Some thoughts on oblique shocks (both hydro and MHD)

1D Hydro Oblique Shocks.

Here is the pseudo color plot of rho with velocity vector field:

Here are lineouts of fluid vars:

The initial conditions have no gradients in y (the Riemann discontinuity is in x). This means the d/dy term in the y-momentum equation go to zero, and py is essentially advected through the grid passively (this would explicitly happen if nDim=1 in the code). There are periodic boundary conditions in y, as well, so this is effectively an infinite 1D problem.

Now, because there are no pressure gradients in y, we would not expect vy to change across the outer shock front. Instead, the only thing that could happen is a change in the x quantities. This is consistent with the lineouts above.

Also interesting is how the component of the velocity perpendicular to the shock front (vx) goes exactly to zero across the shock. At first I thought this must again be because there are no gradients in the setup that would drive changes in vy across the shock. So, if vx did not go to zero across the boundary, vy would change. Thus, vx necessarily must go to zero across the shock, regardless of mach, angle, etc. However, upon further thought, I don't think this is valid. Vy is a parallel component to the shock, and thus should be constant across the shock no matter what. So why does vx go to zero?

1D MHD Oblique Shocks.

The case is a little different in MHD. In MHD, each of the fluid velocities are kept in the Euler equations for our solvers, even when nDim=1. Is this because now, there can be gradients in y generated from the field, even when none might exist initially? We certainly see different behavior in the lineouts for the MHD case. Where there was no change in vy across shocks in 1D hydro, there are changes in vy across 1D MHD shocks:

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