Euler - Paradign-shift in fluid mechanics enabling massive energy savings

Authors: Johan Jansson (, Claes Johnson, Ridgway Scott, Rebecca Durst, Linde Van Beers

Adaptive Euler for HiLiftPW4 - sweep over angle of attack
  • Today the industry does not trust aerodynamics simulation - calls it "Colorful Fluid Dynamics"
  • Our Euler aerodynamics paradigm-shift makes simulation reliable - direct simulation of natural laws
  • You can now reliably design, optimize, certify and innovate aircraft, wind turbines, ships, etc. in the web browser, 100x faster and cheaper than industry standard.
  • Strong NASA recognition of breakthrough Euler aerodynamics from NASA Branch Chief of Computational Aerodynamics Cetin Kiris
  • Delivered as DigiMat online course, largest online course in Sweden with 30000+ participants.

Concrete benefits for academia and industry

  • Innovate and optimize aerodynamic designs of vehicles, power generation, etc. - increase energy efficiency and e.g. range of vehicles.
  • Reduce computational cost and energy use by at least 100x-10000x.

Peer Review

Our results and methodology were peer-reviewed by the NASA leaders of the High Lift Prediction Workshop, considered to be the most important benchmark for aerodynamics in the field. NASA Branch Chief of Computational Aerodynamics Cetin Kiris, wrote a public review as part of the workshop summary here:

W-030 [Johan Janssons team] shows promise with a rapid LES solution procedure with measurable improvements over RANS but is not representative of typical WMLES due to the assumed Reynolds number invariance (Euler Eqs). The validity of this procedure for high lift applications needs to be investigated more critically.

This is "as good as it gets" statement in a peer-review in a setting like this.

Technical Overview and References

AIAA Aviation 2022 Paper

AIAA Aviation 2022 Paper: Predictive Euler CFD - Resolution of NASA Vision 2030

AIAA Aviation 2022 Presentation Video

Euler Paper (with more details)

Pedagogic overview of Adaptive Euler and HiLiftPW 2-4 results - DigiMat Pro online course

("Real Flight Simulation" and "Adaptivity")

Here a range of learning activities with Jupyter/Google Colab are available, starting from simple to advanced.

See more references at:

Interactive Adaptive Euler Digital Math web simulator site - "Modern Scientific Paper"

Launched in conjunction with AIAA Aviation 2022 June 26!

Adaptive Euler for HiLiftPW4 at aoa=21.5 (stall angle)

Try yourself in your web browser!

Click this Jupyter/Google Colab notebook

Run with Google Colab Pro (10USD/month) , then 20 cores are used and the simulation only takes appx. 6 hours.

This work is developed as part of the Digital Math framework - as the foundation of modern science based on constructive digital mathematical computation. We invite you to run and modify the simulations yourself in your web browser. The anove link is the Digital Math web environment with the Open Source Real Flight Simulator/FEniCS software for reproducing the results in the paper at in principle ``zero'' cost. You can also find more detailed presentation and results on this page.

Modern Scientific Paper presentation and interactive, modifiable, runnable, reproducible simulation based scientific paper