A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation

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Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial ... continued below

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Banks, J W & Hittinger, J A November 24, 2009.

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Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.

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PDF-file: 12 pages; size: 2.5 Mbytes

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  • Journal Name: IEEE Transactions on Plasma Science, vol. 38, no. 9, September 10, 2010, pp. 2198-2207; Journal Volume: 38; Journal Issue: 9

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  • Report No.: LLNL-JRNL-420843
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 991524
  • Archival Resource Key: ark:/67531/metadc1013957

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  • November 24, 2009

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  • Oct. 14, 2017, 8:36 a.m.

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  • Oct. 27, 2017, 6:01 p.m.

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Banks, J W & Hittinger, J A. A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation, article, November 24, 2009; Livermore, California. (https://digital.library.unt.edu/ark:/67531/metadc1013957/: accessed March 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.