Drag-minimising bodies in confined Stokes flows

Abstract

Slow viscous flow around a fixed body generates a shape-dependent drag. We explore the drag-minimising shapes of bodies centred between two parallel plates in two-dimensional viscous flow. The channel width introduces a length scale so that the optimal profile is area-dependent. We solve the shape optimisation problem numerically over a wide range of areas. We also compute the optimal elliptical shapes and this identifies how these shapes should be slightly altered to reduce the drag with reductions of up to 3.8% attained at high areas. More broadly, we derive two properties of general optimal shapes within the confined flow: the magnitude of the surface vorticity is approximately (but not e..