High Order Upwind Schemes for Multidimensional Magnetohydrodynamics

A general method for constructing high order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint \divb=0 for the magnetic field vector \bb, is proposed. The suggested procedure is based on {\em consistency} arguments, by taking into account the specific operator structure of MHD equations with respect to the reference Euler equations of gas-dynamics. This approach leads in a natural way to a staggered representation of the \bb field numerical data where the divergence-free condition in the cell-averaged form, corresponding to second order accurate numerical derivatives, is exactly fulfilled. To extend this property to higher order schemes, we then give general prescriptions to satisfy a $(r+1)^{th}$ order accurate \divb=0 relation for any numerical \bb field having a $r^{th}$ order interpolation accuracy. Consistency arguments lead also to a proper formulation of the upwind procedures needed to integrate the induction equations, assuring the exact conservation in time of the divergence-free condition and the related continuity properties for the \bb vector components. As an application, a third order code to simulate multidimensional MHD flows of astrophysical interest is developed using ENO-based reconstruction algorithms. Several test problems to illustrate and validate the proposed approach are finally presented.Comment: 34 pages, including 14 figure

Athena: A New Code for Astrophysical MHD

A new code for astrophysical magnetohydrodynamics (MHD) is described. The code has been designed to be easily extensible for use with static and adaptive mesh refinement. It combines higher-order Godunov methods with the constrained transport (CT) technique to enforce the divergence-free constraint on the magnetic field. Discretization is based on cell-centered volume-averages for mass, momentum, and energy, and face-centered area-averages for the magnetic field. Novel features of the algorithm include (1) a consistent framework for computing the time- and edge-averaged electric fields used by CT to evolve the magnetic field from the time- and area-averaged Godunov fluxes, (2) the extension to MHD of spatial reconstruction schemes that involve a dimensionally-split time advance, and (3) the extension to MHD of two different dimensionally-unsplit integration methods. Implementation of the algorithm in both C and Fortran95 is detailed, including strategies for parallelization using domain decomposition. Results from a test suite which includes problems in one-, two-, and three-dimensions for both hydrodynamics and MHD are given, not only to demonstrate the fidelity of the algorithms, but also to enable comparisons to other methods. The source code is freely available for download on the web.Comment: 61 pages, 36 figures. accepted by ApJ

Dispersive wave runup on non-uniform shores

Historically the finite volume methods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of such schemes to dispersive PDEs. Namely, we solve numerically a representative of Boussinesq type equations in view of important applications to the coastal hydrodynamics. Numerical results of the runup of a moderate wave onto a non-uniform beach are presented along with great lines of the employed numerical method (see D. Dutykh et al. (2011) for more details).Comment: 8 pages, 6 figures, 18 references. This preprint is submitted to FVCA6 conference proceedings. Other author papers can be downloaded at http://www.lama.univ-savoie.fr/~dutykh

Форми минулого часу в пам’ятках Середньої Наддніпрянщини

У статті розглянуто роль говірок північного та південно-західного наріч в історії формування середньонаддніпрянського говору. На матеріалі пам’яток староукраїнської мови кінця XVII − початку XVIII ст. з території Середньонаддніпрянщини досліджено форми минулого особового часу в зіставленні з такими ж формами давньоукраїнської мови та з сучасним діалектним матеріалом.В статье рассмотрена роль говоров северного и юго-западного наречий в истории формирования среднеподнепровского диалекта. На материале письменных памятников староукраинского языка конца XVII и начала XVIII вв. из территории Среднего Поднепровья исследованы формы прошедшего личного времени в сопоставлении с такими же формами древнеукраинского языка и современного диалектного материала.The article deals with the role of dialects of the northern and the south-western narich in the history of forming of the middlenaddnipryanskyi manner of speaking. The forms of the past tense in comparison with the same forms of modern language were investigated on the material of pam’yatok of staroukrainian language of the end of the XVII to the beginning of the XVIII centuries

Comment on Viscous Stability of Relativistic Keplerian Accretion Disks

Recently Ghosh (1998) reported a new regime of instability in Keplerian accretion disks which is caused by relativistic effects. This instability appears in the gas pressure dominated region when all relativistic corrections to the disk structure equations are taken into account. We show that he uses the stability criterion in completely wrong way leading to inappropriate conclusions. We perform a standard stability analysis to show that no unstable region can be found when the relativistic disk is gas pressure dominated.Comment: 9 pages, 4 figures, uses aasms4.sty, submitted for ApJ Letter

Numerical simulations of the Accretion-Ejection Instability in magnetised accretion disks

The Accretion-Ejection Instability (AEI) described by Tagger & Pellat (1999) is explored numerically using a global 2d model of the inner region of a magnetised accretion disk. The disk is initially currentless but threaded by a vertical magnetic field created by external currents, and frozen in the flow. In agreement with the theory a spiral instability, similar in many ways to those observed in self-gravitating disks, develops when the magnetic field is, within a factor of a few, at equipartition with the disk thermal pressure. Perturbations in the flow build up currents and create a perturbed magnetic field within the disk. The present non-linear simulations give good evidence that such an instability can occur in the inner region of accretion disks, and generate accretion of gas and vertical magnetic flux toward the central object, if the equilibrium radial profiles of density and magnetic flux exceed a critical threshold.Comment: single tar file with GIF figure

Numerical simulations of kink instability in line-tied coronal loops

The results from numerical simulations carried out using a new shock-capturing, Lagrangian-remap, 3D MHD code, Lare3d are presented. We study the evolution of the m=1 kink mode instability in a photospherically line-tied coronal loop that has no net axial current. During the non-linear evolution of the kink instability, large current concentrations develop in the neighbourhood of the infinite length mode rational surface. We investigate whether this strong current saturates at a finite value or whether scaling indicates current sheet formation. In particular, we consider the effect of the shear, defined by where is the fieldline twist of the loop, on the current concentration. We also include a non-uniform resistivity in the simulations and observe the amount of free magnetic energy released by magnetic reconnection

A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding

Enterovirus D68-The New Polio?

Enterovirus D68 (EV-D68) has emerged over the recent years, with large outbreaks worldwide. Increased occurrence has coincided with improved clinical awareness and surveillance of non-polio enteroviruses. Studies showing its neurotropic nature and the change in pathogenicity have established EV-D68 as a probable cause of Acute Flaccid Myelitis (AFM). The EV-D68 storyline shows many similarities with poliovirus a century ago, stimulating discussion whether EV-D68 could be ascertaining itself as the "new polio." Increasing awareness amongst clinicians, incorporating proper diagnostics and integrating EV-D68 into accessible surveillance systems in a way that promotes data sharing, will be essential to reveal the burden of disease. This will be a necessary step in preventing EV-D68 from becoming a threat to public health