Spherical Blast Waves Test 
Various papers have presented results from similar spherical blast wave tests, e.g. Zachary, Malagoli, A., & Colella,P., SIAM J. Sci. Comp., 15, 263 (1994); Balsara, D., & Spicer, D., JCP 149, 270 (1999); Londrillo, P. & Del Zanna, L., ApJ 530, 508 (2000).
Different authors set this problem up in different ways. To test Athena, we used a rectangular domain, 0.5 ≤ x ≤ 0.5; 0.75 ≤ y ≤ 0.75. The boundary conditions are periodic everywhere. This nonsquare domain and periodic boundary conditions produces complex shockshock and shockCD interactions at late times.
The initial density is 1.0, the pressure is 0.1, and the gas constant is γ = 5/3. Initial velocities are zero everywhere. Within the region r < 0.1, the pressure is set to 10.0 (that is, 100 times the ambient pressure). For the MHD problem, the initial magnetic field is uniform everywhere with B_{x} / (4π)^{1/2} = B_{y} / (4π)^{1/2} = 1/√2.
To be honest, this test is not very quantitative, but makes great movies!
At early times, it is important that the outgoing blast wave is spherical and shows no grid alignment effects.
At late times, the interaction of the blast wave with the CD at the edge of the evacuated bubble in the center produces filaments of dense gas by the RichtmyerMeshkov instability. It is important these fingers are sharp and not diffused away. Moreover, for the hydrodynamical problem, the pattern of the fingers should be EXACTLY symmetric toptobottom and lefttoright. For the MHD problem, the RichtmyerMeshkov instability is suppressed, and no fingers are evident.
Results computed with Athena using the HLLC solver and the third order algorithm on a 400x600 grid are shown below. The images show the density on a linear color map between 0.08 and 6.5. The image on the left is at t = 0.2, the image on the right is at t = 1.5
Note the pattern of dense fingers in the interior produced by the RichtmyerMeshkov instability is exactly symmetric.
Click on the right image to download a .gif movie (39.5MB).

Results computed with Athena using the Roe solver and the third order algorithm on a 400x600 grid are shown below. The images show the density on a linear color map between 0.08 and 6.5. The image on the left is at t = 0.2, the image on the right is at t = 1.0
Note the RichtmyerMeshkov instability is supressed by the magnetic field, and no fingers are evident in the interior of the bubble. Also note the bubble is strongly aligned along the magnetic field.
Click on the right image to download a .gif movie (32MB).
