# 2-D double Mach reflection shock wedge test

This is an example of complex boundary conditions, and the emergence of a complex self-similar structure in the multiple shocks that form from a simple initial geometry. A horizontal Mach 10 shocked flow impinges on a ramp, or wedge, at an angle of 30 degrees up from the horizontal.

In the simulation the shock is setup as an oblique shock, and the wedge is set as a partially reflecting horizontal lower boundary. The horizontal axis is 4.0 units long, and is a free outflow for the first $1/6$ units, then reflecting for the rest of the boundary. The upper boundary is updated with the time-dependent oblique shock location. The left and boundary is constant with the post oblique shock values, and the right boundary is free.

The remaining problem parameters are:

- Adiabatic index: gamma = 1.4.
- Grid domain: 0.0 <
*x*< 4.0, 0.0 <*y*< 2.0 - Shock: Mach 10,
*v_s*= 10.0, - Angle: 30 degrees.
- Pre-shock conditions:
*P*= 1.0,*d*= 1.4,*v*= 0.0. - Post-shock conditions:
*P*= 116.5,*d*= 8,*v*= 8.25.*v_x*= 7.14471,*v_y*= -4.125 - Time limit:
*t*= 0.25.

As the shock moves, it impinges on the reflecting part of the lower boundary and a complex shock reflection structure forms. The simulation was run for a range of resolutions, from *h* = 50 to *h *= 800.

The overall appearance, in the density variable, is shown in the lower panel of the figures below. Key features include:

**A**, the leading edge of the wedge.**B -- C -- D**, a remnant artifact from the initial shock location.**E -- F -- G**. A slipping contact line,**E**,that leads around to a forward moving stem structure,**F**, with a vortex head,**G**.**S**The oblique shock travelling in the direction of the arrow.

The upper panels show the leading structure as a function of increasing resolution, showing the essential features even at the lowest resolution, while the saturated Kelvin-Helmholtz instabilities occur in the slip layers,**E -- F -- G**, at sufficiently high resolutions.

min 5 max 19