A novel p-harmonic descent approach applied to fluid dynamic shape optimization

Abstract We introduce a novel method for the implementation of shape optimization non-parameterized shapes in fluid dynamics applications, where we propose to use derivative determine deformation fields with help $$p-$$ p - Laplacian $$p > 2$$ > 2 . This approach is closely related computation steepest descent directions functional $$W^{1,\infty }-$$ W 1 , ∞ topology and refers recent publication Deckelnick et al. (A $$W^{1,\infty}$$ optimisation Lipschitz domains, 2021), this idea proposed. Our demonstrated drag-minimal free floating bodies. The validated against existing approaches respect convergence algorithm, obtained shape, regarding quality computational grid after large deformations. numerical results strongly indicate that }$$ -topology—though numerically more demanding—seems be superior over classical invoking Hilbert space methods, concerning convergence, mesh deformations, particular when optimal features sharp corners.