Breakthrough math model could unlock 3,836 mph hypersonic flight

Researchers at San Diego State University, in collaboration with Stanford University, have developed a novel computational mathematics model that simulates the behavior of gas and fuel droplets in detonation waves occurring in hypersonic propulsion systems such as scramjets and rotating detonation engines. This model, termed the Liouville method, builds on classical equations like the Fokker–Planck and Langevin models to predict particle dynamics at speeds exceeding Mach 5 (approximately 3,836 mph). Funded by the US Air Force Office of Scientific Research, the model provides new insights into the stability and thermal behavior of gases near hypersonic vehicles, addressing critical challenges that arise when flight conditions become unstable at these extreme speeds. Beyond its primary application in advancing hypersonic military aircraft design, the model has potential interdisciplinary uses in climate science and medicine, where understanding particle dynamics and shock wave interactions is essential. For example, it could improve climate modeling by better describing particle behavior in the atmosphere and assist medical techniques that use