Shu and Osher's Shocktube Test 
Shu, C and Osher, S., "Efficient Implementation of Essentially NonOscillatory ShockCapturing Schemes, II", J. Computational Physics, 83, 3278 (1989). The test is Example 8.
This test is a hydrodynamic shocktube where the left and the right states are given as follows. Left: (ρ=3.857143; Vx= 2.629369, P = 10.33333) Right: (ρ=1 + 0.2 sin(5 π x); Vx=0; P=1). Essentially it is a Mach=3 shock interacting with a sine wave in density.
This test shows the difficulty of capturing both smallscale smooth flow, and shocks.
Results for the density at time=0.47 computed with Athena using the thirdorder Roe solver on an array of 800 cells (solid line) and 200 cells (squares) with a Courant number of 0.8 and γ = 1.4. Note that the plot is normalized to a spatial extent of [1,1] as opposed to the [4,4] shown in the reference. By comparing to Fig. 14c in the text, it is possible to see the significant improvement in performance per zone at low resolution. At a resolution of 200 cells, all of the shortwavelength extrema are captured, albeit with a lower amplitude than the 800 cell calculation. The velocity and pressure profiles do not contain as much interesting structure and are not shown.
