A Mach 3 Wind Tunnel with a Step

This example is a classical test example dating at least back to the famous paper of Woodward and Colella: The numerical simulation of two-dimensional fluid flow with strong shocks, Journal of Computational Physics, 54, pp. 115-173 (1984).

The test case describes a Mach 3 flow in a wind tunnel. The tunnel is 1 length unit high and 3 length units long. The step is 0.2 length units high and is located 0.6 length units from the left-hand end of the tunnel. The walls are reflective.

In the figure to the right we show the density at time 4.0 computed by front tracking and dimensional splitting on the same three grids as used by Woodward and Colella (dx = 1/20, 1/40, 1/80). The number of equally spaced time steps are 160, 320, and 640, respectively. This corresponds to an approximate CFL number 2.0

The general shape and position of the shocks are accurately represented. The shocks are thin, and thus some numerical instabilities of strong shocks are evident at the bottom and behind the Mach stem where the shocks are nearly aligned with the grid. The contact discontinuity emerging from the Mach stem is present on all grids, but is spread somewhat as it moves away from the three-shock interaction point. Unfortunately, the results are marred by the presence of a expansion shock in the rarefaction fan.

An emulated Schlieren mpeg-movie is available for the simulation on the middle grid.

Two mpeg-movies are also available, demonstrating the effect of varying the TV threshold parameters in the adaptive grid refinement algorithm. (small parameters, large parameters).