Calculation of the Ideal MHD Equations by the CESE Method without Special Treatment for the Divergence-free Constraint of Magnetic Field

2003 ◽  
Author(s):  
Moujin Zhang ◽  
S.-T. John Yu ◽  
Sin-Chung Chang ◽  
Isaiah Blankson
Keyword(s):  
Magnetic Field ◽  
Mhd Equations ◽  
Special Treatment ◽  
Ideal Mhd ◽  
Divergence Free ◽  
The Ideal

An Efficient Implementation of the Divergence Free Constraint in a Discontinuous Galerkin Method for Magnetohydrodynamics on Unstructured Meshes

2017 ◽  
Vol 21 (2) ◽  
pp. 423-442 ◽  
Author(s):  
Christian Klingenberg ◽  
Frank Pörner ◽  
Yinhua Xia
Keyword(s):  
Magnetic Field ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Efficient Method ◽  
Numerical Experiments ◽  
Unstructured Meshes ◽  
Mhd Equations ◽  
Ideal Magnetohydrodynamics ◽  
Divergence Free ◽  
The Ideal

AbstractIn this paper we consider a discontinuous Galerkin discretization of the ideal magnetohydrodynamics (MHD) equations on unstructured meshes, and the divergence free constraint (∇·B=0) of its magnetic field B. We first present two approaches for maintaining the divergence free constraint, namely the approach of a locally divergence free projection inspired by locally divergence free elements [19], and another approach of the divergence cleaning technique given by Dedner et al. [15]. By combining these two approaches we obtain a efficient method at the almost same numerical cost. Finally, numerical experiments are performed to show the capacity and efficiency of the scheme.

scholarly journals Magnetohydrodynamic equilibria in barotropic stars

2013 ◽  
Vol 9 (S302) ◽  
pp. 419-422 ◽  
Author(s):  
C. Armaza ◽  
A. Reisenegger ◽  
J. A. Valdivia ◽  
P. Marchant
Keyword(s):  
Magnetic Field ◽  
Realistic Model ◽  
Mhd Equations ◽  
Numerical Code ◽  
General Description ◽  
Ideal Mhd ◽  
Magnetic Stars ◽  
Shafranov Equation ◽  
Barotropic Equation ◽  
The Ideal

AbstractAlthough barotropic matter does not constitute a realistic model for magnetic stars on short timescales, it would be interesting to confirm a recent conjecture that states that magnetized stars with a barotropic equation of state would be dynamically unstable (Reisenegger 2009). In this work we construct a set of barotropic equilibria, which can eventually be tested using a stability criterion. A general description of the ideal MHD equations governing these equilibria is summarized, allowing for both poloidal and toroidal magnetic field components. A new finite-difference numerical code is developed in order to solve the so-called Grad-Shafranov equation describing the equilibrium of these configurations, and some properties of the equilibria obtained are briefly discussed.

Solving Magnetohydrodynamic Equations Without Special Treatment for Divergence-Free Magnetic Field

AIAA Journal ◽  
2004 ◽  
Vol 42 (12) ◽  
pp. 2605-2608 ◽  
Author(s):  
Moujin Zhang ◽  
S.-T. John Yu ◽  
Shang-Chuen Lin ◽  
Sin-Chung Chang ◽  
Isaiah Blankson
Keyword(s):  
Magnetic Field ◽  
Special Treatment ◽  
Magnetohydrodynamic Equations ◽  
Divergence Free

Axisymmetric Magnetohydrodynamic Equilibria without a Wall

1993 ◽  
Vol 48 (12) ◽  
pp. 1131-1150
Author(s):  
D. Lortz ◽  
W. Haimerl
Keyword(s):  
Magnetic Field ◽  
Homogeneous Magnetic Field ◽  
Mhd Equations ◽  
External Current ◽  
Flux Function ◽  
Plasma Torus ◽  
Ideal Magnetohydrodynamic ◽  
Axisymmetric Configuration ◽  
A Current ◽  
The Ideal

Abstract Starting from the ideal magnetohydrodynamic (MHD) equations, we consider the following axisymmetric configuration: a current-carrying plasma torus in a homogeneous magnetic field that is aligned parallel to the torus axis. At a certain field strength this configuration is in equilibrium without need of external current singularities such as wires or walls.The magnetic flux function is expanded in small inverse aspect ratio. The geometry of this configuration is completely determined to second order as a function of the profile parameters.

scholarly journals DYNAMO EFFECTS IN MAGNETIZED IDEAL PLASMA COSMOLOGIES

2008 ◽  
Vol 23 (11) ◽  
pp. 1697-1710 ◽  
Author(s):  
KOSTAS KLEIDIS ◽  
APOSTOLOS KUIROUKIDIS ◽  
DEMETRIOS PAPADOPOULOS ◽  
LOUKAS VLAHOS
Keyword(s):  
Magnetic Field ◽  
Cosmological Model ◽  
Homogeneous Magnetic Field ◽  
Mhd Equations ◽  
Cosmological Perturbations ◽  
Gravitational Instabilities ◽  
Ideal Magnetohydrodynamic ◽  
The Magnetic Field ◽  
Ideal Plasma ◽  
The Ideal

The excitation of cosmological perturbations in an anisotropic cosmological model and in the presence of a homogeneous magnetic field has been studied, using the ideal magnetohydrodynamic (MHD) equations. In this case, the system of partial differential equations which governs the evolution of the magnetized cosmological perturbations can be solved analytically. Our results verify that fast-magnetosonic modes propagating normal to the magnetic field, are excited. But, what is most important, is that, at late times, the magnetic-induction contrast(δB/B) grows, resulting in the enhancement of the ambient magnetic field. This process can be particularly favored by condensations, formed within the plasma fluid due to gravitational instabilities.

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