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Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance

Mathematical Physics 2026-05-01 v2 Numerical Analysis math.MP Numerical Analysis Optimization and Control

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.

Keywords

Cite

@article{arxiv.2311.01774,
  title  = {Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance},
  author = {Alexandre Anahory Simoes and Anthony Bloch and Leonardo Colombo},
  journal= {arXiv preprint arXiv:2311.01774},
  year   = {2026}
}

Comments

6 pages, conference

R2 v1 2026-06-28T13:10:26.571Z