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We introduce a novel method for the implementation of shape optimziation influid dynamics applications, where we propose to use the shape derivative todetermine deformation fields with the help of the $p-$ Laplacian for $p > 2$.This approach is closely related to the computation of steepest descentdirections of the shape functional in the $W^{1,\infty}-$ topology. Ourapproach is demonstrated for shape optimization related to drag-minimal freefloating bodies. The method is validated against existing approaches withrespect to convergence of the optimization algorithm, the obtained shape, andregarding the quality of the computational grid after large deformations. Ournumerical results strongly indicate that shape optimization related to the$W^{1,\infty}$-topology -- though numerically more demanding -- seems to besuperior over the classical approaches invoking Hilbert space methods,concerning the convergence, the obtained shapes and the mesh quality afterlarge deformations, in particular when the optimal shape features sharpcorners.

A Novel $p$-Harmonic Descent Approach Applied to Fluid Dynamic Shape Optimization