Efficient optimisation procedure for design problems in fluid mechanics

• A complete optimisation procedure is proposed for fluid mechanics problems.
• High-order derivation is used to parameterise the flow-field.
• Fast optimisation is achieved with a genetic algorithm and high-order derivation.
• Self-organizing maps provide a clear overview of the high-dimensional optimised set.

A complete methodology designed to deal efficiently with multi-parameter and multi-objective optimisation problems in fluid mechanics is proposed. To cope with the said problems, the method uses a genetic algorithm to perform the optimisation through the evolution of a set of configurations. To avoid unreasonable calculation time that would be induced by the direct simulation of every configuration, the genetic algorithm is coupled with a parametrisation technique specially designed for fast and accurate evaluations of flows. The technique introduces a high-order differentiation of a baseline flow with respect to the design parameters. The flow derivatives are then used to extrapolate the flow-field for any parameter value, which is much faster than a direct simulation of the flow. The results of the optimisation are analysed using self-organizing maps. This technique allows a clear representation of sets of data lying in highly dimensional spaces. The self-organizing maps are used to provide a clear insight in the mechanisms at stake for the optimisation process.