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Clément Moreau, Kenta Ishimoto, Yannick Privat, Shapes optimising grand resistance tensor entries for a rigid body in a Stokes flow

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DOI: 10.23952/jano.7.2025.3.06
Volume 7, Issue 3, 1 December 2025, Pages 377-398

 

Abstract. We investigate the optimal shapes for the hydrodynamic resistance of a rigid body set in motion in a Stokes flow. At this low Reynolds number regime, the hydrodynamic drag properties of an object are encoded in a finite number of parameters contained in the grand resistance tensor. Considering these parameters as objective functions, we use calculus of variations techniques to derive a general shape derivative formula, allowing to specify how to deform the body shape to improve the objective value of any given resistance tensor entry. We then describe a practical algorithm for numerically computing the optimized shapes and apply it to several examples. Numerical results reveal interesting new geometries for various criteria and perspectives into optimal hydrodynamic profiles.

 

How to Cite this Article:
C. Moreau, K. Ishimoto, Y. Privat, Shapes optimising grand resistance tensor entries for a rigid body in a Stokes flow, J. Appl. Numer. Optim. 7 (2025), 377-398.