Analysis of locally-aligned and non-aligned discretisation schemes for reactor-scale tokamak edge turbulence simulations

Edge turbulence codes will play a key role in the interpretation of ITER data and for reliable predictions of EU-DEMO. At present, such codes are not yet capable of routine simulations at reactor scale, and instead focus on smaller experiments like TCV or ASDEX Upgrade. Numerical methods have to be identified that scale to reactor size, and are able to cope with the highly anisotropic turbulent structures and simultaneously with the complex magnetic geometry in the edge with X-point(s), the vessel wall and divertor targets present. Particularly for such conditions two main approaches, non-aligned discretisation schemes and a locally-aligned discretisation scheme (commonly referred to as Flux-Coordinate Independent approach (FCI)), have emerged. We analyse both schemes concerning their applicability and scalability to next generation fusion reactors. We find that the ratio of the computational ( R0 )2 cost of a non-aligned scheme compared to aligned scheme scales as oc qps for shear Alfven dynamics, )3 and as ( R0 qps for electron heat conduction, where R0 is the major radius of a tokamak, q an estimate for the safety factor at the edge and ps is the drift scale representing the typical size of turbulent structures to be resolved. Locally-aligned schemes can therefore be considered strongly favourable for reactor scale tokamaks concerning computational performance. On the other hand, locally-aligned schemes suffer from a more complex treatment of boundary conditions, for which an immersed boundary approach (IBA) was recently proposed. We demonstrate numerically the validity of this method in combination with the FCI approach. Finally, we present a first attempt of an ITER edge turbulence simulation with the FCI code GRILLIX at realistic parameters and in realistic geometry.& COPY; 2023 Elsevier B.V. All rights reserved.