Two aerospace engineering researchers at San Diego State University have developed a cutting-edge mathematical model that could significantly impact the future of hypersonic military aircraft, while also offering potential benefits in climate science and medicine.

The model focuses on predicting the behavior of fuel droplets and gas particles in detonation waves—extremely fast-moving shock waves present in scramjets and rocket engines used in hypersonic flight. By offering insight into how these particles move and interact, the new model enables more precise and advanced systems modeling than previously possible.

Developed by Professor Gustaaf Jacobs and Assistant Professor Qi Wang from SDSU’s College of Engineering, the model was created in collaboration with Daniel Tartakovsky from Stanford University. The research was supported by funding from the US Air Force Office of Scientific Research.

The team’s work centers on interacting particle systems and aims to enhance the understanding of gas stability and how it impacts engine performance at hypersonic speeds. Previously, scientists had limited data on the trajectories of liquid and gas particles under these extreme conditions, making this breakthrough a significant step forward.

Their approach—referred to as the Liouville method—builds on established mathematical frameworks, including the Fokker–Planck equation and the Langevin model, both of which describe particle motion in dynamic systems. The new method uses a data-driven framework to infer particle behavior and predict their positions in response to changing velocities over time.

The model provides key insights into the thermal and stability behavior of gases near high-speed aircraft surfaces. At speeds above Mach 5, even small disruptions can lead to severe consequences, including total engine failure. By better understanding and predicting these behaviors, the new model offers a path toward safer and more reliable hypersonic propulsion systems.

The research, published in the journal Physics of Fluids, draws inspiration from work that originated during the Manhattan Project and continues to evolve to meet the demands of modern high-speed aerospace technology.

By Impact Lab