# Time-domain BEM solution of convection-diffusion-type MHD equations

2008-04-20
Bozkaya, N.
Tezer, Münevver
The two-dimensional convection-diffusion-type equations are solved by using the boundary element method (BEM) based on the time-dependent fundamental solution. The emphasis is given on the solution of magnetohydrodynamic (MHD) duct flow problems with arbitrary wall conductivity. The boundary and time integrals in the BEM formulation are computed numerically assuming constant variations of the unknowns on both the boundary elements and the time intervals. Then, the solution is advanced to the steady-state iteratively. Thus, it is possible to use quite large time increments and stability problems are not encountered. The time-domain BEM solution procedure is tested on some convection-diffusion problems and the MHD duct flow problem with insulated walls to establish the validity of the approach. The numerical results for these sample problems compare very well to analytical results. Then, the BEM formulation of the MHD duct flow problem with arbitrary wall conductivity is obtained for the first time in such a way that the equations are solved together with the coupled boundary conditions. The use of time-dependent fundamental solution enables us to obtain numerical solutions for this problem for the Hartmann number values up to 300 and for several values of conductivity parameter. Copyright (C) 2007 John Wiley & Sons, Ltd.
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS

# Suggestions

 Boundary element solution of unsteady magnetohydrodynamic duct flow with differential quadrature time integration scheme Bozkaya, Canan; Tezer, Münevver (Wiley, 2006-06-20) A numerical scheme which is a combination of the dual reciprocity boundary element method (DRBEM) and the differential quadrature method (DQM), is proposed for the solution of unsteady magnetohydro-dynamic (MHD) flow problem in a rectangular duct with insulating walls. The coupled MHD equations in velocity and induced magnetic field are transformed first into the decoupled time-dependent convection-diffusion-type equations. These equations are solved by using DRBEM which treats the time and the space deriva...
 Two-level finite element method with a stabilizing subgrid for the incompressible Navier-Stokes equations NESLİTÜRK, ALİ İHSAN; Aydın Bayram, Selma; Tezer, Münevver (Wiley, 2008-10-20) We consider the Galerkin finite element method for the incompressible Navier-Stokes equations in two dimensions. The domain is discretized into a set of regular triangular elements and the finite-dimensional spaces emploved consist of piecewise continuous linear interpolants enriched with the residual-free bubble functions. To find the bubble part of the Solution, a two-level finite element method with a stabilizing subgrid of a single node is described, and its application to the Navier-Stokes equation is ...
 Effects of the Jacobian evaluation on Newton's solution of the Euler equations Onur, O; Eyi, Sinan (Wiley, 2005-09-20) Newton's method is developed for solving the 2-D Euler equations. The Euler equations are discretized using a finite-volume method with upwind flux splitting schemes. Both analytical and numerical methods are used for Jacobian calculations. Although the numerical method has the advantage of keeping the Jacobian consistent with the numerical residual vector and avoiding extremely complex analytical differentiations, it may have accuracy problems and need longer execution time. In order to improve the accurac...
 The DRBEM solution of incompressible MHD flow equations Bozkaya, Nuray; Tezer, Münevver (Wiley, 2011-12-10) This paper presents a dual reciprocity boundary element method (DRBEM) formulation coupled with an implicit backward difference time integration scheme for the solution of the incompressible magnetohydrodynamic (MHD) flow equations. The governing equations are the coupled system of Navier-Stokes equations and Maxwell's equations of electromagnetics through Ohm's law. We are concerned with a stream function-vorticity-magnetic induction-current density formulation of the full MHD equations in 2D. The stream f...
 Solution to transient Navier-Stokes equations by the coupling of differential quadrature time integration scheme with dual reciprocity boundary element method Bozkaya, Canan; Tezer, Münevver (Wiley, 2009-01-20) The two-dimensional time-dependent Navier-Stokes equations in terms of the vorticity and the stream function are solved numerically by using the coupling of the dual reciprocity boundary element method (DRBEM) in space with the differential quadrature method (DQM) in time. In DRBEM application, the convective and the time derivative terms in the vorticity transport equation are considered as the nonhomogeneity in the equation and are approximated by radial basis functions. The solution to the Poisson equati...
Citation Formats
N. Bozkaya and M. Tezer, “Time-domain BEM solution of convection-diffusion-type MHD equations,” INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, pp. 1969–1991, 2008, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38025.