M. Tezer-Sezgin

Solution of magnetohydrodynamic flow in a rectangular duct by differential quadrature method

Abstract The polynomial based differential quadrature and the Fourier expansion based differential quadrature method are applied to solve magnetohydrodynamic (MHD) flow equations in a rectangular duct in the presence of a transverse external oblique magnetic field. Numerical solution for velocity and induced magnetic field is obtained for the steady-state, fully developed, incompressible flow of a conducting fluid inside of the duct. Equal and unequal grid point discretizations are both used in the domain and it is found that the polynomial based differential quadrature method with a reasonable number of unequally spaced grid points gives accurate numerical solution of the MHD flow problem. Some graphs are presented showing the behaviours of the velocity and the induced magnetic field for several values of Hartmann number, number of grid points and the direction of the applied magnetic field.

BEM solution of MHD flow in a pipe coupled with magnetic induction of exterior region

In this paper, numerical solutions are presented for the MHD flow in a pipe surrounded by an electrically conducting medium, and under the influence of a transverse magnetic field. The boundary element method is used which discretizes only the pipe wall and is suitable for the infinite exterior region. Coupled MHD equations for the velocity and induced magnetic field inside the pipe, and the induced magnetic field equation for the outside medium are solved simultaneously taking into account also coupled boundary conditions on the pipe wall for exterior and interior magnetic fields. The boundary integral equation in the exterior region is restricted to the boundary of the pipe due to the regularity condition at infinity. Numerical results indicate that the coupling of BEM approaches for inside and outside regions has the ability to produce satisfactory results even the ratio of fluid magnetic Reynolds number to external medium magnetic Reynolds number reaches to 500. Computations are also carried out for different Reynolds numbers and values of magnetic pressure of the fluid in the pipe.

Solution of Navier–Stokes Equations Using FEM with Stabilizing Subgrid

The Galerkin finite element method (FEM) is used for solving the incompressible Navier–Stokes equations in 2D. Regular triangular elements are used to discretize the domain and the finite-dimensional spaces employed consist of piecewise continuous linear interpolants enriched with the residual-free bubble (RFB) functions. To find the bubble part of the solution, a two-level FEM with a stabilizing subgrid of a single node is described in our previous paper [Int. J. Numer. Methods Fluids 58, 551–572 (2007)]. The results for backward facing step flow and flow through 2D channel with an obstruction on the lower wall show that the proper choice of the subgrid node is crucial to get stable and accurate solutions consistent with the physical configuration of the problems at a cheap computational cost.