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
MACH WEDGE DENSITY. THE UPPER PANELS SHOW A UNIT AREA CENTERED ON X = 3.0, Y = 0.5, AT T = 0.25. THE NUMBERS IN THE UPPER LEFT CORNERS 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.