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<p>In this study, optimal control problems for the Navier-Stokes-<InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> (NS-<InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>) model and the Navier-Stokes-<InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation> (NS-<InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>) model are considered. Optimality conditions are derived, and semi-discrete a priori error estimates for all fluid variables are analyzed for both models. Numerical tests are performed to verify the accuracy of the theoretical findings and to demonstrate the effectiveness of optimal control. Given the proven utility of the NS-<InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(\alpha \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> and NS-<InlineEquation ID="IEq10"> <EquationSource Format="TEX">\(\omega \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation> models in fluid dynamics, this study addresses a significant gap by exploring the potential of optimal control to enhance the performance, efficiency, safety, and environmental impact of fluid systems.</p>

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Optimal Control problems of NS-\(\alpha \) and NS-\(\omega \) turbulence models: analysis and numerical tests

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年1月30日

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  • Gülnur Haçat,
  • Aytekin Çıbık,
  • Fikriye Yılmaz,
  • Songül Kaya

摘要

In this study, optimal control problems for the Navier-Stokes- \(\alpha \) α (NS- \(\alpha \) α ) model and the Navier-Stokes- \(\omega \) ω (NS- \(\omega \) ω ) model are considered. Optimality conditions are derived, and semi-discrete a priori error estimates for all fluid variables are analyzed for both models. Numerical tests are performed to verify the accuracy of the theoretical findings and to demonstrate the effectiveness of optimal control. Given the proven utility of the NS- \(\alpha \) α and NS- \(\omega \) ω models in fluid dynamics, this study addresses a significant gap by exploring the potential of optimal control to enhance the performance, efficiency, safety, and environmental impact of fluid systems.