An implicit energy-conservative 2D Fokker-Planck algorithm - I. Differencescheme

Numerical energy conservation in Fokker-Planck problems requires the energy moment of the Fokker-Planck equation to cancel exactly. However, standard discretization techniques not only do not observe this requirement (thus pr ecluding exact energy conservation), but they also demand very refined mesh es to keep the energy error under control. In this paper, a new difference scheme for multidimensional Fokker-Planck problems that improves the numeri cal cancellation of the energy moment is proposed. Crucial to this new deve lopment is the reformulation of the friction term in the Fokker-Planck coll ision operator using Maxwell stress tensor formalism, As a result, the Fokk er-Planck collision operator rakes the form of a double divergence operatin g on a tensor, which is suitable for particle and energy conservative diffe rencing. Numerical results show that the new discretization scheme improves the cancellation of the energy moment integral over standard approaches by at least an order of magnitude. (C) 2000 Academic Press.