Numerical method for conform reflection

Kushnarov, Andriy
Conformal map has application in a lot of areas of science, e.g., fluid flow, heat conduction, solidification, electromagnetic, etc. Especially conformal map applied to elasticity theory can provide most simple and useful solution. But finding of conformal map for custom domain is not trivial problem. We used a numerical method for building a conformal map to solve torsion problem. In addition it was considered an infinite system method to solve the same problem. Results are compared.


Boundary element method solution of initial and boundary value problems in fluid dynamics and magnetohydrodynamics
Bozkaya, Canan; Tezer, Münevver; Department of Mathematics (2008)
In this thesis, the two-dimensional initial and boundary value problems invol\-ving convection and diffusion terms are solved using the boundary element method (BEM). The fundamental solution of steady magnetohydrodynamic (MHD) flow equations in the original coupled form which are convection-diffusion type is established in order to apply the BEM directly to these coupled equations with the most general form of wall conductivities. Thus, the solutions of MHD flow in rectangular ducts and in infinite regions...
Critical behavior of the spontaneous polarization and the dielectric susceptibility close to the cubic-tetragonal transition in BaTiO3
Yurtseven, Hasan Hamit (2015-09-01)
Using Landau mean field model, the spontaneous polarization and the dielectric susceptibility are analyzed as functions of temperature and pressure close to the cubic-tetragonal (ferroelectric-paraelectric) transition in BaTiO3. From the analysis of the dielectric susceptibility and the spontaneous polarization, the critical exponents are deduced in the classical and quantum limits for BaTiO3. From the critical behavior of the dielectric susceptibility, the spontaneous polarization can be described for the ...
Exact and FDM solutions of 1D MHD flow between parallel electrically conducting and slipping plates
Arslan, Sinem; Tezer, Münevver (Springer Science and Business Media LLC, 2019-08-01)
In this study, the steady, laminar, and fully developed magnetohydrodynamic (MHD) flow is considered in a long channel along with the z-axis under an external magnetic field which is perpendicular to the channel axis. The fluid velocity u and the induced magnetic field b depend on the plane coordinates x and y on the cross-section of the channel. When the lateral channel walls are extended to infinity, the problem turns out to be MHD flow between two parallel plates (Hartmann flow). Now, the variations of u...
Discontinuous galerkin finite elements method with structure preserving time integrators for gradient flow equations
Sarıaydın Filibelioğlu, Ayşe; Karasözen, Bülent; Department of Scientific Computing (2015)
Gradient flows are energy driven evolutionary equations such that the energy decreases along solutions. There have been surprisingly a large number of well-known partial differential equations (PDEs) which have the structure of a gradient flow in different research areas such as fluid dynamics, image processing, biology and material sciences. In this study, we focus on two systems which can be modeled by gradient flows;Allen-Cahn and Cahn-Hilliard equations. These equations model the phase separation in mat...
FEM solution of natural convection flow in square enclosures under magnetic field
Turk, O.; Tezer, Münevver (Emerald, 2013-01-01)
Purpose - The purpose of the paper is to obtain finite element method (FEM) solution of steady, laminar, natural convection flow in inclined enclosures in the presence of an oblique magnetic field. The momentum equations include the magnetic effect, and the induced magnetic field due to the motion of the electrically conducting fluid is neglected. Quadratic triangular elements are used to ensure accurate approximation for second order derivatives of stream function appearing in the vorticity equation.
Citation Formats
A. Kushnarov, “Numerical method for conform reflection,” M.S. - Master of Science, Middle East Technical University, 2010.