Asymptotic-preserving methods for an anisotropic model of electrical potential in a tokamak

Philippe Angot (1) , Thomas Auphan (1) , Olivier Guès (1)

1 Analyse appliquée

A 2D nonlinear model for the electrical potential in the edge plasma in a tokamak generates a stiff problem due to the low resistivity in the direction parallel to the magnetic field lines. An asymptotic-preserving method based on a micro-macro decomposition is studied in order to have a well-posed problem, even when the parallel resistivity goes to $0$. Numerical tests with a finite difference scheme show a bounded condition number for the linearised discrete problem solved at each time step, which confirms the theoretical analysis on the continuous problem.

Mots clés: Evolution problem; nonlinear anisotropic model; asymptotic-preserving method; numerical tests

Domaines: Analyse numérique [math.NA]

Philippe Angot, Thomas Auphan, Olivier Guès. Asymptotic-preserving methods for an anisotropic model of electrical potential in a tokamak. International Symposium of Finite Volumes for Complex Applications VII (FVCA7), Jun 2014, Berlin, Germany. pp.471-478, ⟨10.1007/978-3-319-05591-6_46⟩. ⟨hal-01018388⟩