2,475 research outputs found
Visco-resistive shear wave dissipation in magnetic X-points
We consider the viscous and resistive dissipation of perpendicularly polarized shear waves propagating within a planar magnetic X-point. To highlight the role played by the two-dimensional geometry, the damping of travelling Alfvèn waves that propagate within an unbounded, but non-orthogonal X-point topology is analyzed. It is shown that the separatrix geometry affects both the dissipation time and the visco-resistive scaling of the energy decay. Our main focus, however, is on developing a theoretical description of standing wave dissipation for orthogonal, line-tied X-points. A combination of numerical and analytic treatments confirms that phase mixing provides a very effective mechanism for dissipating the wave energy. We show that wave decay comprises two main phases, an initial rapid decay followed by slower eigenmode evolution, both of which are only weakly dependent on the visco-resistive damping coefficients
A New MHD Code with Adaptive Mesh Refinement and Parallelization for Astrophysics
A new code, named MAP, is written in Fortran language for
magnetohydrodynamics (MHD) calculation with the adaptive mesh refinement (AMR)
and Message Passing Interface (MPI) parallelization. There are several optional
numerical schemes for computing the MHD part, namely, modified Mac Cormack
Scheme (MMC), Lax-Friedrichs scheme (LF) and weighted essentially
non-oscillatory (WENO) scheme. All of them are second order, two-step,
component-wise schemes for hyperbolic conservative equations. The total
variation diminishing (TVD) limiters and approximate Riemann solvers are also
equipped. A high resolution can be achieved by the hierarchical
block-structured AMR mesh. We use the extended generalized Lagrange multiplier
(EGLM) MHD equations to reduce the non-divergence free error produced by the
scheme in the magnetic induction equation. The numerical algorithms for the
non-ideal terms, e.g., the resistivity and the thermal conduction, are also
equipped in the MAP code. The details of the AMR and MPI algorithms are
described in the paper.Comment: 44 pages, 16 figure
Accurate, Meshless Methods for Magneto-Hydrodynamics
Recently, we developed a pair of meshless finite-volume Lagrangian methods
for hydrodynamics: the 'meshless finite mass' (MFM) and 'meshless finite
volume' (MFV) methods. These capture advantages of both smoothed-particle
hydrodynamics (SPH) and adaptive mesh-refinement (AMR) schemes. Here, we extend
these to include ideal magneto-hydrodynamics (MHD). The MHD equations are
second-order consistent and conservative. We augment these with a
divergence-cleaning scheme, which maintains div*B~0 to high accuracy. We
implement these in the code GIZMO, together with a state-of-the-art
implementation of SPH MHD. In every one of a large suite of test problems, the
new methods are competitive with moving-mesh and AMR schemes using constrained
transport (CT) to ensure div*B=0. They are able to correctly capture the growth
and structure of the magneto-rotational instability (MRI), MHD turbulence, and
the launching of magnetic jets, in some cases converging more rapidly than AMR
codes. Compared to SPH, the MFM/MFV methods exhibit proper convergence at fixed
neighbor number, sharper shock capturing, and dramatically reduced noise, div*B
errors, and diffusion. Still, 'modern' SPH is able to handle most of our tests,
at the cost of much larger kernels and 'by hand' adjustment of artificial
diffusion parameters. Compared to AMR, the new meshless methods exhibit
enhanced 'grid noise' but reduced advection errors and numerical diffusion,
velocity-independent errors, and superior angular momentum conservation and
coupling to N-body gravity solvers. As a result they converge more slowly on
some problems (involving smooth, slowly-moving flows) but more rapidly on
others (involving advection or rotation). In all cases, divergence-control
beyond the popular Powell 8-wave approach is necessary, or else all methods we
consider will systematically converge to unphysical solutions.Comment: 35 pages, 39 figures. MNRAS. Updated with published version. A public
version of the GIZMO MHD code, user's guide, test problem setups, and movies
are available at http://www.tapir.caltech.edu/~phopkins/Site/GIZMO.htm
Constrained Hyperbolic Divergence Cleaning for Smoothed Particle Magnetohydrodynamics
We present a constrained formulation of Dedner et al's hyperbolic/parabolic
divergence cleaning scheme for enforcing the \nabla\dot B = 0 constraint in
Smoothed Particle Magnetohydrodynamics (SPMHD) simulations. The constraint we
impose is that energy removed must either be conserved or dissipated, such that
the scheme is guaranteed to decrease the overall magnetic energy. This is shown
to require use of conjugate numerical operators for evaluating \nabla\dot B and
\nabla{\psi} in the SPMHD cleaning equations. The resulting scheme is shown to
be stable at density jumps and free boundaries, in contrast to an earlier
implementation by Price & Monaghan (2005). Optimal values of the damping
parameter are found to be {\sigma} = 0.2-0.3 in 2D and {\sigma} = 0.8-1.2 in
3D. With these parameters, our constrained Hamiltonian formulation is found to
provide an effective means of enforcing the divergence constraint in SPMHD,
typically maintaining average values of h |\nabla\dot B| / |B| to 0.1-1%, up to
an order of magnitude better than artificial resistivity without the associated
dissipation in the physical field. Furthermore, when applied to realistic, 3D
simulations we find an improvement of up to two orders of magnitude in momentum
conservation with a corresponding improvement in numerical stability at
essentially zero additional computational expense.Comment: 28 pages, 25 figures, accepted to J. Comput. Phys. Movies at
http://www.youtube.com/playlist?list=PL215D649FD0BDA466 v2: fixed inverted
figs 1,4,6, and several color bar
Magnetohydrodynamics dynamical relaxation of coronal magnetic fields. I. Parallel untwisted magnetic fields in 2D
Context. For the last thirty years, most of the studies on the relaxation of
stressed magnetic fields in the solar environment have onlyconsidered the
Lorentz force, neglecting plasma contributions, and therefore, limiting every
equilibrium to that of a force-free field. Aims. Here we begin a study of the
non-resistive evolution of finite beta plasmas and their relaxation to
magnetohydrostatic states, where magnetic forces are balanced by
plasma-pressure gradients, by using a simple 2D scenario involving a
hydromagnetic disturbance to a uniform magnetic field. The final equilibrium
state is predicted as a function of the initial disturbances, with aims to
demonstrate what happens to the plasma during the relaxation process and to see
what effects it has on the final equilibrium state. Methods. A set of numerical
experiments are run using a full MHD code, with the relaxation driven by
magnetoacoustic waves damped by viscous effects. The numerical results are
compared with analytical calculations made within the linear regime, in which
the whole process must remain adiabatic. Particular attention is paid to the
thermodynamic behaviour of the plasma during the relaxation. Results. The
analytical predictions for the final non force-free equilibrium depend only on
the initial perturbations and the total pressure of the system. It is found
that these predictions hold surprisingly well even for amplitudes of the
perturbation far outside the linear regime. Conclusions. Including the effects
of a finite plasma beta in relaxation experiments leads to significant
differences from the force-free case
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