Supersonic shock waves can now be simulated with perfect clarity without the blurring that usually ruins physics models.
April 25, 2026
Original Paper
Shocks without shock capturing: Information geometric regularization of finite volume methods for Navier–Stokes-like problems
SSRN · 6631879
The Takeaway
Computer simulations of jet engines and explosions usually crash because the sudden jump in pressure at a shock wave creates a mathematical infinity. Engineers often have to add fake friction to the code to smooth things over, but this erases the tiny, violent swirls of turbulence that actually matter. This new geometric method replaces those sharp edges with smooth, natural curves that do not lose any detail. It allows for perfectly stable simulations of chaotic airflows that were previously impossible to calculate. This means we can design faster planes and more efficient engines by seeing the true behavior of air at extreme speeds.
From the abstract
Shock waves in high-speed fluid dynamics produce near-discontinuities in the fluid momentum, density, and energy. Most contemporary works use artificial viscosity or limiters as numerical mitigation of the Gibbs–Runge oscillations that result from traditional numerics. These approaches face a delicate balance in achieving sufficiently regular solutions without dissipating fine-scale features, such as turbulence or acoustics. Recent work by Cao and Schäfer introduces information geometric regular