Numerical Algorithms for Axisymmetric Fokker–Planck–Landau Operators

We establish a simplified form of the axisymmetric Fokker–Planck–Landau operator. In doing so, we derive a weak formulation of this operator on which we get directly the conservation properties and the decay of the entropy as it is the case for the three-dimensional operator. A symmetrized version of this formulation leads to a class of numerical schemes which satisfy these physical properties at the discrete level. Fast numerical algorithms used in previous works are shown to be efficient in the cylindrical geometry. Finally, some numerical tests are presented at the end of this paper.