A Numerical Instability in an ADI Algorithm for Gyrokinetics

Belli, E.A. ; Hammett, G.W.

Princeton University. Plasma Physics Laboratory.

关键词: Wavelengths Computational Physics;    Dimensions;    70 Plasma Physics And Fusion Technology;    Implementation;    Numerical Methods;   

DOI  :  10.2172/836494
RP-ID  :  PPPL-4034
RP-ID  :  AC02-76CH03073
RP-ID  :  836494

美国|英语

来源: UNT Digital Library

【 摘 要 】

We explore the implementation of an Alternating Direction Implicit (ADI) algorithm for a gyrokinetic plasma problem and its resulting numerical stability properties. This algorithm, which uses a standard ADI scheme to divide the field solve from the particle distribution function advance, has previously been found to work well for certain plasma kinetic problems involving one spatial and two velocity dimensions, including collisions and an electric field. However, for the gyrokinetic problem we find a severe stability restriction on the time step. Furthermore, we find that this numerical instability limitation also affects some other algorithms, such as a partially implicit Adams-Bashforth algorithm, where the parallel motion operator v{sub {parallel}} {partial_derivative}/{partial_derivative}z is treated implicitly and the field terms are treated with an Adams-Bashforth explicit scheme. Fully explicit algorithms applied to all terms can be better at long wavelengths than these ADI or partially implicit algorithms.