The simulations show interactions between a planar shock and various heterogeneities. These examples are inspired by the 3-D shock-bubble interaction example used by Langseth and LeVeque to illustrates the induced vorticity and mixing when a shock wave runs through a inhomogeneous media.
The setup is as follows (upper left). A circle with radius 0.2 is centered at (0.3,0.0) in the domain [-0.1,1.5]x[-0.5,0.5]. The gas is initially at rest and has unit density and pressure. Inside the circle the density is 0.1. The incoming shock wave starts at x = 0 and propagates in the positive x-direction. The pressure behind the shock is 10, giving a 2.95 Mach shock. Due to symmetry, we use computational domain [-0.1,1.5]x[-0.5,0.0] with a reflective boundary at the symmetry line y = 0.
Resolving vorticities is a question of resolution and numerical viscosity. The front tracking method is formally first order. However, comparisons with CLAWPACK for the shock-bubble problem, shows that our method produces results that are superior compared with the first order method in CLAWPACK and approximately equal those of the second order method with the minmod limiter (the most diffusive limiter).
We present results from three different simulations. In each simulation we have used the symmetry property and equally spaced time steps. The final computational time is 0.40. We present snapshots of the density depicted as emulated Schlieren images.
A 640 x 200 grid with no refinement and 256 time steps:
For the last two runs the images have been reduced to half size. Moreover, some noise was generated when saving the images on the JPEG format due to the image compression.