A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov–Poisson Equation

Myers, A.; Colella, P.; Straalen, B. Van

doi:10.1137/16M105962X

Title: A 4^th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov–Poisson Equation

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Abstract

Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new particle-in- cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. H. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509-3537]. It treats all of the stages of the standard PIC update|charge deposition, force interpolation, the field solve, and the particle push|with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. Here, we demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2^nd-order method. As expected, the 4^th-order method can achieve accuracy comparable to that of the 2nd-order method and with considerably fewer resolution elements.

Authors:

Myers, A. ^[1]; Colella, P. ^[1]; Straalen, B. Van ^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Publication Date:: Tue May 09 00:00:00 EDT 2017

Research Org.:: Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1525188

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: SIAM Journal on Scientific Computing

Additional Journal Information:: Journal Volume: 39; Journal Issue: 3; Journal ID: ISSN 1064-8275

Publisher:: SIAM

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; particle-in-cell (PIC) methods; higher order; phase-space remapping; numerical noise; Vlasov-Poisson equation

Citation Formats


                    Myers, A., Colella, P., and Straalen, B. Van. A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov–Poisson Equation.  United States: N. p., 2017. 
Web.  doi:10.1137/16M105962X.

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                    Myers, A., Colella, P., & Straalen, B. Van. A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov–Poisson Equation.  United States.  https://doi.org/10.1137/16M105962X

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                    Myers, A., Colella, P., and Straalen, B. Van. Tue .  
"A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov–Poisson Equation".  United States.  https://doi.org/10.1137/16M105962X.  https://www.osti.gov/servlets/purl/1525188.

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@article{osti_1525188,

  title        = {A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov–Poisson Equation},

  author       = {Myers, A. and Colella, P. and Straalen, B. Van},

  abstractNote = {Numerical solutions to the Vlasov-Poisson system of equations have important applications to both plasma physics and cosmology. In this paper, we present a new particle-in- cell (PIC) method for solving this system that is 4th-order accurate in both space and time. Our method is a high-order extension of one presented previously [B. Wang, G. H. Miller, and P. Colella, SIAM J. Sci. Comput., 33 (2011), pp. 3509-3537]. It treats all of the stages of the standard PIC update|charge deposition, force interpolation, the field solve, and the particle push|with 4th-order accuracy, and includes a 6th-order accurate phase-space remapping step for controlling particle noise. Here, we demonstrate the convergence of our method on a series of one- and two- dimensional electrostatic plasma test problems, comparing its accuracy to that of a 2nd-order method. As expected, the 4th-order method can achieve accuracy comparable to that of the 2nd-order method and with considerably fewer resolution elements.},

  doi          = {10.1137/16M105962X},

  journal      = {SIAM Journal on Scientific Computing},

  number       = 3,

  volume       = 39,

  place        = {United States},

  year         = {Tue May 09 00:00:00 EDT 2017},

  month        = {Tue May 09 00:00:00 EDT 2017}

}

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Title: A 4th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov–Poisson Equation

Abstract

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Title: A 4^th-Order Particle-in-Cell Method with Phase-Space Remapping for the Vlasov–Poisson Equation