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

Radial convection of finite ion temperature, high amplitude plasma blobs

We present results from simulations of seeded blob convection in the scrape-off-layer of magnetically confined fusion plasmas. We consistently incorporate high fluctuation amplitude levels and finite Larmor radius (FLR) effects using a fully nonlinear global gyrofluid model. This is in line with conditions found in tokamak scrape-off-layers (SOL) regions. Varying the ion temperature, the initial blob width, and the initial amplitude, we found an FLR dominated regime where the blob behavior is significantly different from what is predicted by cold-ion models. The transition to this regime is very well described by the ratio of the ion gyroradius to the characteristic gradient scale length of the blob. We compare the global gyrofluid model with a partly linearized local model. For low ion temperatures we find that simulations of the global model show more coherent blobs with an increased cross-field transport compared to blobs simulated with the local model. The maximal blob amplitude is significantly higher in the global simulations than in the local ones. When the ion temperature is comparable to the electron temperature, global blob simulations show a reduced blob coherence and a decreased cross-field transport in comparison with local blob simulations

Streamline integration as a method for structured grid generation in X-point geometry

We investigate structured grids aligned to the contours of a two-dimensional flux-function with an X-point (saddle point). Our theoretical analysis finds that orthogonal grids exist if and only if the Laplacian of the flux-function vanishes at the X-point. In general, this condition is sufficient for the existence of a structured aligned grid with an X-point. With the help of streamline integration we then propose a numerical grid construction algorithm. In a suitably chosen monitor metric the Laplacian of the flux-function vanishes at the X-point such that a grid construction is possible. We study the convergence of the solution to elliptic equations on the proposed grid. The diverging volume element and cell sizes at the X-point reduce the convergence rate. As a consequence, the proposed grid should be used with grid refinement around the X-point in practical applications. We show that grid refinement in the cells neighboring the X-point restores the expected convergence rate

The influence of temperature dynamics and dynamic finite ion Larmor radius effects on seeded high amplitude plasma blobs

Thermal effects on the perpendicular convection of seeded pressure blobs in the scrape-off layer of magnetised fusion plasmas are investigated. Our numerical study is based on a four field full-F gyrofluid model, which entails the consistent description of high fluctuation amplitudes and dynamic finite Larmor radius effects. We find that the maximal radial blob velocity increases with the square root of the initial pressure perturbation and that a finite Larmor radius contributes to highly compact blob structures that propagate in the poloidal direction. An extensive parameter study reveals that a smooth transition to this compact blob regime occurs when the finite Larmor radius effect strength, defined by the ratio of the magnetic field aligned component of the ion diamagnetic to the $\vec{E}\times\vec{B}$ vorticity, exceeds unity. The maximal radial blob velocities agree excellently with the inertial velocity scaling law over more than an order of magnitude. We show that the finite Larmor radius effect strength affects the poloidal and total particle transport and present an empirical scaling law for the poloidal and total blob velocities. Distinctions to the blob behaviour in the isothermal limit with constant finite Larmor radius effects are highlighted

Print and Screen, Muriel Cooper at MIT

Muriel Cooper (1925–94) worked at the Massachusetts Institute of Technology (MIT) for more than four decades as a graphic designer, an educator, and a researcher. Beginning in the early 1950s, she was the first designer in MIT’s Office of Publications, where she visualized the latest scientific research in print. In the late 1960s, she became the first Design and Media Director for the MIT Press, rationalizing its publishing protocols and giving form to some of the period’s most significant texts in the histories of art, design, and architecture, among other fields. In the mid-1970s, Cooper co-founded the Visible Language Workshop in MIT’s Department of Architecture. There she taught experimental printing and explored new imaging technologies in photography and video. And from the 1980s until her death, Cooper was a founding faculty member of the MIT Media Lab, where she turned her attention to the human-computer interface. Cooper helped cultivate a design culture at MIT. And before her premature death, she established some of the metaphors and mentored some of the designers that have shaped our contemporary digital landscape. Few 20th century designers have made significant contributions in both print and digital media, or helped to navigate the epochal transition between the two. Yet Cooper, in designing and redesigning roles for herself within new fields at MIT, did just that. Over her career and across multiple media, Cooper’s concerns remained quite consistent: She focused on developing both design tools and user experiences that would provide greater control and quicker feedback, eventually to be aided by machine intelligence. She sought to create experiences that were dynamic rather than static and simultaneous rather than linear, ones that engaged multiple media and a range of human senses. Cooper applied her knowledge of print design to software, and considered print and the process of its production as a prototype for the experiences that she would seek on screen. She also borrowed freely from media such as photography and film to inspire some of the effects she would later explore in new media. Cooper’s career traced an arc, in her practice and her pedagogy, from a focus on objects to one on systems. And her relationship to the digital evolved from a set of effects to be emulated in other media to seeing the computer at first as a tool, then as an assistant, and finally, as the medium itself. At the same time, she participated in a broader shift during this period from the paradigm of the humanist subject to the digitally augmented, “posthuman” condition of the present. In her interests and her achievements, Cooper exceeded any traditional definition of a graphic designer. At the same time, her work has defined the present state of the field. This dissertation, the first dedicated to Cooper, charts her pathbreaking career at MIT while also shedding new light on vital moments in the history of art, design, architecture, and media in postwar America

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

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