Udo Ziegler

A nested grid refinement technique for magnetohydrodynamical flows

Abstract A grid refinement technique for high resolution magnetohydrodynamical flows is described. It is based on the use of multiple nested grids having successively higher resolution. The numerical algorithm is formulated in such a way that the advection part of the hydrodynamical equations are solved in conservative form on the whoel integration domain. In particular, the divergence free constraint for the magnetic field, ▿ · B = 0 , is fulfilled during the simulation. Several numerical tests are presented demonstrating the applicability of the nested grid code to many astrophysical problems including phenomena in which steep gradients such as shocks or contact discontinuities appear.

Direct simulations of a supernova-driven galactic dynamo

Context. Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Previous analytical models, based on the evolution of isolated, non-interacting supernova remnants, predicted a dominant vertical pumping that would render dynamo action improbable. Aims. In the present work, we address the issue of vertical transport, which is thought to be the key process that inhibits dynamo action in the galactic context. We aim to demonstrate that supernova driving is a powerful mechanism to amplify galactic magnetic fields. Methods. We conduct direct numerical simulations in the framework of resistive magnetohydrodynamics. Our local box model of the interstellar medium comprises optically-thin radiative cooling, an external gravitational potential, and background shear. Dynamo coefficients for mean-field models are measured by means of passive test fields. Results. Our simulations show that supernova-driven turbulence in conjunction with shear leads to an exponential amplification of the mean magnetic field. We found turbulent pumping to be directed inward and approximately balanced by a galactic wind.

Global hydromagnetic simulations of a planet embedded in a dead zone : Gap opening, gas accretion, and formation of a protoplanetary jet

We present global hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations with mesh refinement of accreting planets embedded in protoplanetary disks (PPDs). The magnetized disk includes Ohmic r ...

NIRVANA+ : An adaptive mesh refinement code for gas dynamics and MHD

Abstract A 2D Cartesian fully adaptive mesh refinement code for problems of gas dynamics and magnetohydrodynamics is presented. The code has been developed as a first step towards a future 3D version to enable fluid dynamical modeling of real-world problems presently beyond a numerical treatment. The refinement concept is based on the well-known strategy of multiple nested, successively refined, structured grid patches overlaid a fixed main grid. Adaptive grid technology is implemented in a numerical scheme which makes use of standard finite difference/finite volume formulations featuring global conservation of mass and the divergence-free magnetic field evolution with high accuracy. The performance of the new code NIRVANA + is checked by hard test computations: the double Mach reflection problem of a strong shock, the circular advection of a current-carrying cylinder, and the dynamical evolution of a magnetohydrodynamic vortex.

A three-dimensional Cartesian adaptive mesh code for compressible magnetohydrodynamics

A Cartesian adaptive mesh code for time-dependent, compressible hydrodynamics (HD) and ideal magnetohydrodynamics (MHD) in three space dimensions has been developed. The strategy of multiple subgrid nesting is used for mesh refinement and is incorporated into an operator-split, mixed finite-difference/finite-volume scheme. Special emphasis is laid on a flexible mesh adjustment realized by rectangular blocks of 4 × 4 × 4 numerical cells. These blocks can recursively be nested and spatially arranged according to local resolution requirements. HD/MHD test calculations are performed to check code functionality and to estimate the efficiency of the applied mesh refinement philosophy.

Dynamo coefficients from local simulations of the turbulent ISM

Observations in polarized emission reveal the existence of large-scale coherent magnetic fields in a wide range of spiral galaxies. Radio-polarization data show that these fields are strongly inclined towards the radial direction, with pitch angles up to 35° and thus cannot be explained by differential rotation alone. Global dynamo models describe the generation of the radial magnetic field from the underlying turbulence via the so called α -effect. However, these global models still rely on crude assumptions about the small-scale turbulence. To overcome these restrictions we perform fully dynamical MHD simulations of interstellar turbulence driven by supernova explosions. From our simulations we extract profiles of the contributing diagonal elements of the dynamo α -tensor as functions of galactic height. We also measure the coefficients describing vertical pumping and find that the ratio between these two effects has been overestimated in earlier analytical work, where dynamo action seemed impossible. In contradiction to these models based on isolated remnants we always find the pumping to be directed inward. In addition we observe that depends on whether clustering in terms of superbubbles is taken into account. Finally, we apply a test field method to derive a quantitative measure of the turbulent magnetic diffusivity which we determine to be ∼2 kpckms–1. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Impact of Temperature-dependent Resistivity and Thermal Conduction on Plasmoid Instabilities in Current Sheets in the Solar Corona

In this paper, we investigate, by means of two-dimensional magnetohydrodynamic simulations, the impact of temperature-dependent resistivity and thermal conduction on the development of plasmoid instabilities in reconnecting current sheets in the solar corona. We find that the plasma temperature in the current-sheet region increases with time and it becomes greater than that in the inflow region. As secondary magnetic islands appear, the highest temperature is not always found at the reconnection X-points, but also inside the secondary islands. One of the effects of anisotropic thermal conduction is to decrease the temperature of the reconnecting X-points and transfer the heat into the O-points, the plasmoids, where it gets trapped. In the cases with temperature-dependent magnetic diffusivity, eta similar to T-3/2, the decrease in plasma temperature at the X-points leads to (1) an increase in the magnetic diffusivity until the characteristic time for magnetic diffusion becomes comparable to that of thermal conduction, (2) an increase in the reconnection rate, and (3) more efficient conversion of magnetic energy into thermal energy and kinetic energy of bulk motions. These results provide further explanation of the rapid release of magnetic energy into heat and kinetic energy seen during flares and coronal mass ejections. In this work, we demonstrate that the consideration of anisotropic thermal conduction and Spitzer-type, temperature-dependent magnetic diffusivity, as in the real solar corona, are crucially important for explaining the occurrence of fast reconnection during solar eruptions.

Shearingbox-implementation for the central-upwind, constraint-transport MHD-code NIRVANA

We describe the implementation of the shearingbox approach into the Godunov-type central-upwind/constraint-transport magnetohydrodynamics code NIRVANA. This will allow for applications which require sheared-periodic boundary conditions as typically used in local Cartesian simulations of differentially rotating systems. We present the algorithm in detail and discuss necessary modifications in the numerical fluxes in order to preserve conserved quantities and to fulfill other analytical constraints as good as seem feasible within the numerical scheme. We check the source terms which come with the shearingbox formulation by investigating the conservation of the epicyclic mode energy. We also perform more realistic simulations of the magneto-rotational instability with initial zero-net-flux vertical magnetic field and compare the obtained stresses and energetics with previous non-conservative results exploring the same parameter regime.

Towards a hybrid dynamo model for the Milky Way

Context. Based on the rapidly increasing all-sky data of Faraday rotation measures and polarised synchrotron radiation, the Milky Ways magnetic field can now be modelled with an unprecedented leve ...

Magnetic field amplification by SN-driven interstellar turbulence

Supernovae are known to be the dominant energy source for driving turbulence in the interstellar medium. Yet, their effect on magnetic field amplification in spiral galaxies is still poorly understood. Analytical models based on the uncorrelated-ensemble approach predicted that any created field will be expelled from the disk before a significant amplification can occur. By means of direct simulations of supernova-driven turbulence, we demonstrate that this is not the case. Accounting for vertical stratification and galactic differential rotation, we find an exponential amplification of the mean field on timescales of 100 Myr. We highlight the importance of rotation in the generation of helicity by showing that a similar mechanism based on Cartesian shear does not lead to a sustained amplification of the mean magnetic field.