  Turbulent dynamics in the scrape-off layer (SOL) of magnetic fusion devices
is intermittent with large fluctuations in density and pressure. Therefore, a
model is required that allows perturbations of similar or even larger magnitude
to the time-averaged background value. The fluid-turbulence code GRILLIX is
extended to such a global model, which consistently accounts for large
variation in plasma parameters. Derived from the drift reduced Braginskii
equations, the new GRILLIX model includes electromagnetic and electron-thermal
dynamics, retains global parametric dependencies and the Boussinesq
approximation is not applied. The penalisation technique is combined with the
flux-coordinate independent (FCI) approach [F. Hariri and M. Ottaviani,
Comput.Phys.Commun. 184:2419, (2013); A. Stegmeir et al., Comput.Phys.Commun.
198:139, (2016)], which allows to study realistic diverted geometries with
X-point(s) and general boundary contours. We characterise results from
turbulence simulations and investigate the effect of geometry by comparing
simulations in circular geometry with toroidal limiter against realistic
diverted geometry at otherwise comparable parameters. Turbulence is found to be
intermittent with relative fluctuation levels of up to 40% showing that a
global description is indeed important. At the same time via direct comparison,
we find that the Boussinesq approximation has only a small quantitative impact
in a turbulent environment. In comparison to circular geometry the fluctuations
are reduced in diverted geometry, which is related to a different zonal flow
structure. Moreover, the fluctuation level has a more complex spatial
distribution in diverted geometry. Due to local magnetic shear, which differs
fundamentally in circular and diverted geometry, turbulent structures become
strongly distorted in the perpendicular direction and are eventually damped
away towards the X-point.
