Topology-inclusive aerodynamic shape optimisation using a cellular automata parameterisation

A novel geometry parameterisation method constructed from a volume-of-solid driven cellular automata is presented. The method is capable of describing complex geometry of arbitrary topology using a set of volume-of-solid parameters applied to a geometry control mesh. This is done by approximating the smooth geometry of minimum surface area subject to a set of localised constraints on contained volume defined by both the control mesh and volume-of-solid parameters. Localised control mesh refinement is possible through splitting of control mesh cells to provide additional degrees of freedom where necessary. The parameterisation is shown to reconstruct over 98% of a library of aerofoil geometries to within a standard wind tunnel-equivalent geometric tolerance, and to recover known analytical optima in supersonic flow. Using gradient-free optimisation methods, the parameterisation is then shown to construct aerodynamic geometries consisting of multiple objects to package a set of existing geometries. Finally, the parameterisation is used to construct an optimal supersonic multi-body geometry with less than half the drag of the equivalent volume optimal single body.