Boundary Control Problems in Convective Heat Transfer with Lifting Function Approach and Multigrid Vanka-Type Solvers
Year: 2015
Communications in Computational Physics, Vol. 18 (2015), Iss. 3 : pp. 621–649
Abstract
This paper deals with boundary optimal control problems for the heat and Navier-Stokes equations and addresses the issue of defining controls in function spaces which are naturally associated with the volume variables by trace restriction. For this reason we reformulate the boundary optimal control problem into a distributed problem through a lifting function approach. The stronger regularity requirements which are imposed by standard boundary control approaches can then be avoided. Furthermore, we propose a new numerical strategy that allows solving the coupled optimality system in a robust way for a large number of unknowns. The optimality system resulting from a finite element discretization is solved by a local multigrid algorithm with domain decomposition Vanka-type smoothers. The purpose of these smoothers is to solve the optimality system implicitly over subdomains with a small number of degrees of freedom, in order to achieve robustness with respect to the regularization parameters in the cost functional. We present the results of some test cases where temperature is the observed quantity and the control quantity corresponds to the boundary values of the fluid temperature in a portion of the boundary. The control region for the observed quantity is a part of the domain where it is interesting to match a desired temperature value.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.130914.230115a
Communications in Computational Physics, Vol. 18 (2015), Iss. 3 : pp. 621–649
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 29
-
A penalty-projection algorithm for a monolithic fluid-structure interaction solver
Cerroni, D. | Manservisi, S.Journal of Computational Physics, Vol. 313 (2016), Iss. P.13
https://doi.org/10.1016/j.jcp.2016.02.041 [Citations: 7] -
Optimal Control of the Wilcox turbulence model with lifting functions for flow injection and boundary control
Chirco, L | Chierici, A | Da Vià, R | Giovacchini, V | Manservisi, SJournal of Physics: Conference Series, Vol. 1224 (2019), Iss. 1 P.012006
https://doi.org/10.1088/1742-6596/1224/1/012006 [Citations: 1] -
New preconditioning techniques for the steady and unsteady buoyancy driven flow problems
Ke, G. | Aulisa, E.Journal of Computational Physics, Vol. 371 (2018), Iss. P.244
https://doi.org/10.1016/j.jcp.2018.05.037 [Citations: 7] -
On mathematical modelling of aeroelastic problems with finite element method
Sváček, Petr | Dančová, P.EPJ Web of Conferences, Vol. 180 (2018), Iss. P.02104
https://doi.org/10.1051/epjconf/201818002104 [Citations: 0] -
A multiscale fluid structure interaction model derived from Koiter shell equations
Chierici, A | Chirco, L | Giovacchini, V | Manservisi, S | Santesarti, GJournal of Physics: Conference Series, Vol. 1599 (2020), Iss. 1 P.012040
https://doi.org/10.1088/1742-6596/1599/1/012040 [Citations: 1] -
Analysis and Computations of Optimal Control Problems for Boussinesq Equations
Chierici, Andrea | Giovacchini, Valentina | Manservisi, SandroFluids, Vol. 7 (2022), Iss. 6 P.203
https://doi.org/10.3390/fluids7060203 [Citations: 6] -
An improved multigrid algorithm for n-irregular meshes with subspace correction smoother
Aulisa, Eugenio | Calandrini, Sara | Capodaglio, GiacomoComputers & Mathematics with Applications, Vol. 76 (2018), Iss. 3 P.620
https://doi.org/10.1016/j.camwa.2018.05.003 [Citations: 5] -
Optimal control problems for the Navier–Stokes system coupled with the k-ω turbulence model
Manservisi, Sandro | Menghini, FilippoComputers & Mathematics with Applications, Vol. 71 (2016), Iss. 11 P.2389
https://doi.org/10.1016/j.camwa.2015.10.003 [Citations: 10] -
A field‐split preconditioning technique for fluid‐structure interaction problems with applications in biomechanics
Calandrini, Sara | Aulisa, Eugenio | Ke, GuoyiInternational Journal for Numerical Methods in Biomedical Engineering, Vol. 36 (2020), Iss. 3
https://doi.org/10.1002/cnm.3301 [Citations: 6] -
On mathematical modelling of aeroelastic problems with finite element method
Sváček, Petr | Dančová, P.EPJ Web of Conferences, Vol. 180 (2018), Iss. P.02104
https://doi.org/10.1051/epjconf/201818002104 [Citations: 0] -
An adjoint-based temperature boundary optimal control approach for turbulent buoyancy-driven flows
Chirco, L | Giovacchini, V | Manservisi, SJournal of Physics: Conference Series, Vol. 1599 (2020), Iss. 1 P.012041
https://doi.org/10.1088/1742-6596/1599/1/012041 [Citations: 0] -
Different approaches for Dirichlet and Neumann boundary optimal control
Bornia, Giorgio | Ratnavale, Saikanth(2018) P.270006
https://doi.org/10.1063/1.5043899 [Citations: 0] -
Numerical simulation of fluid-structure interactions with stabilized finite element method
Sváček, Petr
Advances in Engineering Software, Vol. 113 (2017), Iss. P.96
https://doi.org/10.1016/j.advengsoft.2016.08.012 [Citations: 2]