Three discontinuous Galerkin schemes for the anisotropic heat conduction equation on non-aligned grids

We present and discuss three discontinuous Galerkin (dG) discretizations for the anisotropic heat conduction equation on non-aligned cylindrical grids. Our most favourable scheme relies on a self-adjoint local dG (LDG) discretization of the elliptic operator. It conserves the energy exactly and converges with arbitrary order. The pollution by numerical perpendicular heat fluxes degrades with superconvergence rates. We compare this scheme with aligned schemes that are based on the flux-coordinate independent approach for the discretization of parallel derivatives. Here, the dG method provides the necessary interpolation. The first aligned discretization can be used in an explicit time-integrator. However, the scheme violates conservation of energy and shows up stagnating convergence rates for very high resolutions. We overcome this partly by using the adjoint of the parallel derivative operator to construct a second self-adjoint aligned scheme. This scheme preserves energy, but reveals unphysical oscillations in the numerical tests, which result in a decreased order of convergence. Both aligned schemes exhibit low numerical heat fluxes into the perpendicular direction. We build our argumentation on various numerical experiments on all three schemes for a general axisymmetric magnetic field, which is closed by a comparison to the aligned finite difference (FD) schemes of References [1,2

The collisional drift wave instability in steep density gradient regimes

The collisional drift wave instability in a straight magnetic field configuration is studied within a full-F gyro-fluid model, which relaxes the Oberbeck-Boussinesq (OB) approximation. Accordingly, we focus our study on steep background density gradients. In this regime we report on corrections by factors of order one to the eigenvalue analysis of former OB approximated approaches as well as on spatially localised eigenfunctions, that contrast strongly with their OB approximated equivalent. Remarkably, non-modal phenomena arise for large density inhomogeneities and for all collisionalities. As a result, we find initial decay and non-modal growth of the free energy and radially localised and sheared growth patterns. The latter non-modal effect sustains even in the nonlinear regime in the form of radially localised turbulence or zonal flow amplitudes.Comment: accepted at Nuclear Fusio

Non-Oberbeck-Boussinesq zonal flow generation

Novel mechanisms for zonal flow (ZF) generation for both large relative density fluctuations and background density gradients are presented. In this non-Oberbeck-Boussinesq (NOB) regime ZFs are driven by the Favre stress, the large fluctuation extension of the Reynolds stress, and by background density gradient and radial particle flux dominated terms. Simulations of a nonlinear full-F gyro-fluid model confirm the predicted mechanism for radial ZF propagation and show the significance of the NOB ZF terms for either large relative density fluctuation levels or steep background density gradients

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two- and three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique. We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak)

Unified transport scaling laws for plasma blobs and depletions

We study the dynamics of seeded plasma blobs and depletions in an (effective) gravitational field. For incompressible flows the radial center of mass velocity of blobs and depletions is proportional to the square root of their initial cross-field size and amplitude. If the flows are compressible, this scaling holds only for ratios of amplitude to size larger than a critical value. Otherwise, the maximum blob and depletion velocity depends linearly on the initial amplitude and is independent of size. In both cases the acceleration of blobs and depletions depends on their initial amplitude relative to the background plasma density, is proportional to gravity and independent of their cross-field size. Due to their reduced inertia plasma depletions accelerate more quickly than the corresponding blobs. These scaling laws are derived from the invariants of the governing drift-fluid equations and agree excellently with numerical simulations over five orders of magnitude. We suggest an empirical model that unifies and correctly captures the radial acceleration and maximum velocities of both blobs and depletions

Controlling in virtuellen Unternehmen -eine Studie- Teil 1: State of the art

Im Rahmen dieser Studie die vom VDMA Bayern unterstützt wird, wurde der Fragestellung der Kooperationen kleiner und mittlerer Unternehmen (KMU) in Netzwerken, Verbänden, Interessensgemeinschaften oder virtueller Unternehmen hinsichtlich der Umsetzung strategischer Geschäftsideen, wie z.B. der Erschließung neuer Märkte, aber auch der Steuerung der Kooperationen im operativen Geschäft, nachgegangen. Globalisierung bedeutet: Konzentration im Konzernbereich, dem die KMU's wirksam nur durch Kooperationen begegnen können. Diese Kooperationen sind im operativen Geschäft erfolgreich auf dem Weg. Wie messbar erfolgreich sie sind, soll mit dieser Studie erforscht werden. Im ersten Teil wird durch intensive Recherche und Analyse des State of the Art die theoretische und praktische Basis für dieses Projekt geschaffen und hier insbesondere die Kooperationsform eines virtuellen Unternehmens analysiert.In the context of this study by the VDMA Bavaria one supports, the question of cooperation of small and middle enterprises (SME) in networks, federations, interest communities or virtual enterprises regarding the conversion of strategic business ideas, like e.g. the development of new markets, in addition, the controlling of co-operation in the operational business one follows. Globalization means: Concentration in the company, which the SME's can meet effectively only by co-operation. These cooperation are successful in the operational business on the way. How measurably successful they are, is to be investigated with this study. In the first part by intensive search and analysis of the State of the art the theoretical and practical basis for this project is created

The Role of Indole and Other Shikimic Acid Derived Maize Volatiles in the Attraction of Two Parasitic Wasps

After herbivore attack, plants release a plethora of different volatile organic compounds (VOCs), which results in odor blends that are attractive to predators and parasitoids of these herbivores. VOCs in the odor blends emitted by maize plants (Zea mays) infested by lepidopteran larvae are well characterized. They are derived from at least three different biochemical pathways, but the relative importance of each pathway for the production of VOCs that attract parasitic wasps is unknown. Here, we studied the importance of shikimic acid derived VOCs for the attraction of females of the parasitoids Cotesia marginiventris and Microplitis rufiventris. By incubating caterpillar-infested maize plants in glyphosate, an inhibitor of the 5-enolpyruvylshikimate-3-phospate (EPSP) synthase, we obtained induced odor blends with only minute amounts of shikimic acid derived VOCs. In olfactometer bioassays, the inhibited plants were as attractive to naive C. marginiventris females as control plants that released normal amounts of shikimic acid derived VOCs, whereas naive M. rufiventris females preferred inhibited plants to control plants. By adding back synthetic indole, the quantitatively most important shikimic acid derived VOC in induced maize odors, to inhibited plants, we showed that indole had no effect on the attraction of C. marginiventris and that M. rufiventris preferred blends without synthetic indole. Exposing C. marginiventris females either to odor blends of inhibited or control plants during oviposition experiences shifted their preference in subsequent olfactometer tests in favor of the experienced odor. Further learning experiments with synthetic indole showed that C. marginiventris can learn to respond to this compound, but that this does not affect its choices between natural induced blends with or without indole. We hypothesize that for naïve wasps the attractiveness of an herbivore-induced odor blend is reduced due to masking by nonattractive compounds, and that during oviposition experiences in the presence of complex odor blends, parasitoids strongly associate some compounds, whereas others are largely ignore

Controlling in virtuellen Unternehmen -eine Studie- Teil 2: Auswertung

Im Rahmen der Controllingstudie, die vom VDMA Bayern unterstützt wird, wurde der Fragestellung der Kooperationen kleiner und mittlerer Unternehmen (KMU) in Netzwerken, Verbänden, Interessensgemeinschaften oder virtueller Unternehmen hinsichtlich der Umsetzung strategischer Geschäftsideen, wie z.B. der Erschließung neuer Märkte, aber auch der Steuerung der Kooperationen im operativen Geschäft und der Erfolgssteuerung mittels unterschiedlichster Controllinginstrumente nachgegangen. Dieser Beitrag beinhaltet nun die Auswertung der Studie und gibt einen Ausblick auf das weitere Forschungsvorhaben.In the context of this study by the VDMA Bavaria one supports, the question of cooperation of small and middle enterprises (SME) in networks, federations, interest communities or virtual enterprises regarding the conversion of strategic business ideas, like e.g. the development of new markets, in addition, the controlling of co-operation in the operational business one follows. This contribution contains the evaluation of the study and gives an outlook on the further research project