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

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2017
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.  

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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.