Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization

Date

2022-10-01

Author

Hacat, Gülnur
Yılmaz, Fikriye Nuray
Çıbık, Aytekin Bayram
Kaya Merdan, Songül

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

443
views

0
downloads

© 2022 Elsevier Inc.This paper presents a family of implicit-explicit (IMEX) time stepping scheme for the optimal control problem of the unsteady Navier-Stokes equations (NSE). The main feature of this kind of optimal control problem is that stabilization terms are proportional to discrete curvature of the solutions. First and second order optimality conditions are used for optimality of the curvature based stabilized Navier-Stokes equations. Complete stability and error analyses of state, adjoint and control variables are presented. Numerical experiments verify theoretical findings and illustrate the improvement of approximate solutions enhancing the efficiency of numerical scheme.

Subject Keywords

Curvature stabilization, Finite element method, Navier-Stokes equations, Optimal control

URI

https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85130527794&origin=inward
https://hdl.handle.net/11511/97550

Journal

Applied Mathematics and Computation

DOI

https://doi.org/10.1016/j.amc.2022.127240

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Time filtered second order backward Euler method for EMAC formulation of Navier-Stokes equations Demir, Medine; Çıbık, Aytekin; Kaya Merdan, Songül (2022-12-15) © 2022 Elsevier Inc.This paper considers the backward Euler based linear time filtering method for the developed energy-momentum-angular momentum conserving (EMAC) formulation of the time dependent-incompressible Navier-Stokes equations in the case of weakly enforced divergence constraint. The method adds time filtering as a post-processing step to the EMAC formulation to enhance the accuracy and to improve the approximate solutions. We show that in comparison with the Backward-Euler based EMAC formulation ...
A priori error analysis of the upwind symmetric interior penalty Galerkin (SIPG) method for the optimal control problems governed by unsteady convection diffusion equations AKMAN, Tugba; Yücel, Hamdullah; Karasözen, Bülent (2014-04-01) In this paper, we analyze the symmetric interior penalty Galerkin (SIPG) for distributed optimal control problems governed by unsteady convection diffusion equations with control constraint bounds. A priori error estimates are derived for the semi- and fully-discrete schemes by using piecewise linear functions. Numerical results are presented, which verify the theoretical results.
Implementation of k-epsilon turbulence models in a two dimensional parallel navier-stokes solver on hybrid grids Kalkan, Onur Ozan; Tuncer, İsmail Hakkı; Department of Aerospace Engineering (2014) In this thesis, the popular k-ε turbulence model is implemented on a parallel, 2-dimensional, explicit, density-based, finite volume based Navier-Stokes solver works on hybrid grids, HYP2D. Among the other versions available in the open literature, standard version of the k-ε turbulence mode is studied. Launder-Spalding and Chieng-Launder wall functions are adapted to the turbulence model in order to investigate the effects of the strong gradients in the vicinity of the wall on the turbulence. In order to i...
Adaptive Symmetric Interior Penalty Galerkin (SIPG) method for optimal control of convection diffusion equations with control constraints Yücel, Hamdullah; Karasözen, Bülent (2014-01-02) In this paper, we study a posteriori error estimates of the upwind symmetric interior penalty Galerkin (SIPG) method for the control constrained optimal control problems governed by linear diffusion-convection-reaction partial differential equations. Residual based error estimators are used for the state, the adjoint and the control. An adaptive mesh refinement indicated by a posteriori error estimates is applied. Numerical examples are presented for convection dominated problems to illustrate the theoretic...
Optimal control and reduced order modelling of Fitzhugh–Nagumo equation Küçükseyhan , Tuğba; Karasözen, Bülent; Uzunca, Murat; Department of Scientific Computing (2017) In this thesis, we investigate model order reduction and optimal control of FitzHugh-Nagumo equation (FHNE). FHNE is coupled partial differential equations (PDEs) of activator-inhibitor types. Diffusive FHNE is a model for the transmission of electrical impulses in a nerve axon, whereas the convective FHNE is a model for blood coagulation in a moving excitable media. We discretize these state FHNEs using a symmetric interior penalty Galerkin (SIPG) method in space and an average vector field (AVF) method in...

Citation Formats

G. Hacat, F. N. Yılmaz, A. B. Çıbık, and S. Kaya Merdan, “Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization,” Applied Mathematics and Computation, vol. 430, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85130527794&origin=inward.