Noiseless Vlasov-Poisson simulations with linearly transformed particles

Pinto, Martin C.; Sonnendrucker, Eric; Friedman, Alex; Grote, David P.; Lund, Steve M.

doi:10.1016/j.jcp.2014.06.032

Title: Noiseless Vlasov-Poisson simulations with linearly transformed particles

Journal Article · Wed Jun 25 00:00:00 EDT 2014 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2014.06.032· OSTI ID:1281673

Pinto, Martin C. ^[1]; Sonnendrucker, Eric ^[2]; Friedman, Alex ^[3]; Grote, David P. ^[3]; Lund, Steve M. ^[3]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); CNRS, UMR 7598, Lab. Jacques-Louis Lions, Paris (France); UPMC Univ. Paris 06, UMR 7598, Lab. Jacques-Louis Lions, Paris (France)
IRMA, UMR 7501, Univ. de Strasbourg & CNRS, Strasbourg Cedex (France); Project-team CALVI, Strasbourg Cedex (France)
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

We introduce a deterministic discrete-particle simulation approach, the Linearly-Transformed Particle-In-Cell (LTPIC) method, that employs linear deformations of the particles to reduce the noise traditionally associated with particle schemes. Formally, transforming the particles is justified by local first order expansions of the characteristic flow in phase space. In practice the method amounts of using deformation matrices within the particle shape functions; these matrices are updated via local evaluations of the forward numerical flow. Because it is necessary to periodically remap the particles on a regular grid to avoid excessively deforming their shapes, the method can be seen as a development of Denavit's Forward Semi-Lagrangian (FSL) scheme (Denavit, 1972 [8]). However, it has recently been established (Campos Pinto, 2012 [20]) that the underlying Linearly-Transformed Particle scheme converges for abstract transport problems, with no need to remap the particles; deforming the particles can thus be seen as a way to significantly lower the remapping frequency needed in the FSL schemes, and hence the associated numerical diffusion. To couple the method with electrostatic field solvers, two specific charge deposition schemes are examined, and their performance compared with that of the standard deposition method. Finally, numerical 1d1v simulations involving benchmark test cases and halo formation in an initially mismatched thermal sheet beam demonstrate some advantages of our LTPIC scheme over the classical PIC and FSL methods. Lastly, benchmarked test cases also indicate that, for numerical choices involving similar computational effort, the LTPIC method is capable of accuracy comparable to or exceeding that of state-of-the-art, high-resolution Vlasov schemes.

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Research Organization:: Lawrence Livermore National Lab., Livermore, CA (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC52-07NA27344

OSTI ID:: 1281673

Report Number(s):: LLNL-JRNL-696802

Journal Information:: Journal of Computational Physics, Vol. 275, Issue C; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 14 works

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