CFD Topology & Shape Optimisation
The general form of an optimisation problem also applies naturally to topology and shape optimisation:
" Minimise a defined cost function by varying a number of defined design variables, obeying a set of fixed constraints " The major advantage of employing adjoint methods (a special way to calculate the sensitivity of the cost function to the design variables) is that the effort of finding the sensitivities for a required cost function is independent of the number of defined variables.
Transferred into the CFD world this can result in the following example setup:
- Inlet and outlet positions are defined, fixed and used as constraints.
- The available space is volume meshed independent of any expected final solution. This differs from conventional CFD engineering practise. Thus the extent of the meshed volume acts as a de facto constraint on the topology to be extracted.
- Each volume cell in the available space is then assigned an individual momentum sink. Consequently, the number of mesh cells equals the number of design variables.
The topology optimisation method described above is limited in resolution by the cell size used to mesh the design space. As a result, the accuracy of its surface definition is limited to the local cell dimensions. However, in a second stage the newly created geometry can be re-meshed and a similar adjoint method used to find the sensitivity of the objective function to the motion of surface. These sensitivities can then be fed into an iterative mesh motion routine to arrive at a highly accurate optimal shape.