2015/05/08 by A. Stegmeir, Stegmeir, Andreas, D. Coster +7 · 3 citations
Engineering · Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Magnetic confinement fusion research #Numerical methods for differential equations #Plasma Physics (physics.plasm-ph) #Superconducting Materials and Applications
paper · pdf · doi:10.48550/arxiv.1505.02040
openalex publication_date 2015/05/08 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28
In the presented field line map approach the simulation domain of a tokamak\nis covered with a cylindrical grid, which is Cartesian within poloidal planes.\nStandard finite-difference methods can be used for the discretisation of\nperpendicular (w.r.t.~magnetic field lines) operators. The characteristic flute\nmode property \(k\∥\≪ k\⊥\) of structures is\nexploited computationally by a grid sparsification in the toroidal direction. A\nfield line following discretisation of parallel operators is then required,\nwhich is achieved via a finite difference along magnetic field lines. This\nincludes field line tracing and interpolation or integration. The main emphasis\nof this paper is on the discretisation of the parallel diffusion operator.\nBased on the support operator method a scheme is constructed which exhibits\nonly very low numerical perpendicular diffusion. The schemes are implemented in\nthe new code GRILLIX, and extensive benchmarks are presented which show the\nvalidity of the approach in general and GRILLIX in particular. The main\nadvantage of the approach is that it does not rely on field/flux-aligned, which\nbecome singular on the separatrix/X-point. Most tokamaks are based on the\ndivertor concept, and the numerical treatment of the separatrix is therefore of\nimportance for simulations of the edge and scrape-off layer.\n