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Songül Kaya Merdan

Department of Mathematics
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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...
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)
© 2020 Elsevier B.V.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 ...
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...
Analysis of Second Order Time Filtered Backward Euler Method for MHD Equations
Cibik, Aytekin; EROĞLU, FATMA GÜLER; Kaya Merdan, Songül (Springer Science and Business Media LLC, 2020-02-01)
he present work is devoted to introduce the backward Euler based modular time filter method for MHD flow. The proposed method improves the accuracy of the solution without a significant change in the complexity of the syst...
Cibik, Aytekin; Eroglu, Fatma G.; Kaya Merdan, Songül (2020-01-01)
This paper investigates the long time stability behavior of multiphysics flow problems, namely the Navier-Stokes equations, natural convection and double-diffusive convection equations with an extrapolated blended BDF time...
A Numerical Study of a Modular Sparse Grad-Div Stabilization Method for Boussinesq Equations
Demir, Medine; Kaya Merdan, Songül (2019-10-10)
This study presents a modular sparse grad-div stabilization method for solving the Boussinesq equations. Unlike the usual grad-div stabilization which produces fully coupled block matrices, the proposed stabilization metho...
Two approaches to creating a turbulence model with increased temporal accuracy
Aggul, Mustafa; Kaya Merdan, Songül; Labovsky, Alexander E. (2019-10-01)
When modeling a turbulent fluid flow, an Approximate Deconvolution Model (ADM) is sometimes chosen - in particular, due to the high order spatial accuracy. A method has been presented in [1], that demonstrates an approach ...
POD-ROM for the Darcy-Brinkman equations with double-diffusive convection
Eroglu, Fatma G.; Kaya Merdan, Songül; Rebholz, Leo G. (Walter de Gruyter GmbH, 2019-09-01)
This paper extends proper orthogonal decomposition reduced order modeling to flows governed by double diffusive convection, which models flow driven by two potentials with different rates of diffusion. We propose a reduced...
A family of second order time stepping methods for the Darcy-Brinkman equations
Cibik, Aytekin; Demir, Medine; Kaya Merdan, Songül (Elsevier BV, 2019-04-01)
This study presents an efficient, accurate, effective and unconditionally stable time stepping scheme for the Darcy-Brinkman equations in double-diffusive convection. The stabilization within the proposed method uses the i...
John, Volker; Kaya Merdan, Songül; Novo, Julia (2018-01-01)
A mantle convection model consisting of the stationary Stokes equations and a time dependent convection-diffusion equation for the temperature is studied. The Stokes problem is discretized with a conforming inf-sup stable ...