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2D 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 figure \ref{f:machwedge}. 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.

Mach Wedge density. Upper Panels show a unit area centered on x - 3.0, $y = 0.5, at t = 0.25. Numbers indicate the linear resolution of the unit square in cells. The lower panel shows the entire 0.0 < x < 4.0, 0.0 < y < 2.0 domain of the simulation at t = 0.25 for the h = 400 resolution simulation. The standard color scale is used for 5 < d < 19