An implicit energy-conservative 2D Fokker-Planck algorithm -- 1. Difference scheme

Journal Article · Thu Jan 20 04:00:00 EST 2000 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1999.6394· OSTI ID:20015680

Chacon, L; Barnes, D C; Knoll, D A; Miley, G H

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 precluding exact energy conservation), but they also demand very refined meshes to keep the energy error under control. In this paper, a new difference scheme for multidimensional Fokker-Planck problems that improves the numerical cancellation of the energy moment is proposed. Crucial to this new development is the reformulation of the friction term in the Fokker-Planck collision operator takes the form of a double divergence operating on a tensor, which is suitable for particle and energy conservative differencing. 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.

• Research Organization: Univ. of Illinois, Urbana, IL (US)
• OSTI ID: 20015680
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 157; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
CONSERVATION LAWS
FINITE DIFFERENCE METHOD
FOKKER-PLANCK EQUATION
PLASMA SIMULATION
THERMONUCLEAR DEVICES
TWO-DIMENSIONAL CALCULATIONS