Shape optimization of slip-driven axisymmetric microswimmers
arxiv(2024)
摘要
In this work, we develop a computational framework that aims at
simultaneously optimizing the shape and the slip velocity of an axisymmetric
microswimmer suspended in a viscous fluid. We consider shapes of a given
reduced volume that maximize the swimming efficiency, i.e., the
(size-independent) ratio of the power loss arising from towing the rigid body
of the same shape and size at the same translation velocity to the actual power
loss incurred by swimming via the slip velocity. The optimal slip and
efficiency (with shape fixed) are here given in terms of two Stokes flow
solutions, and we then establish shape sensitivity formulas of adjoint-solution
that provide objective function derivatives with respect to any set of shape
parameters on the sole basis of the above two flow solutions. Our computational
treatment relies on a fast and accurate boundary integral solver for solving
all Stokes flow problems. We validate our analytic shape derivative formulas
via comparisons against finite-difference gradient evaluations, and present
several shape optimization examples.
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