• 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.

• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1151-1164
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• 2020

The aim of this paper is to establish Liouville type results for the stationary MHD equations. In particular, we show that the velocity and magnetic field, belonging to some Lorentz spaces, must be zero. Moreover, we also obtain Liouville type theorem for the case of axially symmetric MHD equations. Our results generalize previous works by Schulz [14] and Seregin-Wang [18].

• Journal of the Korean Mathematical Society
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• v.48 no.3
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• pp.465-474
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• 2011

In this paper, logarithmically regularity criteria for the 3D MHD equations are established in terms of the Morrey-Camapanto space.

• Nuclear Engineering and Technology
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• v.51 no.3
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• pp.654-664
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• 2019

The geometrical and electromagnetic variables of a rectangular-type magnetohydrodynamic (MHD) circulation system are optimized to solve MHD equations for the active decay heat removal system of a prototype Gen-IV sodium fast reactor. Decay heat must be actively removed from the reactor coolant to prevent the reactor system from exceeding its temperature limit. A rectangular-type MHD circulation system is adopted to remove this heat via an active system that produces developed pressure through the Lorentz force of the circulating sodium. Thus, the rectangular-type MHD circulation system for a circulating loop is modeled with the following specifications: a developed pressure of 2 kPa and flow rate of $0.02m^3/s$ at a temperature of 499 K. The MHD equations, which consist of momentum and Maxwell's equations, are solved to find the minimum input current satisfying the nominal developed pressure and flow rate according to the change of variables including the magnetic flux density and geometrical variables. The optimization shows that the rectangular-type MHD circulation system requires a current of 3976 A and a magnetic flux density of 0.037 T under the conditions of the active decay heat removal system.

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1085-1102
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• 2023

In this study the magneto hydrodynamic (MHD) micro polar fluid flow of a viscous incompressible fluid past a porous medium in the presence of chemical reaction is considered. This work is devoted to investigate the Soret effect and Electromagnetic radiation effect and analyze analytically. In the energy equation the applied magnetic field strength and in the concentration equation the Soret effect are incorporated. The basic PDE (partial differential equations) are reduced to ODE (ordinary differential equations) using non dimensional variables. Then the analytical solution of the dimensionless equations are found using perturbation technique. The features of the fluid flow parameters are analyzed, discussed and explained graphically. The graphical solutions are found using MATLAB R2019b. Skin friction coefficient at the wall, Couple stress coefficient at the plate and the local surface heat flux are also thoroughly examined. Overall, this study sheds light on the complex interplay between physical parameters in the behavior of MHD micro-polar fluid past a porous medium in the presence of chemical reaction.

• Journal of The Korean Astronomical Society
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• v.34 no.4
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• pp.275-279
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• 2001

The study of incompressible magnetohydrodynamic (MHD) turbulence gives useful insights on many astrophysical problems. We describe a pseudo-spectral MHD code suitable for the study of incompressible turbulence. We review our recent' works on direct three-dimensional numerical simulations for MHD turbulence in a periodic box. In those works, we use a pseudo-spectral code to solve the incompressible MHD equations. We first discuss the structure and properties of turbulence as functions of scale. The results are consistent with the scaling law recently proposed by Goldreich & Sridhar. The scaling law is based on the concept of scale-dependent isotropy: smaller eddies are more elongated than larger ones along magnetic field lines. This scaling law substantially changes our views on MHD turbulence. For example, as noted by Lazarian & Vishniac, the scaling law can provide a fast reconnection rate. We further discuss how the study of incompressible MHD turbulence can help us to understand physical processes in interstellar medium (ISM) by considering imbalanced cascade and viscous damped turbulence.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.83-102
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• 2015

The present paper analyses the radiation effects of mass transfer on steady nonlinear MHD boundary layer flow of a viscous incompressible fluid over a nonlinear porous stretching surface in a porous medium in presence of heat generation. The liquid metal is assumed to be gray, emitting, and absorbing but non-scattering medium. Governing nonlinear partial differential equations are transformed to nonlinear ordinary differential equations by utilizing suitable similarity transformation. The resulting nonlinear ordinary differential equations are solved numerically using Runge-Kutta fourth order method along with shooting technique. Comparison with previously published work is obtained and good agreement is found. The effects of various governing parameters on the liquid metal fluid dimensionless velocity, dimensionless temperature, dimensionless concentration, skin-friction coefficient, Nusselt number and Sherwood number are discussed with the aid of graphs.

• 한국전산유체공학회:학술대회논문집
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• 2006.05a
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• pp.385-385
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• 2006

• 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.

• Nuclear Engineering and Technology
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• v.21 no.1
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• pp.32-39
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• 1989

A method for determining the optimum ideal MHD $\beta$limit and the operation conditions is presented for an axisymmetric tokamak reactor with a circular cross section. The $\beta$limit is calculated under the constraints of ideal MHD instability criteria with varying the operation conditions which depend on the toroidal current density distributions. Semiempirical laws deduced from experimental observations are used for the toroidal current density distributions. Analytic derivations of various equations required to determine the $\beta$limit are carried out from the empirical equations. Various distributions of the $\beta$limit are obtained by the numerical calculations for different distributions of the toroidal current density. The resulting values of the maximum $\beta$limited by ideal MHD instabilities are expressed by a scaling law in terms of the tokamak geometry and the safety factor.