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arXiv · 2311.01774

Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance

Alexandre Anahory Simoes·Anthony Bloch·Leonardo Colombo
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Abstract

It was shown in \cite{bloch2000optimal} that an optimal control formulation for incompressible ideal fluid flow yields Euler's equations. In this paper, we consider a variational obstacle-avoidance formulation for incompressible ideal flows by introducing a barrier-type potential in the associated optimal control functional. This leads to \textit{modified Euler equations for an inviscid fluid}, in which the barrier term acts on the Lagrangian configuration and appears in the Eulerian description as a shift in the effective pressure. We also present a numerical illustration of the reduced Eulerian dynamics, showing that the barrier term induces a localized deformation of the flow near the obstacle region, consistent with its role as an obstacle-avoidance penalization.

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Alexandre Anahory Simoes, Anthony Bloch, Leonardo Colombo. 2023-11-03. Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance. https://arxiv.org/abs/2311.01774

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