Research Fellows
Pavlos Alexias
Early Stage Researcher 4 at Engys IT
The substance of shape optimization is to manipulate an existing geometry under a set of constraints in order to improve a given objective function. In computational fluid dynamics (CFD) the geometry is described, in a discrete sense, by a set of points with a specific topology. Thus, any change on the geometry’s boundary requires an update of the inner mesh to be able to proceed with the shape optimization. The most efficient way to cope with this problem is to use a mesh adaptation tool (mesh morpher) which propagates the movement of the boundary (surface mesh) to the interior mesh in an effective way. Even if we are using a mesh morpher that can maintain high mesh quality there are cases that the updated mesh can no longer satisfy the quality criteria. This can happen in cases with extreme deformations where the basic features of the shape are changed completely and refinement or remeshing is necessary to capture these changes. In such cases, it is useful to have an automated procedure that creates a new mesh based on the current geometry when the quality mesh criteria are no longer satisfied. This will allow the restoration of the mesh quality and uniformity and will allow continuing with the shape optimization.
A comparison study of two shape optimization applications is demonstrated. Both cases have the same initial geometry and initial conditions. The difference lies in the fact that for the first case we will use a high-fidelity mesh morpher that allows us to converge the problem without the need to re-mesh. Whereas for the second case we will use a simple Laplacian morpher that produces low-quality metrics and the effect of the re-meshing on the optimization procedure will be examined. The next graph illustrates the objective function for every optimization for the two different cases. As it can be seen at the 8th iteration a remeshing took place which had an impact on the solution not just because of the updated geometry but the mesh itself.
The next three figures illustrate the initial (left) and the two final shapes for two different optimizations. The two geometries are almost identical, which is expected since the two optimization
