Extension of GRILLIX. Towards a global fluid turbulence code for realistic magnetic geometries

In order to understand the physics in the scrape-off layer (SOL) of tokamaks and simulate the turbulent cross field transport, numerical codes have become an important tool. The simulation of the edge and SOL poses a major challenge, due to the complex physics and geometry. The widely used field or flux-aligned coordinate systems become ill defined at the X-point and separatrix of a tokamak. The solution to this issue was presented with the plasma turbulence code GRILLIX, which uses a flux-coordinate independent approach (FCI), enabling the simultaneous simulation of the closed and open field line region. A cylindrical grid is used, posing no singularities at the X-point and separatrix. Parallel operators are discretized via a field line map along a field line. Moreover the Cartesian grid within each poloidal plane allows an efficient and consistent simulation of the plasma turbulence. The functionality of the FCI approach was demonstrated within the simple Hasegawa-Wakatani plasma turbulence model. However this model is not suited for the simulation of the complex physics in the SOL. In this work the turbulence simulation efforts within the FCI approach are taken to further depth. The drift-reduced Braginskii model, which is more suited for the SOL, is implemented in GRILLIX. Along this line, the focus is on the consistent and tested implementation of a global electrodynamic model, finally posing a solid and reliable foundation for further development of GRILLIX and turbulence simulations. In this context 'global' means, that nowhere in the model any assumptions about the density and temperature fluctuations amplitude are made. For this goal, many subtle points regarding the widely used Boussinesq approximation, which was relaxed in this thesis, conservation properties of the model and electromagnetic dynamics are considered. In order to reduce the complexity, firstly simulations are performed within a simplified slab geometry, where also a comparison to experimental turbulence data from LAPD device was possible. Finally it helped to perform the transition to more realistic and complex geometries, where the FCI approach shows successfully its capabilities.