Songül Kaya Merdan

Department of Mathematics
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Deferred correction method for the continuous data assimilation model
AĞGÜL, MUSTAFA; Çıbık, Aytekin; Eroglu, Fatma G.; Kaya Merdan, Songül (2023-10-01)
This paper presents a numerical assessment of a continuous data assimilation (CDA) model for incompressible Navier–Stokes equations. The proposed model employs the deferred correction method, which is an approach to increa...
On an optimal control problem of the Leray-alpha model
Hacat, Gülnur; Çıbık, Aytekin Bayram; Yılmaz, Fikriye Nuray; Kaya Merdan, Songül (2023-07-01)
This study considers semi-discrete optimal control problem of Navier–Stokes equations which are regularized by the Leray- model. After deriving optimality conditions, a priori error estimates of all fluid variables are inv...
An Improved Arrow–Hurwicz Method for the Steady-State Navier–Stokes Equations
Takhirov, Aziz; Çıbık, Aytekin Bayram; Eroğlu, Fatma Güler; Kaya Merdan, Songül (2023-06-01)
This paper presents a novel Arrow–Hurwicz type method for approximating the steady-state Navier Stokes equations using the finite element method. The novel method is inspired from artificial compressibility regularization ...
Artificial compression method for MHD system in Elsässer variables
Aggul, Mustafa; Eroglu, Fatma Güler; Kaya Merdan, Songül (2023-03-01)
We introduce an artificial compression (AC) method for simulations of the MHD system in Elsässer Variables. The proposed method decouples unknowns such as pressure, which acts as a Lagrange multiplier ensuring divergence c...
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-St...
Error estimates for the optimal control of Navier-Stokes equations using curvature based stabilization
Hacat, Gülnur; Yılmaz, Fikriye Nuray; Çıbık, Aytekin Bayram; Kaya Merdan, Songül (2022-10-01)
© 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 cont...
Defect-deferred correction method based on a subgrid artificial viscosity model for fluid-fluid interaction
AĞGÜL, MUSTAFA; Kaya Merdan, Songül (Elsevier BV, 2021-02-01)
© 2020 IMACSA defect-deferred correction method, increasing both temporal and spatial accuracy, for fluid-fluid interaction problem with nonlinear interface condition is considered by geometric averaging of the previous tw...
On the performance of curvature stabilization time stepping methods for double-diffusive natural convection flows in the presence of magnetic field
Cibik, Aytekin; Eroglu, Fatma G.; Kaya Merdan, Songül (Springer Science and Business Media LLC, 2021-01-01)
© 2021, Springer Science+Business Media, LLC, part of Springer Nature.This paper considers analytically and numerically the curvature-based stabilization method for double-diffusive natural convection flows in the presence...
A projection based variational multiscale method for a fluid–fluid interaction problem
Ağgül, Mustafa ; Eroğlu, Fatma Güler ; Kaya Merdan, Songül; Labovsky, Alexer E. (Elsevier BV, 2020-06-15)
The proposed method aims to approximate a solution of a fluid–fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplifi...
A second order decoupled penalty projection method based on deferred correction for MHD in Elsässer variable
Erkmen, Dilek; Kaya Merdan, Songül; Cibik, Aytekin (Elsevier BV, 2020-06-01)
© 2019 Elsevier B.V.We study the deferred correction method for the magnetohydrodynamics (MHD) system written in Elsässer variables. The proposed algorithm is based on the penalty projection with grad-div stabilized Taylor...
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