The Double Mach Reflection Test

Reference:

Woodward, P.R., & Colella, P., "The Numerical Simulation of Two-Dimensional Fluid Flow with Strong Shocks", JCP, 54, 115 (1984). The test is described in section 4(c).

Description:

This is a classic test of hydrodynamical algorithms. The paper by W&C contains a complete description of the problem which will not be repeated here.

What's important about this test?

Again, W&C contains an excellent description of the physics of this test. The critical component of the result which differentiates between methods is the appearance of the dense jet along the wall, which is sensitive to numerical diffusion.

Results:

Results computed with Athena using the Roe solver on a 390x120 grid (Δ x = Δ y = 1/120) are shown below. Contour plots of the density at the final time t = 0.2 are shown using 30 levels. No artificial viscosity, flatteners, or extra diffusion of any kind was used.

The plot on the left shows the result computed using the second order algorithm. The plot on the right shows the result computed using the third order algorithm. These plots can be compared to the bottom panel in Figure 9e and 9f in WC respectively.