A Singularity-Free Coordinate System for X-point Geometries
  A Flux Coordinate Independent (FCI) approach for anisotropic systems, not based on magnetic flux coordinates has been introduced in [F. Hariri and M. Ottaviani, Comput. Phys. Commun., 184,2419 (2013)]. In this paper, we show that the approach can tackle magnetic configurations including X-points. Using the code FENICIA, an equilibrium with a magnetic island has been used to show the robustness of the FCI approach to cases in which a magnetic separatrix is present in the system, either by design or as a consequence of instabilities. Numerical results are in good agreement with the analytic solutions of the sound-wave propagation problem. Conservation properties are verified. Finally, the critical gain of the FCI approach in situations including the magnetic separatrix with an X-point is demonstrated by a fast convergence of the code with the numerical resolution in the direction of symmetry. The results highlighted in this paper show that the FCI approach should be able to address turbulent transport problems in X-point geometries. 
F. Hariri, P. Hill, M. Ottaviani, Y. Sarazin
physics.plasm-ph