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# Mach 3 Wind Tunnel with a Step

The problem of a wind tunnel containing a step was first described by Emery (1968), who used it to compare several hydrodynamical methods which are only of historical interest now. Woodward and Colella (1984) later used it to compare several more advanced methods, including PPM.

The problem uses a two-dimensional rectangular domain three units wide and one unit high. Between x=0.6 and x=3 along the x-axis is a step 0.2 units high. The step is treated as a reflecting boundary, as are the lower and upper boundaries in the y direction. For the right-hand x boundary we use an outflow (zero gradient) boundary condition, while on the left-hand side we use an inflow boundary. In the inflow boundary zones we set the density to 1.4, the pressure to 1, and the velocity to 3, with the latter directed parallel to the x-axis. With a gamma of 1.4 this corresponds to a Mach 3 flow. The domain itself is also initialized with these values. Because the outflow is supersonic throughout the calculation, we do not expect reflections from the right-hand boundary.

We have run this problem using FLASH 1.0 with 5 levels of adaptive mesh refinement (AMR). With a top-level grid of 15x5 blocks, each of which has 8x8 zones, this corresponds to an effective grid of 3840x1280 zones.

Movies (QuickTime format)
Density
Pressure with AMR block structure

Images
5-level run Density with velocity arrows for t=0 to 2 (GIF, Postscript)
Density with velocity arrows for t=2.5 to 4 (GIF, Postscript)
Comparisons Density at t=4 for 2, 3, 4, and 5 levels of refinement (GIF, Postscript)
Detail of the Kelvin-Helmholtz instability observed at the slip line behind the Mach stem for 2, 3, 4, and 5 levels of refinement (GIF, Postscript)

References
Emery, A. F. 1968, J. Comp. Phys., 2, 306
Woodward, P. and Colella, P. 1984, J. Comp. Phys., 54, 115

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ricker@flash.uchicago.edu