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MHD Equations (mhd + equation)

Distribution by Scientific Domains

Physics and Astronomy	42%

Selected Abstracts

Turbulent Dynamics of Beryllium Seeded Plasmas at the Edge of Tokamaks

CONTRIBUTIONS TO PLASMA PHYSICS, Issue 3-5 2010
R.V. Shurygin
Abstract Numerical simulation of turbulent MHD dynamics of beryllium seeded plasmas at the edge of tokamaks is performed. The model is based on the 4-fluid {,, n, pe, pi } reduced nonlinear Braginsky's MHD equations. Neutral hydrogen flow from the wall is described with a diffusion model. Beryllium line radiation is taken into consideration. The Be ion distribution over ionization states is calculated using the reduced model. Electron impact ionization, three body, photo- and dielectronic recombination and charge-exchange with neutral hydrogen are taken into account. Coronal equilibrium is not supposed. Simulations are performed for T-10 parameters. Radial distributions of averaged temperatures and their fluctuation levels, species flows, impurity radiation power, and impurity ions concentrations are obtained as functions of the Be concentration at the wall. The impurity radiation is shown to act on the turbulent oscillation level significantly if the total Be concentration at the wall exceeds 3 · 1011cm,3. The impurity turbulent transversal flow is directed inward and exceeds neoclassical flow significantly. The parallel conductivity and, as a consequence, turbulent transport are increased significantly by impurity radiation. The radiation loss dependence on the neutral Hydrogen concentration at the wall is also examined. The hydrogen concentration increasing the plasma density also rises. The relative beryllium concentration decreases. In total, these two effects are compensated, and the level of radiation losses is changed insignificantly (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

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

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2008
N. Bozkaya
Abstract 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 © 2007 John Wiley & Sons, Ltd. [source]

Global well-posedness of the Cauchy problem for certain magnetohydrodynamic-, models

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 13 2010
Yi Du
Abstract This paper is devoted to study the Cauchy problem for certain incompressible magnetohydrodynamics-, model. In the Sobolev space with fractional index s>1, we proved the local solutions for any initial data, and global solutions for small initial data. Furthermore, we also prove that as ,,0, the MHD-, model reduces to the MHD equations, and the solutions of the MHD-, model converge to a pair of solutions for the MHD equations. Copyright © 2010 John Wiley & Sons, Ltd. [source]

On stability of Alfvén discontinuities

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 3 2009
Konstantin Ilin
Abstract We study Alfvén discontinuities for the equations of ideal compressible magnetohydrodynamics (MHD). The Alfvén discontinuity is a characteristic discontinuity for the hyperbolic system of the MHD equations but, as for shock waves, the gas crosses its front. By numerical testing of the Lopatinskii condition, we carry out spectral stability analysis, i.e. we find the parameter domains of stability and violent instability of planar Alfvén discontinuities. We also show that Alfvén discontinuities can be only weakly stable in the sense that the uniform Lopatinskii condition is never satisfied. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Remark on the regularity for weak solutions to the magnetohydrodynamic equations

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 14 2008
Cheng He
Abstract We study the regularity criteria for weak solutions to the incompressible magnetohydrodynamic (MHD) equations. Some regularity criteria, which are related only with u+B or u,B, are obtained for weak solutions to the MHD equations. Copyright © 2008 John Wiley & Sons, Ltd. [source]

Smoothed Particle Magnetohydrodynamics , III.

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2005
Multidimensional tests, ·B= 0 constraint
ABSTRACT In two previous papers (Papers I and II), we have described an algorithm for solving the equations of Magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses dissipative terms in order to capture shocks and has been tested on a wide range of one-dimensional problems in both adiabatic and isothermal MHD. In this paper, we investigate multidimensional aspects of the algorithm, refining many of the aspects considered in Papers I and II and paying particular attention to the code's ability to maintain the ,·B= 0 constraint associated with the magnetic field. In particular, we implement a hyperbolic divergence cleaning method recently proposed by Dedner et al. in combination with the consistent formulation of the MHD equations in the presence of non-zero magnetic divergence derived in Papers I and II. Various projection methods for maintaining the divergence-free condition are also examined. Finally, the algorithm is tested against a wide range of multidimensional problems used to test recent grid-based MHD codes. A particular finding of these tests is that in Smoothed Particle Magnetohydrodynamics (SPMHD), the magnitude of the divergence error is dependent on the number of neighbours used to calculate a particle's properties and only weakly dependent on the total number of particles. Whilst many improvements could still be made to the algorithm, our results suggest that the method is ripe for application to problems of current theoretical interest, such as that of star formation. [source]

Nonlinear simulations of magnetic Taylor-Couette flow with currentfree helical magnetic fields

ASTRONOMISCHE NACHRICHTEN, Issue 9 2006
J. Szklarski
Abstract Themagnetorotational instability (MRI) in cylindrical Taylor-Couette flow with external helical magnetic field is simulated for infinite and finite aspect ratios. We solve the MHD equations in their small Prandtl number limit and confirm with timedependent nonlinear simulations that the additional toroidal component of the magnetic field reduces the critical Reynolds number from O (106) (axial field only) to O (103) for liquid metals with their small magnetic Prandtl number. Computing the saturated state we obtain velocity amplitudes which help designing proper experimental setups. Experiments with liquid gallium require axial field ,50 Gauss and axial current ,4 kA for the toroidal field. It is sufficient that the vertical velocity uz of the flow can be measured with a precision of 0.1 mm/s. We also show that the endplates enclosing the cylinders do not destroy the traveling wave instability which can be observed as presented in earlier studies. For TC containers without and with endplates the angular momentum transport of the MRI instability is shown as to be outwards. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]