2,205 research outputs found
Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
We examine the effect of accuracy of high-order spectral element methods,
with or without adaptive mesh refinement (AMR), in the context of a classical
configuration of magnetic reconnection in two space dimensions, the so-called
Orszag-Tang vortex made up of a magnetic X-point centered on a stagnation point
of the velocity. A recently developed spectral-element adaptive refinement
incompressible magnetohydrodynamic (MHD) code is applied to simulate this
problem. The MHD solver is explicit, and uses the Elsasser formulation on
high-order elements. It automatically takes advantage of the adaptive grid
mechanics that have been described elsewhere in the fluid context [Rosenberg,
Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows
both statically refined and dynamically refined grids. Tests of the algorithm
using analytic solutions are described, and comparisons of the Orszag-Tang
solutions with pseudo-spectral computations are performed. We demonstrate for
moderate Reynolds numbers that the algorithms using both static and refined
grids reproduce the pseudo--spectral solutions quite well. We show that
low-order truncation--even with a comparable number of global degrees of
freedom--fails to correctly model some strong (sup--norm) quantities in this
problem, even though it satisfies adequately the weak (integrated) balance
diagnostics.Comment: 19 pages, 10 figures, 1 table. Submitted to New Journal of Physic
On the applicability of Taylor's hypothesis in streaming magnetohydrodynamic turbulence
We examine the range of applicability of Taylor's hypothesis used in
observations of magnetic turbulence in the solar wind. We do not refer to
turbulence theory. We simply ask whether in a turbulent magnetohydrodynamic
flow the observed magnetic frequency spectrum can be interpreted as mapping of
the wavenumber turbulence into the stationary spacecraft frame. In addition to
the known restrictions on the angle of propagation with respect to the
fluctuation spectrum and the question on the wavenumber dependence of the
frequency in turbulence which we briefly review, we show that another
restriction concerns the inclusion or exclusion of turbulent fluctuations in
the velocity field. Taylor's hypothesis in application to magnetic (MHD)
turbulence encounters its strongest barriers here. It is applicable to magnetic
turbulence only when the turbulent velocity fluctuations can practically be
completely neglected against the bulk flow speed. For low flow speeds the
transformation becomes rather involved. This account makes even no use of the
additional scale dependence of the turbulent frequency, viz. the existence of a
"turbulent dispersion relation".Comment: 31 pages, 3 figures, submitted to Earth, Planets & Spac
WhiskyMHD: a new numerical code for general relativistic magnetohydrodynamics
The accurate modelling of astrophysical scenarios involving compact objects
and magnetic fields, such as the collapse of rotating magnetized stars to black
holes or the phenomenology of gamma-ray bursts, requires the solution of the
Einstein equations together with those of general-relativistic
magnetohydrodynamics. We present a new numerical code developed to solve the
full set of general-relativistic magnetohydrodynamics equations in a dynamical
and arbitrary spacetime with high-resolution shock-capturing techniques on
domains with adaptive mesh refinements. After a discussion of the equations
solved and of the techniques employed, we present a series of testbeds carried
out to validate the code and assess its accuracy. Such tests range from the
solution of relativistic Riemann problems in flat spacetime, over to the
stationary accretion onto a Schwarzschild black hole and up to the evolution of
oscillating magnetized stars in equilibrium and constructed as consistent
solutions of the coupled Einstein-Maxwell equations.Comment: minor changes to match the published versio
Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
This article serves as a summary outlining the mathematical entropy analysis
of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD
equations as they are particularly useful for mathematically modeling a wide
variety of magnetized fluids. In order to be self-contained we first motivate
the physical properties of a magnetic fluid and how it should behave under the
laws of thermodynamics. Next, we introduce a mathematical model built from
hyperbolic partial differential equations (PDEs) that translate physical laws
into mathematical equations. After an overview of the continuous analysis, we
thoroughly describe the derivation of a numerical approximation of the ideal
MHD system that remains consistent to the continuous thermodynamic principles.
The derivation of the method and the theorems contained within serve as the
bulk of the review article. We demonstrate that the derived numerical
approximation retains the correct entropic properties of the continuous model
and show its applicability to a variety of standard numerical test cases for
MHD schemes. We close with our conclusions and a brief discussion on future
work in the area of entropy consistent numerical methods and the modeling of
plasmas
Convergence of approximate deconvolution models to the mean Magnetohydrodynamics Equations: Analysis of two models
We consider two Large Eddy Simulation (LES) models for the approximation of
large scales of the equations of Magnetohydrodynamics (MHD in the sequel). We
study two -models, which are obtained adapting to the MHD the approach
by Stolz and Adams with van Cittert approximate deconvolution operators. First,
we prove existence and uniqueness of a regular weak solution for a system with
filtering and deconvolution in both equations. Then we study the behavior of
solutions as the deconvolution parameter goes to infinity. The main result of
this paper is the convergence to a solution of the filtered MHD equations. In
the final section we study also the problem with filtering acting only on the
velocity equation
Magnetohydrodynamic normal mode analysis of plasma with equilibrium pressure anisotropy
In this work, we generalise linear magnetohydrodynamic (MHD) stability theory
to include equilibrium pressure anisotropy in the fluid part of the analysis. A
novel 'single-adiabatic' (SA) fluid closure is presented which is complementary
to the usual 'double-adiabatic' (CGL) model and has the advantage of naturally
reproducing exactly the MHD spectrum in the isotropic limit. As with MHD and
CGL, the SA model neglects the anisotropic perturbed pressure and thus loses
non-local fast-particle stabilisation present in the kinetic approach. Another
interesting aspect of this new approach is that the stabilising terms appear
naturally as separate viscous corrections leaving the isotropic SA closure
unchanged. After verifying the self-consistency of the SA model, we re-derive
the projected linear MHD set of equations required for stability analysis of
tokamaks in the MISHKA code. The cylindrical wave equation is derived
analytically as done previously in the spectral theory of MHD and clear
predictions are made for the modification to fast-magnetosonic and slow ion
sound speeds due to equilibrium anisotropy.Comment: 19 pages. This is an author-created, un-copyedited version of an
article submitted for publication in Plasma Physics and Controlled Fusion.
IOP Publishing Ltd is not responsible for any errors or omissions in this
version of the manuscript or any version derived from i
Calculation of solar wind flows about terrestrial planets
A computational model was developed for the determination of the plasma and magnetic field properties of the global interaction of the solar wind with terrestrial planetary magneto/ionospheres. The theoretical method is based on an established single fluid, steady, dissipationless, magnetohydrodynamic continuum model, and is appropriate for the calculation of supersonic, super Alfvenic solar wind flow past terrestrial planets. A summary is provided of the important research results
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