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Adaptive Mesh Refinement in Computational Astrophysics - Methods and Applications
BALSARA DINSHAW The Korean Astronomical Society 2001 Journal of The Korean Astronomical Society Vol.34 No.4
The advent of robust, reliable and accurate higher order Godunov schemes for many of the systems of equations of interest in computational astrophysics has made it important to understand how to solve them in multi-scale fashion. This is so because the physics associated with astrophysical phenomena evolves in multi-scale fashion and we wish to arrive at a multi-scale simulational capability to represent the physics. Because astrophysical systems have magnetic fields, multi-scale magnetohydrodynamics (MHD) is of especial interest. In this paper we first discuss general issues in adaptive mesh refinement (AMR), We then focus on the important issues in carrying out divergence-free AMR-MHD and catalogue the progress we have made in that area. We show that AMR methods lend themselves to easy parallelization. We then discuss applications of the RIEMANN framework for AMR-MHD to problems in computational astophysics.
Amplification of magnetic fields by supernova-driven turbulence
Kim, J.,Balsara, D. S. WILEY-VCH Verlag 2006 Astronomische Nachrichten Vol.327 No.5
<P>Observations of μG magnetic fields in radio galaxies at cosmological epochs as early as around z = 2 have shortened the available time for dynamo action. This fact suggests that the mean-field dynamo mechanism in a global galactic scale either is too slow to amplify a seed field generated by the Biermann battery effect to the level of the observed field strength at z ∼ 2 or needs much stronger seed fields of an order of 10<SUP>–10</SUP> G. A “contamination” picture that amplified magnetic fields in smaller objects, such as stars or AGNs, within a relatively shorter timescale spread out through supernova ejecta, stellar winds, and AGN jets to nearby environments is gaining momentum. In line with this picture, we demonstrate, through three-dimensional numerical experiments, that magnetic fields can be amplified by supernova-driven turbulence with two orders of magnitude smaller e-folding timescale than that of the mean-field dynamo mechanism. Therefore, supernova-driven turbulence may play an important role in amplifying small-scale B -fields in any astrophysical systems that have harbored massive stars. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)</P>
Turbulence Driven by Supernova Explosions in a Radiatively-Cooling Magnetized Interstellar Medium
KIM JONGSOO,BALSARA DINSHAW,MAC LOW MORDECAI-MARK The Korean Astronomical Society 2001 Journal of The Korean Astronomical Society Vol.34 No.4
We study the properties of supernova (SN) driven interstellar turbulence with a numerical magnetohydrodynamic (MHD) model. Calculations were done using the RIEMANN framework for MHD, which is highly suited for astrophysical flows because it tracks shocks using a Riemann solver and ensures pressure positivity and a divergence-free magnetic field. We start our simulations with a uniform density threaded by a uniform magnetic field. A simplified radiative cooling curve and a constant heating rate are also included. In this radiatively-cooling magnetized medium, we explode SNe one at a time at randomly chosen positions with SN explosion rates equal to and 12 times higher than the Galactic value. The evolution of the system is basically determined by the input energy of SN explosions and the output energy of radiative cooling. We follow the simulations to the point where the total energy of the system, as well as thermal, kinetic, and magnetic energy individually, has reached a quasi-stationary value. From the numerical experiments, we find that: i) both thermal and dynamical processes are important in determining the phases of the interstellar medium, and ii) the power index n of the $B-p^n$ relation is consistent with observed values.
ALFVÉNIC TURBULENCE BEYOND THE AMBIPOLAR DIFFUSION SCALE
Burkhart, Blakesley,Lazarian, A.,Balsara, D.,Meyer, C.,Cho, J. IOP Publishing 2015 The Astrophysical journal Vol.805 No.2
<P>We investigate the nature of the Alfvenic turbulence cascade in two-fluid magnetohydrodynamic (MHD) simulations in order to determine if turbulence is damped once the ion and neutral species become decoupled at a critical scale called the ambipolar diffusion scale (L-AD). Using mode decomposition to separate the three classical MHD modes, we study the second-order structure functions of the Alfven mode velocity field of both neutrals and ions in the reference frame of the local magnetic field. On scales greater than L-AD we confirm that two-fluid turbulence strongly resembles single-fluid MHD turbulence. Our simulations show that the behavior of two-fluid turbulence becomes more complex on scales less than L-AD. We find that Alfvenic turbulence can exist past L-AD when the turbulence is globally super-Alfvenic, with the ions and neutrals forming separate cascades once decoupling has taken place. When turbulence is globally sub-Alfvenic and hence strongly anisotropic, with a large separation between the parallel and perpendicular decoupling scales, turbulence is damped at L-AD. We also find that the power spectrum of the kinetic energy in the damped regime is consistent with a k(-4) scaling (in agreement with the predictions of Lazarian et al.).</P>