Numerical algorithms and simulations of boundary dynamic control for optimal mixing in unsteady Stokes flows Article Swipe
Xiaoming Zheng
,
Weiwei Hu
,
Jiahong Wu
·
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2306.10690
YOU?
·
· 2023
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2306.10690
This work develops an efficient and accurate optimization algorithm to study the optimal mixing problem driven by boundary control of unsteady Stokes flows, based on the theoretical foundation laid by Hu and Wu in a series of work. The scalar being mixed is purely advected by the flow and the control is a force exerted tangentially on the domain boundary through the Navier slip conditions. The control design has potential applications in many industrial processes such as rotating wall driven mixing, micromixers with acoustic waves, and artificial cilia mixing. The numerical algorithms have high complexity, high accuracy demand, and high computing expense, due to the multiscale nature of the mixing problem and the optimization requirements. A crucial problem is the computation of the G$â$teaux derivative of the cost functional. To this end, a hybrid approach based on variational formula and finite difference is built with high accuracy and efficiency to treat various types of control input functions. We have experimented with various optimization schemes including the steepest descent algorithm, the conjugate gradient method and two line search options (backtracking and exact line search). We are able to identify and implement the best combinations. The numerical simulations show that the mixing efficacy is limited when only one single type of control is applied, but can be enhanced when more diverse control types and more time segmentation are utilized. The mix-norm in the optimal mixings decays exponentially. The numerical study in this work demonstrates that boundary control alone could be an effective strategy for mixing in incompressible flows.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2306.10690
- https://arxiv.org/pdf/2306.10690
- OA Status
- green
- Cited By
- 1
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4381568097
All OpenAlex metadata
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- OpenAlex ID
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https://openalex.org/W4381568097Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2306.10690Digital Object Identifier
- Title
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Numerical algorithms and simulations of boundary dynamic control for optimal mixing in unsteady Stokes flowsWork title
- Type
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preprintOpenAlex work type
- Language
-
enPrimary language
- Publication year
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2023Year of publication
- Publication date
-
2023-06-19Full publication date if available
- Authors
-
Xiaoming Zheng, Weiwei Hu, Jiahong WuList of authors in order
- Landing page
-
https://arxiv.org/abs/2306.10690Publisher landing page
- PDF URL
-
https://arxiv.org/pdf/2306.10690Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
-
https://arxiv.org/pdf/2306.10690Direct OA link when available
- Concepts
-
Line search, Mixing (physics), Computer science, Boundary (topology), Mathematical optimization, Optimal control, Mathematics, Algorithm, Mathematical analysis, Physics, RADIUS, Computer security, Quantum mechanicsTop concepts (fields/topics) attached by OpenAlex
- Cited by
-
1Total citation count in OpenAlex
- Citations by year (recent)
-
2024: 1Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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| abstract_inverted_index.derivative | 124 |
| abstract_inverted_index.difference | 141 |
| abstract_inverted_index.efficiency | 148 |
| abstract_inverted_index.foundation | 27 |
| abstract_inverted_index.functions. | 156 |
| abstract_inverted_index.industrial | 73 |
| abstract_inverted_index.multiscale | 105 |
| abstract_inverted_index.complexity, | 94 |
| abstract_inverted_index.computation | 120 |
| abstract_inverted_index.conditions. | 64 |
| abstract_inverted_index.functional. | 128 |
| abstract_inverted_index.micromixers | 81 |
| abstract_inverted_index.simulations | 195 |
| abstract_inverted_index.theoretical | 26 |
| abstract_inverted_index.variational | 137 |
| abstract_inverted_index.applications | 70 |
| abstract_inverted_index.demonstrates | 241 |
| abstract_inverted_index.experimented | 159 |
| abstract_inverted_index.optimization | 7, 113, 162 |
| abstract_inverted_index.segmentation | 224 |
| abstract_inverted_index.tangentially | 55 |
| abstract_inverted_index.(backtracking | 178 |
| abstract_inverted_index.combinations. | 192 |
| abstract_inverted_index.requirements. | 114 |
| abstract_inverted_index.exponentially. | 234 |
| abstract_inverted_index.incompressible | 254 |
| cited_by_percentile_year | |
| countries_distinct_count | 0 |
| institutions_distinct_count | 3 |
| sustainable_development_goals[0].id | https://metadata.un.org/sdg/9 |
| sustainable_development_goals[0].score | 0.4099999964237213 |
| sustainable_development_goals[0].display_name | Industry, innovation and infrastructure |
| citation_normalized_percentile |