Modelling air flow around a cruising aircraft, a high speed train going through a tunnel or a space probe entering Mars' atmosphere, fuel combustion in an engine or indeed the flow of water in the Mont-Saint-Michel Bay, all these complex problems in aero- or hydro-dynamics make use of models from fluid mechanics. To solve them, industry currently uses computation code developed twenty five years ago.
Code they are constantly adapting to perfect the modelling of phenomena, deal with increasingly complex geometries and attempt to take better account of physical phenomena, uncertainties, etc. Up to now, the growing power of computers, and then parallel computing architecture, have sufficed. But this approach is now reaching its limits. "To go further," says Rémi Abgrall, joint founder of the SCALAPPLIX project, "numerical methods really need to be improved from both a mathematical and computer science viewpoint. That is the aim of the ADDECCO project. Over five years, we are going to suggest, develop and confirm new methods of interest to industry, likely to have a strong impact on their code.
To the best of my knowledge, this is the first time an attempt has been made to apply techniques from compressible fluid mechanics modelling while including such complex geometries exactly. It is likely to radically alter not only aerodynamic simulation, but also many other fields such as acoustics, geophysics or magneto-hydrodynamics.
The editor of several specialist scientific computation journals, Rémi Abgrall was among the first to promote these new methods which handle three categories of problem differently. First of all, dealing with unknowns and uncertainty in models – unknowns as regards geometry, physical phenomena, flows, etc. Instead of allocating them fixed values in the first instance, the methods suggest considering them as random variables. Next, dealing with objects' geometry. To improve this, Rémi Abgrall will use the numerical computation method that he has been developing for some ten years with the aim of solving, with the same formal accuracy and very efficiently, problems both of flow discontinuity (shock waves) and questions relating to more regular flow areas. "This problem was put to me by an engineer from Dassault Aviation," he relates. "I didn't have the time to think about it… until a nasty fall from my bike meant I was out of action for three months.
I used the time to start formalising the approach." The outcome was a precise numerical schematic, robust and flexible enough to be able to handle, with the same mathematical functions, both geometry defined by CAD (computer-aided design) and the physical variables describing the flow. Lastly, the third category of problem is simplified modelling of the most complex flows, knows as nonstationary flows (unstable over time). The method developed by Rémi Abgrall is expected, here too, to provide a breakthrough solution. How? By improving calculation accuracy without a massive increase in volume, thanks to solution representations more closely connected to the physics of flows than to the mathematical constraints which have hitherto guided the design of numerical methods.
"The efficiency of numerical methods is key."
Bruno Stoufflet, scientific director at Dassault Aviation, has been working with Rémi Abgrall and other Inria teams for around fifteen years, in particular on evaluating the aerodynamic performance of business and combat aircraft.
We use digital simulations before designing an aircraft. They enable us to predict performance and to make the best architecture choices, with the best compromise on the basis of the target objectives. We accordingly evaluate not only aerodynamic parameters such as lift, but also aircraft structure and stealth characteristics. These methods are effective to a lesser or greater degree in terms of accuracy and speed of performance evaluation. Computer calculations require simplified formulations of physical phenomena. Through their great knowledge of numerical methods and their mathematical analysis, SCALAPPLIX researchers are helping us minimise the numerical errors that this introduces.