Radial basis function and dual reciprocity boundary element solutions of fluid dynamics problems

Gürbüz, Merve
In this thesis, the two-dimensional, laminar steady or unsteady flow of a viscous, incompressible, electrically conducting fluid is considered in channels of several geometries under the impact of a uniform magnetic field with different orientations. Magnetohydrodynamic (MHD) flow governed by the hydrodynamic and electromagnetic equations is solved numerically with or without Stokes approximation and with or without magnetic induction due to the large or small values of Reynolds and magnetic Reynolds numbers, respectively. The numerical results of these MHD flow problems are obtained by using the radial basis function (RBF) approximation, the dual reciprocity boundary element method (DRBEM) and the direct interpolation boundary element method (DIBEM). The computational efficiency and easy implementation of RBF approximation is made use of to obtain the solutions of the considered MHD flow problems in terms of all the primitive variables. The MHD Stokes and the MHD incompressible flows subjected to the magnetic field in the pipe-axis direction are also studied including electric potential. The RBF approximation is also imposed to solve the MHD and the MHD Stokes convection flows in cavities. The MHD convection flow affected by both the Lorentz force and the buoyancy force is modeled by the MHD flow equations coupled with the temperature equation including the viscous dissipation term. The numerical results for all MHD flow problems are simulated in terms of streamlines, equivorticity lines, isotherms, pressure and electric potential contours in different geometries for several values of physical parameters. The use of radial basis function approximation is also extended to transient Navier-Stokes, MHD convection flow and full MHD flow equations. Since the explicit Euler method is used for the time discretization, the numerical stability analysis is performed computationally through the spectral radius of the coefficient matrices in the RBF discretized systems for the optimal values of the time increment, relaxation parameters and the non-dimensional physical parameters.  


Numerical solutions of boundary value problems; applications in ferrohydrodynamics and magnetohydrodynamics
Şenel, Pelin; Tezer, Münevver; Department of Mathematics (2017)
In this thesis, steady, laminar, fully developed flows in pipes subjected to a point magnetic source or uniform magnetic field are simulated by the dual reciprocity boundary element method (DRBEM). The Navier-Stokes and energy equations are solved in terms of the velocity, pressure and the temperature of the fluid which are all of the original variables of the problem. The missing pressure equation is derived and pressure boundary conditions are generated by a finite difference approximation and the DRBEM c...
RBF Solution of Incompressible MHD Convection Flow in a Pipe
Gürbüz, Merve; Tezer, Münevver (2016-10-12)
The steady convection flow of a viscous, incompressible and electrically conducting fluid is considered in a lid-driven cavity under the effect of a uniform horizontally applied magnetic field. The governing equations are the Navier-Stokes equations of fluid dynamics including buoyancy and Lorentz forces and the energy equation including Joule heating and viscous dissipation. These coupled equations are solved iteratively in terms of velocity components, stream function, vorticity, pressure and temperature ...
Numerical solution of buoyancy MHD flow with magnetic potential
Pekmen, B.; Tezer, Münevver (2014-04-01)
In this study, dual reciprocity boundary element method (DRBEM) is applied for solving the unsteady flow of a viscous, incompressible, electrically conducting fluid in channels under the effect of an externally applied magnetic field and buoyancy force. Magnetohydrodynamics (MHD) equations are coupled with the energy equation due to the heat transfer by means of the Boussinessq approximation. Then, the 20 non-dimensional full MHD equations in terms of stream function, temperature, magnetic potential, curren...
Numerical Solution of MHD Incompressible Convection Flow in Channels
Gurbuz, Merve; Tezer, Münevver (2019-1-01)
The purpose of this paper is to study numerically the influence of the magnetic field, buoyancy force and viscous dissipation on the convective flow and temperature of the fluid in a square cavity, lid-driven cavity, and lid-driven cavity with an obstacle at the center. The continuity, momentum and energy equations are coupled including buoyancy and magnetic forces, and energy equation contains Joule heating and viscous dissipation. The equations are solved in terms of stream function, vorticity and tempera...
A Numerical approach for the solutions of fluid dynamics problems in the presence of magnetic field
Oğlakkaya, Fatma Sidre; Bozkaya, Canan; Department of Mathematics (2018)
This thesis is conducted to investigate numerically the two-dimensional steady or unsteady, laminar flow of viscous, incompressible and electrically conducting fluids in complex geometries subject to either uniform inclined magnetic field or nodal magnetic sources. Specifically, the hydromagnetic natural/mixed convection of either conventional fluid or water-based nanofluid flow and the heat transfer are considered in irregular enclosures with wavy walls. The equations governing the steady magnetohydrodynam...
Citation Formats
M. Gürbüz, “Radial basis function and dual reciprocity boundary element solutions of fluid dynamics problems,” Ph.D. - Doctoral Program, Middle East Technical University, 2017.