Exploring Design Space by Using Digital Geometry and Level-Set Morphing Methods

This paper was produced for the 2019 NAFEMS World Congress in Quebec Canada

Resource Abstract

Digital Geometry is a method for representing 3-dimensional objects as a collection of ‘voxels’ or volume elements, analogous to the digital rendering of a 2-dimensional picture using pixels. Sub voxel-scale information is represented as a distance field, managed as a level-set and stored at each voxel location within the domain. The surface of the geometry is represented by the iso-surface of the distance field, L=0.

Cambridge Flow Solutions have developed a tool which manipulates the level-set (and thus the surface of the geometry) in response to a speed function. This approach enables large scale changes to the geometry characterised by ‘morphing’ – i.e. a smooth continuous shape change between end-states. In this presentation we seek to show the enormous flexibility of the design space offered by this method and a sample of techniques that can be used to explore it.

Given two different geometry end states A and B, the level-set morphing method immediately gives access to all the intermediate evolution states as A morphs to become B. Any number of these ‘hybrids’ might offer a better outcome for the objective function than either end-state and, in general, none of them are straightforwardly accessible via standard BRep based parameterised CAD.

Another dimension is added to the design space when considering the relative spatial positioning of A and B. The intermediate hybrid ‘set’ that is calculated for each level-set morph is different depending on how B is initially positioned relative to A and in this presentation we show ways to exploit this additional design space parameter.

With two parameters in play (relative position of B to A and degree of morph ‘evolution’) we explore the design space for a typical aerodynamic optimisation study. By using an automated workflow to create a Design of Experiment and extract a response surface for an objective function we can discover non-intuitive places in the design space which lead to novel designs with improved performance. All the candidate designs are created within the meshing/analysis environment and are independent of any external BRep based CAD constraints.

Document Details

AuthorEvans. R
Date 18th June 2019
OrganisationCambridge Flow Solutions


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