A Numerical Instability in an ADI Algorithm for Gyrokinetics

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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 ... continued below

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684 Kilobytes pages

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Belli, E.A. & Hammett, G.W. December 17, 2004.

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Description

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.

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684 Kilobytes pages

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INIS; OSTI as DE00836494

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  • Other Information: PBD: 17 Dec 2004

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  • Report No.: PPPL-4034
  • Grant Number: AC02-76CH03073
  • DOI: 10.2172/836494 | External Link
  • Office of Scientific & Technical Information Report Number: 836494
  • Archival Resource Key: ark:/67531/metadc784791

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  • December 17, 2004

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  • Dec. 3, 2015, 9:30 a.m.

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  • June 10, 2016, 6:08 p.m.

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Belli, E.A. & Hammett, G.W. A Numerical Instability in an ADI Algorithm for Gyrokinetics, report, December 17, 2004; Princeton, New Jersey. (digital.library.unt.edu/ark:/67531/metadc784791/: accessed April 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.