NUMERICAL STABILITY OF RBF APPROXIMATION FOR UNSTEADY MHD FLOW EQUATIONS

2019-01-01
Gurbuz, Merve
Tezer, Münevver
In this study, the radial basis function (RBF) approximation is applied for solving the unsteady fluid flow and magnetohydrodynamic (MHD) convection flow problems with the use of explicit Euler time discretization and relaxation parameters to accelerate the convergence. The stability analysis is also carried out in terms of the spectral radius of related RBF discretized coefficient matrices. The optimal choices of the time increment, relaxation parameters and physical problem parameters are found for achieving stable solutions. It is observed that the maximum eigenvalues of the coefficient matrices decrease with an increase in the time increment when the relaxation parameters are decreasing. Although the time derivative is discretized using explicit Euler method, one does not need to use small time increment for obtaining stable results. The flow, isotherms and pressure behaviors are simulated at steady-state for several values of problem parameters using time increment and relaxation parameters which lead to stable solutions.
APPLIED AND COMPUTATIONAL MATHEMATICS

Suggestions

Numerical Solution and Stability Analysis of Transient MHD Duct Flow
Tezer, Münevver (2018-11-01)
This paper simulates the 2D transient magnetohydrodynamic (MHD) flow in a rectangular duct in terms of the velocity of the fluid and the induced magnetic field by using the radial basis function (RBF) approximation. The inhomogeneities in the Poisson’s type MHD equations are approximated using the polynomial functions (1+r) and the particular solution is found satisfying both the equations and the boundary conditions (no-slip and insulated walls). The Euler scheme is used for advancing the solution to ste...
Linear-linear basis functions for MLFMA solutions of magnetic-field and combined-field integral equations
Ergül, Özgür Salih (2007-04-01)
We present the linear-linear (LL) basis functions to improve the accuracy of the magnetic-field integral equation (MFIE) and the combined-field integral equation (CFIE) for three-dimensional electromagnetic scattering problems involving closed conductors. We consider the solutions of relatively large scattering problems by employing the multilevel fast multipole algorithm. Accuracy problems of MFIE and CFIE arising from their implementations with the conventional Rao-Wilton-Glisson (RWG) basis functions can...
Dual reciprocity boundary element method for magnetohydrodynamic flow using radial basis functions
Tezer, Münevver (2002-02-01)
A dual reciprocity boundary element method is given to obtain the solution in terms of velocity and induced magnetic field for the study of MHD (magnetohydrodynamic) flow through a rectangular duct having insulating walls. The equations are transformed to two types of nonlinear Poisson equations and the right-hand sides in these equations are approximated using combinations of two classes of radial basis functions (the value of the function and its normal derivatives are utilized for approximation). Computa...
Numerical simulation of transient turbulent flow in a heated pipe
Uygur, Ahmet Bilge; Selçuk, Nevin; Oymak, Olcay; Department of Chemical Engineering (2002)
A computational fluid dynamics (CFD) code based on direct numerical simulation (DNS) and the method of lines MOL approach developed previously for the solution of transient two-dimensional Navier-Stokes equations for turbulent, incompressible, internal, non-isothermal flows with constant wall temperature was applied to prediction of turbulent flow and temperature fields in flows dominated by forced convection in circular tubes with strong heating. Predictive ability of the code was tested by comparing its r...
MHD Stokes flow and heat transfer in a lid-driven square cavity under horizontal magnetic field
Gurbuz, Merve; Tezer, Münevver (2018-04-01)
This study considers the steady flow of a viscous, incompressible and electrically conducting fluid in a lid-driven square cavity under the effect of a uniform horizontally applied magnetic field. The governing equations are obtained from the Navier-Stokes equations including buoyancy and Lorentz force terms and the energy equation including Joule heating and viscous dissipation terms. These equations are solved iteratively in terms of velocity components, stream function, vorticity, temperature, and pressu...
Citation Formats
M. Gurbuz and M. Tezer, “NUMERICAL STABILITY OF RBF APPROXIMATION FOR UNSTEADY MHD FLOW EQUATIONS,” APPLIED AND COMPUTATIONAL MATHEMATICS, pp. 123–134, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/53148.