A volumetric geometry and topology parameterisation for fluids-based optimisation

A new geometry and topology parameterisation method is presented which is based on creating a parameterisation grid of cells and reconstructing surfaces from the fraction of the cell volume defined to be solid, with the volume fractions acting as design variables. This method is able to include topological changes alongside fine-level geometric control, and therefore offers a significant increase in flexibility. In this work, the geometric capabilities of the method are confirmed by successfully constructing a variety of surfaces, using both arbitrary object outlines and aerofoil geometries. The method is then used in a range of optimisation problems covering the design of a coastal defence, increasing fluid damping within an oscillating box by the addition of baffles, and design of a multi-body configuration for minimum drag in supersonic flow. These problems demonstrate the benefits of a parameterisation for fluids modelling that is capable of topological changes and which can be used with global search as well as gradient-based methods.