Optimal Control of the Wilcox turbulence model with lifting functions for flow injection and boundary control

Chirco, Leonardo; Chierici, Andrea; Vià, Roberto Da; Giovacchini, Valentina; Manservisi, Sandro

doi:10.1088/1742-6596/1224/1/012006

Cited by 3 publications

(6 citation statements)

References 9 publications

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“…The lifting function method for the non-homogeneous boundary conditions is often used in the continuous Galerkin finite-element setting to reformulate a boundary control problem into a distributed one [42][43][44]. The method imposes the non-homogeneous (Dirichlet) conditions to the problem through lifting.…”

Section: The Lifting Function Methodsmentioning

confidence: 99%

A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems

Star¹

2022

CiCP

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A Finite-Volume based POD-Galerkin reduced order model is developed for fluid dynamics problems where the (time-dependent) boundary conditions are controlled using two different boundary control strategies: the lifting function method, whose aim is to obtain homogeneous basis functions for the reduced basis space and the penalty method where the boundary conditions are enforced in the reduced order model using a penalty factor. The penalty method is improved by using an iterative solver for the determination of the penalty factor rather than tuning the factor with a sensitivity analysis or numerical experimentation.The boundary control methods are compared and tested for two cases: the classical lid driven cavity benchmark problem and a Y-junction flow case with two inlet channels and one outlet channel. The results show that the boundaries of the reduced order model can be controlled with the boundary control methods and the same order of accuracy is achieved for the velocity and pressure fields. Finally, the reduced order models are 270-308 times faster than the full order models for the lid driven cavity test case and 13-24 times for the Y-junction test case.

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Section: The Lifting Function Methodsmentioning

confidence: 99%

A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems

Star¹

2022

CiCP

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“…In this way, the boundary control parameter is limited to Sobolev space H 1 (Γ c ), although its natural space is H 1 2 (Γ c ). To enforce u c to belong to its natural space it is possible to implement a fractional norm or to adopt a lifting function approach already presented in [8]. In this work we choose to enforce stronger regularity requirements.…”

Section: Boundary Control and Cost Functionalmentioning

confidence: 99%

“…The conditions for the state variables over Γ w are reported in (8) and therefore the boundary integral vanishes with…”

Section: Optimality Systemmentioning

confidence: 99%

“…In [7] the turbulence is controlled acting on the wall temperature and the buoyancy forces. In [8] a lifting function approach has been implemented in order to reformulate a boundary control problem into a distributed one for the RANS system closed with the Wilcox k-ω model. According to this approach, boundary controls are defined in the appropriate function boundary spaces restriction of the natural state volume spaces.…”

Section: Introductionmentioning

confidence: 99%

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An Adjoint Method for the Optimal Boundary Control of Turbulent Flows Modeled with the Rans System

Chierici¹,

Chirco²,

Giovacchini³

et al. 2021

14th WCCM-ECCOMAS Congress

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In recent years, the optimal control in fluid dynamics has gained attention for the design and the optimization of engineering devices. One of the main challenges concerns the application of the optimal control theory to turbulent flows modeled by the Reynolds averaging Navier-Stokes equations. In this work we propose the implementation of an optimal boundary control problem for the Reynolds-Averaged Navier-Stokes system closed with a two-equations turbulence model. The optimal boundary velocity is sought in order to achieve several objectives such as the enhancement of turbulence or the matching of the velocity field over a well defined domain region. The boundary where the control acts can be the main inlet section or additional injection holes placed along the domain. By minimizing the augmented Lagrangian functional we obtain the optimality system comprising the state, the adjoint, and the control equations. Furthermore, we propose numerical strategies that allow to solve the optimality system in a robust way for such a large number of unknowns.

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“…The controls can be chosen for large classes of design parameters. Examples are boundary controls such as injection or suction of fluid [1] and heating or cooling temperature controls [2][3][4], distributed controls such as heat sources or magnetic fields [5], and shape controls such as geometric domains [6]. Finally, a specific set of partial differential equations for the state variables defines the constraints.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Computations of Optimal Control Problems for Boussinesq Equations

Chierici

Giovacchini

Manservisi

2022

Fluids

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The main purpose of engineering applications for fluid with natural and mixed convection is to control or enhance the flow motion and the heat transfer. In this paper, we use mathematical tools based on optimal control theory to show the possibility of systematically controlling natural and mixed convection flows. We consider different control mechanisms such as distributed, Dirichlet, and Neumann boundary controls. We introduce mathematical tools such as functional spaces and their norms together with bilinear and trilinear forms that are used to express the weak formulation of the partial differential equations. For each of the three different control mechanisms, we aim to study the optimal control problem from a mathematical and numerical point of view. To do so, we present the weak form of the boundary value problem in order to assure the existence of solutions. We state the optimization problem using the method of Lagrange multipliers. In this paper, we show and compare the numerical results obtained by considering these different control mechanisms with different objectives.

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Optimal Control of the Wilcox turbulence model with lifting functions for flow injection and boundary control

Cited by 3 publications

References 9 publications

A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems

A Novel Iterative Penalty Method to Enforce Boundary Conditions in Finite Volume POD-Galerkin Reduced Order Models for Fluid Dynamics Problems

An Adjoint Method for the Optimal Boundary Control of Turbulent Flows Modeled with the Rans System

Analysis and Computations of Optimal Control Problems for Boussinesq Equations

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