This test case consists of a shock traveling over a dense magnetic cloud. The problem is set up as a [-1.0, -1.5] x [3.5, 1.5] rectangle. In the beginning, a Ma=8 shock is initialized in the right half of the computational domain at x=2.5, while a circular dense cloud with a radius of r=0.3 is placed at x=2.85. The pre-shock density and pressure outside of the cloud are both set to unity, the flow speed in x-direction is set such that the shock is kept “static” during the calculation. The post-shock state is determined by the Rankine-Hugoniot conditions. The magnetic field is zero everywhere in the domain except for the cloud, where it is initialized as circular with a maximum of 1.3. Inside the cloud, a smooth function is applied to bring the cloud density of 2.0 in line with the surroundings.
The following image shows a density plot at t=0.9. The cloud has traveled over the shock and is now deformed. We can see slight roll-up.
A purely hydrodynamic Euler calculations was performed with the same setting. Here, the absence of the magnetic field permits a stronger roll-up phenomena, once the cloud interacts with the shock. This corresponds to findings in the literature.