Finite element analysis of a projection-based stabilization method for the Darcy-Brinkman equations in double-diffusive convection

2013-02-01
Cibik, Aytekin
Kaya Merdan, Songül
This paper presents a projection-based stabilization method of the double-diffusive convection in Darcy-Brinkman flow. In particular, it is concerned with the convergence analysis of the velocity, temperature and concentration in the time dependent case. Numerical experiments are presented to verify both the theory and the effectiveness of the method. (C) 2012 IMACS. Published by Elsevier B.V. All rights reserved.
APPLIED NUMERICAL MATHEMATICS

Suggestions

Finite element modeling of micro particle separation using ultrasonic standing waves
Süleyman, Büyükkoçak; Çetin, Barbaros; Özer, Mehmet Bülent (2014-08-07)
Acoustophoresis which means separation of particles and cells using acoustic waves is becoming an intensive research subject. The method is based on inducing an ultrasonic compression standing wave inside a microchannel. A finite element approach is used to model the acoustic and electro-mechanical behavior of the piezoelectric material, the micro-channel geometry as well as the fluid inside the channel. The choices of silicon and PDMS materials are investigated as the chip materials for the resonator. A se...
Analysis of RC walls with a mixed formulation frame finite element
Sarıtaş, Afşin (2013-10-01)
This paper presents a mixed formulation frame element with the assumptions of the Timoshenko shear beam theory for displacement field and that accounts for interaction between shear and normal stress at material level. Nonlinear response of the element is obtained by integration of section response, which in turn is obtained by integration of material response. Satisfaction of transverse equilibrium equations at section includes the interaction between concrete and transverse reinforcing steel. A 3d plastic...
Finite element modeling of scattering from objects in rectangular waveguides
Gülbaş, Hüseyin; Kuzuoğlu, Mustafa; Özlem, Özgün; Department of Electrical and Electronics Engineering (2017)
Numerical analysis of scattering parameters of split ring resonators which are one of the microwave circuit elements is performed by the Finite Element Method in this thesis. The fundamentals of the model and analysis method will be discussed firstly. Afterwards, the basics of Finite Element Method including weak variational form of the wave equation, 3D formulations and application to scattering parameters will be presented. The concepts of Perfectly Matched Layer and resonators will be examined in detail....
A projection-based stabilized finite element method for steady-state natural convection problem
Çıbık, Aytekin; Kaya Merdan, Songül (Elsevier BV, 2011-9)
We formulate a projection-based stabilization finite element technique for solving steady-state natural convection problems. In particular, we consider heat transport through combined solid and fluid media. This stabilization does not act on the large flow structures. Based on the projection stabilization idea, finite element error analysis of the problem is investigated and optimal errors for the velocity, temperature and pressure are established. We also present some numerical tests which both verify the ...
A subgrid stabilization finite element method for incompressible magnetohydrodynamics
Belenli, Mine A.; Kaya Merdan, Songül; Rebholz, Leo G.; Wilson, Nicholas E. (2013-07-01)
This paper studies a numerical scheme for approximating solutions of incompressible magnetohydrodynamic (MHD) equations that uses eddy viscosity stabilization only on the small scales of the fluid flow. This stabilization scheme for MHD equations uses a Galerkin finite element spatial discretization with Scott-Vogelius mixed finite elements and semi-implicit backward Euler temporal discretization. We prove its unconditional stability and prove how the coarse mesh can be chosen so that optimal convergence ca...
Citation Formats
A. Cibik and S. Kaya Merdan, “Finite element analysis of a projection-based stabilization method for the Darcy-Brinkman equations in double-diffusive convection,” APPLIED NUMERICAL MATHEMATICS, pp. 35–49, 2013, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/39525.