Jürgen Dreher

Racoon: A parallel mesh-adaptive framework for hyperbolic conservation laws

We report on the development of a computational framework for the parallel, mesh-adaptive solution of systems of hyperbolic conservation laws like the time-dependent Euler equations in compressible gas dynamics or Magneto-Hydrodynamics (MHD) and similar models in plasma physics. Local mesh refinement is realized by the recursive bisection of grid blocks along each spatial dimension, implemented numerical schemes include standard finite-differences as well as shock-capturing central schemes, both in connection with Runge-Kutta type integrators. Parallel execution is achieved through a configurable hybrid of POSIX-multi-threading and MPI distribution with dynamic load balancing. One-, two- and three-dimensional test computations for the Euler equations have been carried out and show good parallel scaling behavior. The Racoon framework is currently used to study the formation of singularities in plasmas and fluids.

Particle simulations of collisionless reconnection in magnetotail configuration including electron dynamics

The role of electron dynamics in collisionless magnetotail reconnection is investigated by using two-dimensional full particle simulations with ion-to-electron mass ratios mi/me set to 1 and 10. The results indicate that the electrons have a stabilizing influence on the ion tearing instability in the sense that growth rates are reduced in runs with the initial electron Larmor radius being sufficiently small in comparison with the ion Larmor radius. A comparison of our results with those obtained by Pritchett [1994] using a significantly different numerical model shows encouraging agreement. The attempt to achieve an approach closer to realistic magnetotail conditions is inhibited by present technical restrictions.

Density-PDFs and Lagrangian statistics of highly compressible turbulence

Abstract In isothermal, highly compressible turbulent flows, density fluctuations follow a log-normal distribution. We establish a connection between these density fluctuations and the probability-density-functions (PDF) of Lagrangian tracer particles advected with the flow. Our predicted particle statistics is tested against large scale numerical simulations, which were performed with 512 3 collocation points and 2 million tracer particles integrated over several dynamical times.

Impact of the floating-point precision and interpolation scheme on the results of DNS of turbulence by pseudo-spectral codes

In this paper we investigate the impact of the floating-point precision and interpolation scheme on the results of direct numerical simulations (DNS) of turbulence by pseudo-spectral codes. Three different types of floating-point precision configurations show no differences in the statistical results. This implies that single precision computations allow for increased Reynolds numbers due to the reduced amount of memory needed. The interpolation scheme for obtaining velocity values at particle positions has a noticeable impact on the Lagrangian acceleration statistics. A tri-cubic scheme results in a slightly broader acceleration probability density function than a tri-linear scheme. Furthermore the scaling behavior obtained by the cubic interpolation scheme exhibits a tendency towards a slightly increased degree of intermittency compared to the linear one.

Axisymmetric Flows in Hall-MHD: A Tendency Towards Finite-Time Singularity Formation

Spontaneous development of shock-like singularities in axisymmetric solutions of the Hall-MHD equations is discussed. It is shown that the Hall-term in Ohms law leads to a Burgers-type equation for the magnetic field evolution in weakly compressible regime. Numerical simulations are used to investigate the validity of this approximation for a particular class of initial conditions.

Femtosecond laser microfabrication of subwavelength structures in photonics

This paper describes experimental and numerical results of the plasma-assisted microfabrication of subwavelength structures by means of point-by point femtosecond laser inscription. It is shown that the spatio-temporal evolution of light and plasma patterns critically depend on input power. Subwavelength inscription corresponds to the supercritical propagation regimes when pulse power is several times self-focusing threshold. Experimental and numerical profiles show quantitative agreement.

Numerical simulation of current sheet formation in a quasiseparatrix layer using adaptive mesh refinement

The formation of a thin current sheet in a magnetic quasiseparatrix layer (QSL) is investigated by means of numerical simulation using a simplified ideal, low-β, MHD model. The initial configuration and driving boundary conditions are relevant to phenomena observed in the solar corona and were studied earlier by Aulanier et al. [Astron. Astrophys. 444, 961 (2005)]. In extension to that work, we use the technique of adaptive mesh refinement (AMR) to significantly enhance the local spatial resolution of the current sheet during its formation, which enables us to follow the evolution into a later stage. Our simulations are in good agreement with the results of Aulanier et al. up to the calculated time in that work. In a later phase, we observe a basically unarrested collapse of the sheet to length scales that are more than one order of magnitude smaller than those reported earlier. The current density attains correspondingly larger maximum values within the sheet. During this thinning process, which is final...

Finite volume WENO methods for hyperbolic conservation laws on Cartesian grids with adaptive mesh refinement

We present a WENO finite volume method for the approximation of hyperbolic conservation laws on adaptively refined Cartesian grids.On each single patch of the AMR grid, we use a modified dimension-by-dimension WENO method, which was recently developed by Buchmuller and Helzel (2014) 1. This method retains the full spatial order of accuracy of the underlying one-dimensional WENO reconstruction for nonlinear multidimensional problems, and requires only one flux computation per interface. It is embedded into block-structured AMR through conservative interpolation functions and a numerical flux fix that transfers data between different levels of grid refinement.Numerical tests illustrate the accuracy of the new adaptive WENO finite volume method. Compared to the classical dimension-by-dimension approach, the new method is much more accurate while it is only slightly more expensive. Furthermore, we also show results of an accuracy study for an adaptive WENO method which uses multidimensional reconstruction of the conserved quantities and a high-order quadrature formula to compute the fluxes. While the accuracy of such a method is comparable with our new approach, it is about three times more expensive than the latter.

FlareLab: early results

The FlareLab experiment at Bochum University has been constructed to generate and investigate plasma-filled magnetic flux tubes similar to arch-shaped solar prominences, which often result in coronal mass ejections (CMEs). In its first version, the device has been used to reproduce and extend previous studies of Bellan et al (1998 Phys. Plasmas 5 1991). Here the plasma source consists of two electrodes, which can be connected to a 1.0 kJ capacitor bank, and of a horseshoe magnet, which provides an arch-shaped guiding field. The discharge is ignited in a cloud of hydrogen gas that has been puffed into the space above the electrodes. In the first few microseconds the plasma current rises at a rate of several kA µs−1, causing the plasma column to pinch along the guiding B-field and to form an expanding loop structure. The observed dynamics of the magnetic flux tubes is analysed by means of three-dimensional MHD simulations in order to determine the influence of parameters like the initial magnetic field geometry on magnetic stability. At present, FlareLab is redesigned to mimic a model that was proposed by Titov and Demoulin (1999 Astron. Astrophys. 351 707) to investigate twisted magnetic configurations in solar flares.

On the self-consistent description of dynamic magnetosphere-ionosphere coupling phenomena with resolved ionosphere

A set of model equations is presented that allows for the self-consistent description of dynamic magnetosphere-ionosphere coupling phenomena with finite ionosphere. The model is very similar to magnetohydrodynamics (MHD), but the plasma-neutral gas interaction in the lower ionosphere is taken into account by a frictional force between ions and neutrals and an ionization-recombination term in the plasma transport equation. Further, the Hall term and the electron pressure term are retained in Ohms law. It is shown that for the collision-dominated E layer, the familiar Pedersen and Hall conductivities can be derived directly from the basic equations. The model is used to numerically simulate the dynamic formation of a magnetospheric-ionospheric current system as the response to prescribed localized magnetospheric convection. Apart from a pair of Birkeland current sheets that are closed by Pedersen currents, associated Hall currents are generated. In addition, density irregularities in the E layer form as a direct consequence of the current closure. They are, however, not related to electron precipitation. For small length scales (≈ 10 km), these density perturbations result in considerably enhanced conductivities below the upward Birkeland currents which in turn lead to a spatial concentration of the latter compared to the downward currents. The timescale for the relaxation of the current system and the ionospheric convection toward a stationary state after the onset of magnetospheric convection is longer than the Alfven travel time and depends on the height-integrated Pedersen conductivity. This is in good agreement with earlier theoretical predictions [Southwood and Kivelson, 1991].