• Journal of the Korean Mathematical Society
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• v.38 no.1
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• pp.147-162
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• 2001

This paper establishes exponential decay estimates for the solution of a stationary magnetohydrodynamics equations in a semi-infinite pipe flow when homogeneous lateral surface boundary conditions are applied.

• Journal of the Korean Mathematical Society
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• v.35 no.4
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• pp.869-880
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• 1998

In this paper, we show that the weak solutions of the time-dependent Magnetohydrodynamics equations in 3 dimensional periodic domain belong to L(equation omitted)(0, T; V$_{r}$) following the method of Foias-Guillope-Temam for Navier-Stokes equations.s.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.2
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• pp.119.2-119.2
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• 2014

Many astrophysical phenomena involve processes of magnetohydrodynamics (MHD) and relativistic magnetohydrodynamics (RMHD). A number of numerical schemes have been developed to solve the equations of ideal MHD and RMHD. Recent codes are based on upwind schemes which solve hyperbolic systems of equations following the characteristics of the systems. Upwind schemes stand out by their robustness, clarity of the underlying physical model, and ability of achieving high resolution. We present MHD and RMHD codes based on the total variation diminishing (TVD) and weighted essentially non-oscillatory (WENO) schemes, which are second and higher order accurate extensions of upwind schemes. We demonstrate the ability and limitation of codes based on upwind schemes through a series of tests.

• Journal of The Korean Astronomical Society
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• v.34 no.4
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• pp.209-213
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• 2001

This paper describes the numerical solution to the hyperbolic system of magnetohydrodynamic (MHD) equations. First, by pointing out the approximations involved, the deal MHD equations are presented. Next, the MHD waves as well as the associated shocks and discontinuities, are presented. Then, based on the hyperbolicity of the ideal MHD equations, the application of upwind schemes, which have been developed for hydrodynamics, is discussed to solve the equations numerically. As an definite example, one and multi-dimensional codes based on the Total Variation Diminishing scheme are presented. The treatment in the multi-dimensional code, which maintains ${\nabla}{\cdot}$B = 0, is described. Through tests, the robustness of the upwind schemes for MHDs is demonstrated.

• Publications of The Korean Astronomical Society
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• v.7 no.1
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• pp.71-77
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• 1992

An axisymmetric, stationary electrodynamic model of the central engine of an active galactic nucleus has been well formulated by Macdonald and Thorne. In this model the relativistic region around the central black hole must be filled by highly conducting plasma and the equations of magnetohydrodynamics are then satisfied. In this paper we analyze magnetohydrodynamic wave propagation in this region. We find that there are three distinct types of waves - the Alfven wave and two magnetosonic waves. The wave equations turn out to be not very different from those in nonrelativistic case except they are redshifted.

• Journal of The Korean Astronomical Society
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• v.28 no.2
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• pp.223-243
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• 1995

We describe the implementation of a multi-dimensional numerical code to solve the equations for idea! magnetohydrodynamics (MHD) in cylindrical geometry. It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. Multiple spatial dimensions are treated through a Strang-type operator splitting. Curvature and source terms are included in a way to insure the formal accuracy of the code to be second order. The constraint of a divergence-free magnetic field is enforced exactly by adding a correction, which involves solving a Poisson equation. The Fourier Analysis and Cyclic Reduction (FACR) method is employed to solve it. Results from a set of tests show that the code handles flows in cylindrical geometry successfully and resolves strong shocks within two to four computational cells. The advantages and limitations of the code are discussed.

• Transactions on Electrical and Electronic Materials
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• v.17 no.5
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• pp.252-256
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• 2016

This paper deals the study of a linear MHD pump solution used to eliminate and to avoid the dangers of the mercury appearing through pollution and contamination. The formulation of the magnetohydrodynamic phenomena is derived from Maxwell and Navier-Stokes equations are solved using the finite volume method. Simulation results highlight the performance of the pump such as the electromagnetic force, the velocity, and the pressure, the application of Ansys-Fluent software validation these results.

• Journal of Electrical Engineering and Technology
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• v.4 no.2
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• pp.249-254
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• 2009

This article deals with the analysis of a coupling between stationary Maxwell's equations, the transient state Navier-Stokes and thermal equations. The resolution of these equations is obtained by introducing the magnetic vector potential A, the vorticity ${\xi}$, the stream function ${\psi}$ and the temperature T. The flux density, the electromagnetic thrust, the electric power density, the velocity, the pressure and the temperature are graphically visualized. Also, the influence of the frequency is presented.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.3
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• pp.245-256
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• 2014

This work is focused on the boundary layer and heat transfer characteristics of hydromagnetic flow over a stretching sheet with variable thickness. Steady, two dimensional, nonlinear, laminar flow of an incompressible, viscous and electrically conducting fluid over a stretching sheet with variable thickness and power law velocity in the presence of variable magnetic field and variable temperature is considered. Governing equations of the problem are converted into ordinary differential equations utilizing similarity transformations. The resulting non-linear differential equations are solved numerically by utilizing Nachtsheim-Swigert shooting iterative scheme for satisfaction of asymptotic boundary conditions along with fourth order Runge-Kutta integration method. Numerical computations are carried out for various values of the physical parameters and the effects over the velocity and temperature are analyzed. Numerical values of dimensionless skin friction coefficient and non-dimensional rate of heat transfer are also obtained.

• Journal of The Korean Astronomical Society
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• v.42 no.5
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• pp.107-123
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• 2009

We investigate the wave properties for isothermal plasma state around to the de Sitter black hole's horizon using 3+1 split of spacetime. The corresponding Fourier analyzed perturbed perfect GRMHD equations are used to obtain the complex dispersion relations. We obtain the real values of the wave number k, from these relations, which are used to evaluate the quantities like phase and group velocities etc. These have been analyzed graphically in the neighborhood of the horizon.