Parametric Surfaces with Volume of Solid Control for Optimisation of Three Dimensional Aerodynamic Topologies

This paper presents a topologically flexible parameterisation method suitable for the optimisation of 3 dimensional aerodynamics using traditional boundary fitted meshes. This parameterisation extends the restricted-snake volume of solid (RSVS) parameterisation previously developed by the authors. This is achieved by extending restricted snakes, a parametric active contour method, into a restricted surface capable of efficiently evolving arbitrary complex topologies handling collisions with no floating point arithmetic. This is integrated with a surface generation rule which allows smooth shapes with intuitive parameterisation of topology. The 3D-RSVS is presented along with results displaying its smooth behaviour, it’s ability to produce shapes of aerodynamic interest and it’s topological flexibility. A hierarchical approach to the volume of solid design variables is presented for the RSVS, allowing automatic design of the grids on which VOS are specified. An optimisation framework is proposed and some example 2 dimensional optimisation results are presented.