Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866915968353042432 |
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| author | Simoes, Alexandre Anahory Bloch, Anthony Colombo, Leonardo |
| author_facet | Simoes, Alexandre Anahory Bloch, Anthony Colombo, Leonardo |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2311_01774 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance Simoes, Alexandre Anahory Bloch, Anthony Colombo, Leonardo Mathematical Physics Numerical Analysis Optimization and Control 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. |
| title | Optimal Control of Incompressible Ideal Flows with Obstacle Avoidance |
| topic | Mathematical Physics Numerical Analysis Optimization and Control |
| url | https://arxiv.org/abs/2311.01774 |