The semi-Lagrangian method on curvilinear grids

Adnane Hamiaz (1, 2) , Michel Mehrenberger (1, 2) , Hocine Sellama (2) , Eric Sonnendrücker (3)

1 TONUS - TOkamaks and NUmerical Simulations
2 IRMA - Institut de Recherche Mathématique Avancée
3 IPP - Max-Planck-Institut für Plasmaphysik [Garching]

We study the semi-Lagrangian method on curvilinear grids. The classical backward semi-Lagrangian method [1] preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme along the lines of [2] is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.

Mots clés: curvilinear grid; semi-Lagrangian method; guiding center model; Vlasov equation; mapped grid

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]; Modélisation et simulation; Physique des plasmas [physics.plasm-ph]; Physique Numérique [physics.comp-ph]

Adnane Hamiaz, Michel Mehrenberger, Hocine Sellama, Eric Sonnendrücker. The semi-Lagrangian method on curvilinear grids. Communications in Applied and Industrial Mathematics, 2016, ⟨10.1515/caim-2016-0024⟩. ⟨hal-01213366⟩