arXiv subjects

Udo Ziegler

Publications and source records attributed to Udo Ziegler.

16 recordsLinked to original sources

arXiv2026

A fast spectral-multigrid Poisson solver in non-Cartesian geometries

Accurate and efficient computation of self-gravity is essential in astrophysical fluid dynamics, particularly in spherical and cylindrical geometries where large radial dynamic ranges and non-axisymmetric structures arise. Poisson solvers in such settings must simultaneously achieve high accuracy, scalability, and flexibility across a wide range of grid configurations and physical regimes. We present a robust and scalable Poisson solver for three-dimensional non-Cartesian geometries, supporting both spherical and cylindrical coordinates with either uniform or logarithmic radial discretizations. The method employs azimuthal Fourier decomposition to transform the 3D Poisson equation into a set of independent 2D Helmholtz equations. These are solved using a geometrically consistent multigrid algorithm that preserves second-order accuracy on both uniform and non-uniform grids. Vacuum boundary conditions are implemented through a screening-mass approach, enabling accurate solutions in domains with open boundaries, inner cavities, and strongly non-axisymmetric mass distributions. Owing to the differing convergence rates of Fourier modes -- where higher-order modes converge more rapidly -- the solver allows efficient mode-by-mode treatment. The combination of spectral decomposition and multigrid acceleration provides an efficient and flexible computational framework. The solver is implemented in the PLUTO code and validated against both analytical solutions and dynamical test problems in spherical and cylindrical geometries. Results demonstrate second-order convergence and excellent agreement with reference solutions. Weak-scaling tests up to 4096 cores show strong parallel performance, with the Poisson solve remaining subdominant to magnetohydrodynamic update cost. This makes the method well suited for large-scale simulations of star formation, accretion disks, and gravitational instabilities.

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arXiv2024

Toward an efficient second-order method for computing the surface gravitational potential on spherical-polar meshes

Astrophysical accretion discs that carry a significant mass compared with their central object are subject to the effect of self-gravity. In the context of circumstellar discs, this can, for instance, cause fragmentation of the disc gas, and -- under suitable conditions -- lead to the direct formation of gas-giant planets. If one wants to study these phenomena, the disc's gravitational potential needs to be obtained by solving the Poisson equation. This requires to specify suitable boundary conditions. In the case of a spherical-polar computational mesh, a standard multipole expansion for obtaining boundary values is not practicable. We hence compare two alternative methods for overcoming this limitation. The first method is based on a known Green's function expansion (termed "CCGF") of the potential, while the second (termed "James' method") uses a surface screening mass approach with a suitable discrete Green's function. We demonstrate second-order convergence for both methods and test the weak scaling behaviour when using thousands of computational cores. Overall, James' method is found superior owing to its favourable algorithmic complexity of $\sim \mathcal{O}(n^3)$ compared with the $\sim\mathcal{O}(n^4)$ scaling of the CCGF method.

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arXiv2023

High $β$ magnetic reconnection at different altitudes in the cool low solar atmosphere

We numerically studied magnetic reconnection in a high $β$ hydrogen-helium plasma at different altitudes from the photosphere to the upper chromosphere. The time dependent ionization degrees were included to get more realistic diffusivities and viscosity, and appropriate radiative cooling models were applied. Our numerical results indicate that the plasmoid instability always plays a vital role in speeding up magnetic reconnection at different atmospheric layers. In addition, both the strong radiative cooling and the magnetic diffusion caused by the electron-neutral collision ($η_{en}$) can significantly accelerate magnetic reconnection below the middle chromosphere. On the other hand, both the ambipolar diffusion and the viscosity result in higher temperature and plasma pressure in the reconnection region in the upper chromosphere, which then hinder the fast reconnection process from developing. The local compression heating triggered by turbulent reconnection mediated with plasmoids is the dominant heating mechanism in the unstable reconnection stage at different atmospheric layers, but the viscous heating and the ambipolar diffusion heating are equally important in the upper chromosphere. The Joule heating contributed by $η_{en}$ dominates during the early quasi-steady reconnection stage below the middle chromosphere, the strong radiative cooling also leads to much stronger compression heating and more generation of thermal energy in this region. Though the plasma $β$ is the same in all the simulation cases at different altitudes, the temperature increase is more significant in the upper chromosphere with much lower density and weaker radiative cooling.

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arXiv2023

NIRwave: A wave-turbulence-driven solar wind model constrained by PSP observations

We generate a model description of the solar wind based on an explicit wave-turbulence-driven heating mechanism, and constrain our model with observational data. We included an explicit coronal heating source term in the general 3D magnetohydrodynamic code NIRVANA to simulate the properties of the solar wind. The adapted heating mechanism is based on the interaction and subsequent dissipation of counter-propagating Alfvén waves in the solar corona, accounting for a turbulent heating rate Q_p. The solar magnetic field is assumed to be an axisymmetric dipole with a field strength of 1 G. Our model results are validated against observational data taken by the Parker Solar Probe (PSP). Our NIRwave solar wind model reconstructs the bimodal structure of the solar wind with slow and fast wind speeds of 410 km/s and 650 km/s respectively. The global mass-loss rate of our solar wind model is 2.6e-14 solar masses per year. Despite implementing simplified conditions to represent the solar magnetic field, the solar wind parameters characterising our steady-state solution are in reasonable agreement with previously established results and empirical constraints. The number density from our wind solution is in good agreement with the derived empirical constraints, with larger deviations for the radial velocity and temperature. In a comparison to a polytropic wind model generated with NIRVANA, we find that our NIRwave model is in better agreement with the observational constraints that we derive.

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arXiv2021

The Ellerman bomb and Ultraviolet burst triggered successively by an emerging magnetic flux rope

Ellerman bombs (EBs) and Ultraviolet (UV) bursts are common brightening phenomena which are usually generated in the low solar atmosphere of emerging flux regions. In this paper, we have investigated the emergence of an initial un-twisted magnetic flux rope based on three-dimensional (3D) magneto-hydrodynamic (MHD) simulations. The EB-like and UV burst-like activities successively appear in the U-shaped part of the undulating magnetic fields triggered by Parker Instability. The EB-like activity starts to appear earlier and lasts for about 80 seconds. Six minutes later, a much hotter UV burst-like event starts to appear and lasts for about 60 seconds. Along the direction vertical to the solar surface, both the EB and UV burst start in the low chromosphere, but the UV burst extends to a higher altitude in the up chromosphere. The regions with apparent temperature increase in the EB and UV burst are both located inside the small twisted flux ropes generated in magnetic reconnection processes, which are consistent with the previous 2D simulations that most hot regions are usually located inside the magnetic islands. However, the twisted flux rope corresponding to the EB is only strongly heated after it floats up to an altitude much higher than the reconnection site during that period. Our analyses show that the EB is heated by the shocks driven by the strong horizontal flows at two sides of the U-shaped magnetic fields. The twisted flux rope corresponding to the UV burst is heated by the driven magnetic reconnection process.

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arXiv2018

Numerical Studies of the Kelvin-Hemholtz Instability in the Coronal Jet

The Kelvin-Hemholtz (K-H) instability in the corona EUV jet is studied via 2.5 MHD numerical simulations. The jet results from magnetic reconnection due to the interation of the new emerging magnetic field and the pre-existing magnetic field in the corona. Our results show that the Alfven Mach number along the jet is about 5-14 just before the instability occurs, and it is even higher than 14 at some local areas. During the K-H instability process, several vortex-like plasma blobs of high temperature and high density appear along the jet, and magnetic fields have also been rolled up and the magnetic configuration including anti-parallel magnetic fields forms, which leads to magnetic reconnection at many X-points and current sheet fragments inside the vortex-like blob. After magnetic islands appear inside the main current sheet, the total kinetic energy of the reconnection outflows decreases, and cannot support the formation of the vortex-like blob along the jet any longer, then the K-H instability eventually disappears. We also present the results about how the guide field and the flux emerging speed affect the K-H instability. We find that the strong guide field inhibits the shock formation in the reconnection upward outflow regions but helps secondary magnetic islands appear earlier in the main current sheet, and then apparently suppresses the K-H instability. As the speed of the emerging magnetic field decreases, the K-H instability appears later, the highest temperature inside the vortex blob gets lower and the vortex structure gets smaller.

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arXiv2017

3D simulations of rising magnetic flux tubes in a compressible rotating interior: The effect of magnetic tension

Context: Long-term variability in solar cycles represents a challenging constraint for theoretical models. Mean-field Babcock-Leighton dynamos that consider non-instantaneous rising flux tubes have been shown to exhibit long-term variability in their magnetic cycle. However a relation that parameterizes the rise-time of non-axisymmetric magnetic flux tubes in terms of stellar parameters is still missing. Aims: We aim to find a general parameterization of the rise-time of magnetic flux tubes for solar-like stars. Methods: By considering the influence of magnetic tension on the rise of non-axisymmetric flux tubes, we predict the existence of a control parameter referred as $Γ_{α_1}^{α_2}$. This parameter is a measure of the balance between rotational effects and magnetic effects (buoyancy and tension) acting on the magnetic flux tube. We carry out two series of numerical experiments (one for axisymmetric rise and one for non-axisymmetric rise) and demonstrate that $Γ_{α_1}^{α_2}$ indeed controls the rise-time of magnetic flux tubes. Results: We find that the rise-time follows a power law of $Γ_{α_1}^{α_2}$ with an exponent that depends on the azimuthal wavenumber of the magnetic flux loop. Conclusions: Compressibility does not impact the rise of magnetic flux tubes, while non-axisymmetry does. In the case of non-axisymmetric rise, the tension force modifies the force balance acting on the magnetic flux tube. We identified the three independent parameters required to predict the rise-time of magnetic flux tubes, that is, the stellar rotation rate, the magnetic flux density of the flux tube, and its azimuthal wavenumber. We combined these into one single relation that is valid for any solar-like star. We suggest using this generalized relation to constrain the rise-time of magnetic flux tubes in Babcock-Leighton dynamo models.

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arXiv2013

Toward a hybrid dynamo model for the Milky Way

(Abridged) Based on the rapidly increasing all-sky data of Faraday rotation measures and polarised synchrotron radiation, the Milky Way's magnetic field is now modelled with an unprecedented level of detail and complexity. We aim to complement this heuristic approach with a physically motivated, quantitative Galactic dynamo model -- a model that moreover allows for the evolution of the system as a whole, instead of just solving the induction equation for a fixed static disc. Building on the framework of mean-field magnetohydrodynamics and extending it to the realm of a hybrid evolution, we perform three-dimensional global simulations of the Galactic disc. Closure coefficients embodying the mean-field dynamo are calibrated against resolved box simulations of supernova-driven interstellar turbulence. The emerging dynamo solutions comprise a mixture of the dominant axisymmetric S0 mode, with even parity, and a subdominant A0 mode, with odd parity. Notably, such a superposition of modes creates a strong localised vertical field on one side of the Galactic disc. We moreover find significant radial pitch angles, which decay with radius -- explained by flaring of the disc. In accordance with previous work, magnetic instabilities appear to be restricted to the less-stirred outer Galactic disc. Their main effect is to create strong fields at large radii such that the radial scale length of the magnetic field increases from 4 kpc (for the case of a mean-field dynamo alone) to about 10 kpc in the hybrid models. There remain aspects (e.g., spiral arms, X-shaped halo fields, fluctuating fields) that are not captured by the current model and that will require further development towards a fully dynamical evolution. Nevertheless, the work presented demonstrates that a hybrid modelling of the Galactic dynamo is feasible and can serve as a foundation for future efforts.

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arXiv2013

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 and magnetohydrodynamic (MHD) simulations with mesh refinement of accreting planets embedded in protoplanetary disks (PPDs). The magnetized disk includes Ohmic resistivity that depends on the overlying mass column, leading to turbulent surface layers and a dead zone near the midplane. The main results are: (i) The accretion flow in the Hill sphere is intrinsically 3D for hydrodynamic and MHD models. Net inflow toward the planet is dominated by high latitude flows. A circumplanetary disk (CPD) forms. Its midplane flows outward in a pattern whose details differ between models. (ii) Gap opening magnetically couples and ignites the dead zone near the planet, leading to stochastic accretion, a quasi-turbulent flow in the Hill sphere and a CPD whose structure displays high levels of variability. (iii) Advection of magnetized gas onto the rotating CPD generates helical fields that launch magnetocentrifugally driven outflows. During one specific epoch a highly collimated, one-sided jet is observed. (iv) The CPD's surface density $\sim30{\rm\,g\,cm^{-2}}$, small enough for significant ionization and turbulence to develop. (v) The accretion rate onto the planet in the MHD simulation reaches a steady value $8 \times 10^{-3} {\rm M_\oplus yr^{-1}}$, and is similar in the viscous hydrodynamic runs. Our results suggest that gas accretion onto a forming giant planet within a magnetized PPD with dead zone allows rapid growth from Saturnian to Jovian masses. As well as being relevant for giant planet formation, these results have important implications for the formation of regular satellites around gas giant planets.

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arXiv2013

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, $η\sim T^{-3/2}$, the decrease in plasma temperature at the $X-$points leads to: (i) increase in the magnetic diffusivity until the characteristic time for magnetic diffusion becomes comparable to that of thermal conduction; (ii) increase in the reconnection rate; and, (iii) 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.

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arXiv2012

Feedback by massive stars and the emergence of superbubbles I. Energy efficiency & Vishniac instabilities

We study the evolution of isolated and merging interstellar bubbles of three stars (25, 32 and 60 M\odot) in a homogeneous background medium with a density of 10 mp /ccm via 3D-hydrodynamic simulations with standard ISM thermodynamics (optically thin radiative cooling and photo-electric heating) and time dependent energy and mass input according to stellar evolutionary tracks. We vary the position of the three stars relative to each other to compare the energy response for cases of isolated, merging and initially cospatial bubbles. Due to mainly the Vishniac instability, our simulated bubbles develop thick shells and filamentary internal structures in column density. The shell widths reach tens of per cent of the outer bubble radius, which compares favourably to observations. More energy is retained in the ISM for more closely packed groups, by up to a factor of three and typically a factor of two for intermediate times after the first supernova. Once the superbubble is established, different positions of the contained stars make only a minor difference to the energy tracks. For our case of three massive stars, the energy deposition varies only very little for distances up to about 30 pc between the stars. Energy injected by supernovae is entirely dissipated in a superbubble on a timescale of about 1 Myr, which increases slightly with the superbubble size at the time of the explosion. The Vishniac instability may be responsible for the broadening of the shells of interstellar bubbles. Massive star winds are significant energetically due to their - in the long run - more efficient, steady energy injection and because they evacuate the space around the massive stars. For larger scale simulations, the feedback effect of close groups of stars or clusters may be subsumed into one effective energy input with insignificant loss of energy accuracy.

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arXiv2008

A galaxy dynamo by supernova-driven interstellar turbulence

Supernovae are the dominant energy source for driving turbulence within the interstellar plasma. Until recently, their effects on magnetic field amplification in disk galaxies remained a matter of speculation. By means of self-consistent simulations of supernova-driven turbulence, we find an exponential amplification of the mean magnetic field on timescales of a few hundred million years. The robustness of the observed fast dynamo is checked at different magnetic Reynolds numbers, and we find sustained dynamo action at moderate Rm. This indicates that the mechanism might indeed be of relevance for the real ISM. Sensing the flow via passive tracer fields, we infer that SNe produce a turbulent alpha effect which is consistent with the predictions of quasilinear theory. To lay a foundation for global mean-field models, we aim to explore the scaling of the dynamo tensors with respect to the key parameters of our simulations. Here we give a first account on the variation with the supernova rate.

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arXiv2008

Magnetic field amplification by SN-driven interstellar turbulence

Within the interstellar medium, supernovae are thought to be the prevailing agents in driving turbulence. Until recently, their effects on magnetic field amplification in disk galaxies remained uncertain. Analytical models based on the uncorrelated-ensemble approach predicted that any created field would be expelled from the disk before it could be amplified significantly. By means of direct simulations of supernova-driven turbulence, we demonstrate that this is not the case. Accounting for galactic differential rotation and vertical stratification, we find an exponential amplification of the mean field on timescales of several hundred million years. We especially 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.

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arXiv2008

Direct simulations of a supernova-driven galactic dynamo

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. 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. 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. 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.

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arXiv2008

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 $35\degr$ 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 $\hatγ$ 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 $\hatγ$ depends on whether clustering in terms of super-bubbles 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 kpc kms.

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arXiv2007

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.

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