps} \end{figure}$ Figure 2: Radiative temperature in the shadow test using the diffusion equation ( upper panel), M₁ closure with fixed eigenvalues ( middle panel), and M₁ closure with calculated eigenvalues ( lower panel).
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5486f3.eps}\end{figure}$ Figure 3: Radial profiles of the radiative temperature in the shadow test using the diffusion equation (dotted line), M₁ closure with fixed eigenvalues (dashed line), and M₁ closure with calculated eigenvalues (solid line).
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In the text

$\begin{figure} \par\includegraphics[width=3.8cm,clip]{5486f4a.eps}\hspace*{4mm} \includegraphics[width=3.8cm,clip]{5486f4b.ps} \end{figure}$ Figure 4: Left panel: HERACLES temperature map. Right panel: isotherms for HERACLES (solid lines) and a Monte-Carlo code (dashed lines).
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In the text

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{5486f5.eps} \end{figure}$ Figure 5: Normalized radiative energy isocontours for $\omega =1$ (solid lines) and $\omega =0.9$ (dashed lines).
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5486f6.eps} \end{figure}$ Figure 6: Subcritical shock: gas (solid line) and radiative (dashed line) temperatures at 1.7e4, 2.8e4, and 3.8e4 s obtained with the M₁ model (thick lines) compared to a constant and isotropic Eddington tensor model (thin lines).
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In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5486f7.eps}\end{figure}$ Figure 7: Supercritical shock: temperatures (thick lines) of gas (solid line) and radiation (dashed line) at 4.0e3, 7.5e3, and 1.3e4 s and the corresponding reduced fluxes (thin lines).
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In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{5486fD1.ps}\end{figure}$ Figure D.1: Normalized CPU time as a function of the number of processors for simulations with a constant cell number per processor.

In the text

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{5486fD2.ps} \end{figure}$ Figure D.2: Residual in a Marshak wave test for the five following methods: 1. purely Gauss-Seidel (GS) iterations, 2. purely GMRES iterations, 3. 30 iterations of GS before GMRES, 4. 50 iterations of GMRES before GS, and 5. yoyo with a switch between GS and GMRES every 10 iterations.

In the text

$\begin{figure} \par\includegraphics[width=3cm,clip]{5486fE1a.ps}\hspace*{4mm}\includegraphics[width=3cm,clip]{5486fE1b.ps}\end{figure}$ Figure E.1: Radiative energy for the beam test: eigenvalues set to $\pm$ c ( left) or calculated ( right).

In the text

$\begin{figure} \par\includegraphics[width=6cm,clip]{5486fE2.ps}\end{figure}$ Figure E.2: Horizontal cut in Fig. E.1 at the middle height. Solid line corresponds to calculated eigenvalues and dashed line to fixed ones.

In the text

$\begin{figure} \par\includegraphics[width=6.6cm,clip]{5486fE3.eps}\end{figure}$ Figure E.3: Sketch of the geometry for the pipe flow test. The simulation box extends from r=0 to r=2 and from z=0 to z=7. The pipe can be divided in three regions. The first one is a cylinder with a radius of 0.5 which extends from z=0 to z=2.5 and from z=4.5 to z=7. The second is a cylinder with a radius of 1.5 extended from z=2.5 to z=3 and from z=4 to z=4.5. Finally the third one is a cylindrical shell with inner radius r=1 and outer radius r=1.5 which extends from z=3 to z=4. The five characteristic points are A(r=0 ; z=0.25), B(0 ; 2.75), C(1.25 ; 3.5), D(0 ; 4.25), E(0 ; 6.75).

In the text

$\begin{figure} \par\includegraphics[width=6.4cm,clip]{5486fE4.eps}\end{figure}$ Figure E.4: Matter temperature at the five characteristic points.

In the text

$\begin{figure} \par\includegraphics[width=2cm,clip]{5486fE5a.eps}\hspace*{4mm} \... ...5b.eps}\hspace*{4mm} \includegraphics[width=2cm,clip]{5486fE5c.eps} \end{figure}$ Figure E.5: Radiative energy for diffusion test: pure advection, static diffusion, diffusion in a moving fluid.

In the text

$\begin{figure} \par\includegraphics[width=6.2cm,clip]{5486fE6.eps}\end{figure}$ Figure E.6: Radiative energy for pure advection: initial pulse (dashed line) and pulse after crossing one eighth of the box (solid line). The pulse is recentered by a factor $\vec{ u}\Delta t$ .

In the text

$\begin{figure} \par\includegraphics[width=3.8cm,clip]{5486fE7a.eps}\hspace*{4mm} \includegraphics[width=3.8cm,clip]{5486fE7b.eps} \end{figure}$ Figure E.7: Radiative energy for: initial pulse (dotted line) and pulse at the end of the simulation with advection (dashed line) and without (solid line). Right panel is a zoom. All the pulses are recentered by a factor $\vec{ u}\Delta t$ .

In the text

$\begin{figure} \par\includegraphics[width=3.8cm,clip]{5486fE8a.ps}\hspace*{4mm} \includegraphics[width=3.8cm,clip]{./5486fE8b.ps}\end{figure}$ Figure E.8: Gas energy versus time in the matter-radiation coupling test. The left (resp. right) subfigure corresponds to an initial matter energy of 10² (resp. 10¹⁰) erg cm^-3. The thick solid line corresponds to the analytical solution, and squares (resp. diamonds, stars, triangles, crosses) to HERACLES simulation with a constant time step equal to 0.1 $\tau (e)$ (resp. 1, 10, 100, 10⁵). Each point corresponds to a time step of the simulation.

In the text

$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5486fE9.ps}\end{figure}$ Figure E.9: Marshak wave test: comparison of Heracles results (radiative energy with a solid line and gas energy with a dashed line) with the Su & Olson (1996) solution (radiative energy with stars and gas energy with crosses) at three different times.

In the text

$\begin{figure} \par\includegraphics[width=7.2cm,clip]{5486f1.eps}\end{figure}$	Figure 1: Eigenvalues of the Jacobian matrix normalized by c.
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$\begin{figure} \par\includegraphics[angle=90,width=7.6cm,clip]{5486f2.eps} \end{figure}$	Figure 2: Radiative temperature in the shadow test using the diffusion equation ( upper panel), M₁ closure with fixed eigenvalues ( middle panel), and M₁ closure with calculated eigenvalues ( lower panel).
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5486f3.eps}\end{figure}$	Figure 3: Radial profiles of the radiative temperature in the shadow test using the diffusion equation (dotted line), M₁ closure with fixed eigenvalues (dashed line), and M₁ closure with calculated eigenvalues (solid line).
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$\begin{figure} \par\includegraphics[width=3.8cm,clip]{5486f4a.eps}\hspace*{4mm} \includegraphics[width=3.8cm,clip]{5486f4b.ps} \end{figure}$	Figure 4: Left panel: HERACLES temperature map. Right panel: isotherms for HERACLES (solid lines) and a Monte-Carlo code (dashed lines).
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$\begin{figure} \par\includegraphics[width=6.2cm,clip]{5486f5.eps} \end{figure}$	Figure 5: Normalized radiative energy isocontours for $\omega =1$ (solid lines) and $\omega =0.9$ (dashed lines).
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5486f6.eps} \end{figure}$	Figure 6: Subcritical shock: gas (solid line) and radiative (dashed line) temperatures at 1.7e4, 2.8e4, and 3.8e4 s obtained with the M₁ model (thick lines) compared to a constant and isotropic Eddington tensor model (thin lines).
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$\begin{figure} \par\includegraphics[width=7.8cm,clip]{5486f7.eps}\end{figure}$	Figure 7: Supercritical shock: temperatures (thick lines) of gas (solid line) and radiation (dashed line) at 4.0e3, 7.5e3, and 1.3e4 s and the corresponding reduced fluxes (thin lines).
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