How do you check a supersonic simulation against reality?

Why it is hard

NASA has done it two ways and both are punishing. Air-to-air, an imaging aircraft orbits at around 30 000 ft while the subject must be supersonic at the precise instant it passes directly underneath; the cameras roll for about three seconds and that window has to coincide exactly. In the two-aircraft case the formation was held to roughly 30 ft longitudinally and 10 ft vertically while the pilot threaded a 200 ft cross-track corridor — and closing the separation to sharpen the image narrows the cone and makes the navigation harder still. The ground-based variant instead waits for the aircraft to eclipse the sun relative to a fixed camera, reading the shock from distortion of the solar granulation through a calcium-K filter. Either way you get seconds of data, from one direction, per sortie.

How we attack it

Note what the published work says the computational difficulty actually is. The signal has to be extracted several body lengths from the aircraft — roughly three, or about eighteen semispans — and over that distance the coalescence of weak pressure disturbances is, in NASA’s own words, sensitive to dissipation and demanding of mesh resolution. The harder the design works to be quiet, the weaker those disturbances, and the more easily a scheme’s own numerical dissipation erases the thing being predicted. Hence grids aligned and stretched along Mach rays, and adjoint-driven adaptive refinement to put cells only where the signal lives. That is the same problem we work on from the other end: not adding resolution until the dissipation stops mattering, but confining the dissipation so that less resolution is needed. A synthetic schlieren is then the natural comparison, because it integrates the same physical quantity the flight camera measures.

What we have established

• The computed image is at Mach 1.05 — the condition NASA’s air-to-air flight imagery was taken at — so the Mach cone sits at 72 degrees rather than the 30 degrees of a textbook Mach 2 case, and the comparison is like for like.
• A synthetic schlieren integrates the same quantity a flight camera does, so the two images are comparable in kind rather than by analogy.
• Shock angle and standoff are geometric, visible, and checkable by eye against published flight imagery.
• Graded mesh refinement puts 149 cells per body length on the airframe and lets the far field coarsen, covering four body lengths of domain in 8.9 million cells — the uniform equivalent is 200 million, which does not fit on the hardware this was run on.
• That whole field was computed in about seven minutes on the integrated GPU of a fanless laptop, in a browser tab.