Field-aligned interpolation for semi-Lagrangian gyrokinetic simulations

Guillaume Latu (1) , Michel Mehrenberger (2, 3) , Yaman Güçlü (4) , Maurizio Ottaviani (1) , Eric Sonnendrücker (4)

1 IRFM - Institut de Recherche sur la Fusion par confinement Magnétique
2 IRMA - Institut de Recherche Mathématique Avancée
3 TONUS - TOkamaks and NUmerical Simulations
4 IPP - Max-Planck-Institut für Plasmaphysik [Garching]

This work is devoted to the study of field-aligned interpolation in semi-Lagrangian codes. 1 In the context of numerical simulations of magnetic fusion devices, this approach is motivated by the observation that gradients of the solution along the magnetic field lines are typically much smaller than along a perpendicular direction. In toroidal geometry, field-aligned interpolation consists of a 1D interpolation along the field line, combined with 2D interpolations on the poloidal planes (at the intersections with the field line). A theoretical justification of the method is provided in the simplified context of constant advection on a 2D periodic domain: unconditional stability is proven, and error estimates are given which highlight the advantages of field-aligned interpolation. The same methodology is successfully applied to the solution of the gyrokinetic Vlasov equation, for which we present the ion temperature gradient (ITG) instability as a classical test-case: first we solve this in cylindrical geometry (screw-pinch), and next in toroidal geometry (circular Tokamak). In the first case, the algorithm is implemented in Selalib (semi-Lagrangian library), and the numerical simulations provide linear growth rates that are in accordance with the linear dispersion analysis. In the second case, the algorithm is implemented in the Gysela code, and the numerical simulations are benchmarked with those employing the standard (not aligned) scheme. Numerical experiments show that field-aligned interpolation leads to considerable memory savings for the same level of accuracy; substantial savings are also expected in reactor-scale simulations.

Mots clés: gyrokinetics; plasma physics; semi-Lagrangian scheme; Tokamak plasma

Domaines: Analyse numérique [math.NA]; Calcul parallèle, distribué et partagé [cs.DC]; Modélisation et simulation; Equations aux dérivées partielles [math.AP]; Physique des plasmas [physics.plasm-ph]

Guillaume Latu, Michel Mehrenberger, Yaman Güçlü, Maurizio Ottaviani, Eric Sonnendrücker. Field-aligned interpolation for semi-Lagrangian gyrokinetic simulations. Journal of Scientific Computing, 2017. ⟨hal-01315889v2⟩