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In the last decade, parameter-free approaches to shape optimization problemshave matured to a state where they provide a versatile tool for complexengineering applications. However, sensitivity distributions obtained fromshape derivatives in this context cannot be directly used as a shape update ingradient-based optimization strategies. Instead, an auxiliary problem has to besolved to obtain a gradient from the sensitivity. While several choices forthese auxiliary problems were investigated mathematically, the complexity ofthe concepts behind their derivation has often prevented their application inengineering. This work aims at an explanation of several approaches to computeshape updates from an engineering perspective. We introduce the correspondingauxiliary problems in a formal way and compare the choices by means ofnumerical examples. To this end, a test case and exemplary applications fromcomputational fluid dynamics are considered.

Parameter-free shape optimization: various shape updates for engineering applications