Velocity optimization of self-equilibrated obstacles in a two-dimensional viscous flow

TL;DR

This paper investigates how to optimize the velocity of obstacles in a 2D viscous flow by shape variation, addressing the complex self-equilibration conditions in a measure-theoretic framework for Stokes and Navier-Stokes equations.

Contribution

It introduces a novel measure-theoretic approach to analyze and optimize obstacle velocities in viscous flows with highly general obstacle shapes.

Findings

Derived conditions for obstacle self-equilibration in measure spaces

Formulated optimization strategies for obstacle velocities

Extended analysis to both Stokes and Navier-Stokes regimes

Abstract

An obstacle is immersed in an externally driven 2D Stokes or Navier-Stokes fluid. We study the self-equilibration conditions for that obstacle under steady state assumptions on the flow. We then seek to optimize the translational and/or angular velocity of the obstacle by varying its shape. To allow general variations, we must consider a very large class of obstacles for which the notion of trace is meaningless. This forces us to revisit the notion of self-equilibration for both Stokes and Navier-Stokes in a measure theoretic environment.