Keywords: optimisation, aerodynamic, CFD, shape parameterisation, domain element, radial basis functions, parallel.

Optimisation has the potential to play key roles in many industries, where improving aerodynamic and structural designs within pre-specified limits and constraints can lead to significant advancements in design. The methods developed and presented here provide a generic and versatile method for high-fidelity fluid-dynamic optimisation of two-dimensional and three-dimensional bodies within practical run times. This combines a novel domain element parameterisation technique, any CFD solver and an advanced parallel gradient-based optimiser.

The domain element method of shape parameterisation presented here uses radial basis functions (RBFs) to provide an interpolation between a domain element and the surface geometry. The parameterisation method links a set of aerodynamic mesh points to a domain element that controls the shape of the design. An RBF inverse mapping occurs between the domain element, the surface geometry and the locations of grid points in the volume mesh, such that the movement of a domain element node smoothly deforms the surface geometry and corresponding volume mesh in a high-quality fashion. The inverse mapping is only required once for the initial design as the values of the parametric coordinates of the grid points with respect to the domain element remain constant throughout the optimisation. Therefore only an initial mesh is required for optimisation and updates to the geometry and the corresponding mesh are provided simultaneously by application of multivariate interpolation; this is extremely fast and efficient and results in very high quality mesh deformation [1].

Design variables are hierarchical such that they can affect the shape at various geometric scales. Gross three-dimensional planform design variables can be combined with fine detailed surface changes to allow complete free-form control. Design variables are intuitive, and only a very low number need be active to produce considerable improvements to designs when the method is combined with optimisation techniques. Complex, multi-element, two- and three-dimensional geometries can be easily parameterised with the domain element position automatically according to local surface geometry, or manually if so desired.

The flexibility and versatility of the parameterisation method developed have enabled the application to many varying aerodynamic shape optimisation problems. A modular optimisation framework has been developed, including an advanced constrained gradient-based optimisation algorithm, and applications include two-dimensional inverse design problems, highly constrained aerofoil and most notably three-dimensional wing optimisations.

The optimisation suite has recently been parallelised to allow optimisation of three-dimensional bodies in practical times. The sensitivity evaluation module has been parallelised to allow parallel evaluation of the required gradients, and this remains independent of the flow solver, so either a serial or parallel version of the flow solver itself may be called, the details of the structure of this optimisation method are presented here. The algorithm has run successfully on over 100 CPUs on two different architectures.

Although only aerodynamic examples are presented, the method developed can easily be applied to any steady-state fluid-dynamic application.

1

Rendall T.C.S., Allen C.B., "Unified Approach to Fluid-Structure Interpolation and Mesh Motion Using Radial Basis Functions", In press, International Journal for Numerical Methods in Engineering, 2007. doi:10.1002/nme.2219

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