A deterministic verification strategy for electrostatic particle-in-cell algorithms in arbitrary spatial dimensions using the method of manufactured solutions

Tranquilli, Paul; Ricketson, Lee; Chacón, Luis

doi:10.1016/j.jcp.2021.110751

A deterministic verification strategy for electrostatic particle-in-cell algorithms in arbitrary spatial dimensions using the method of manufactured solutions

Journal Article · 01 October 2021 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2021.110751· OSTI ID:1906366

Tranquilli, Paul ^[1]; Ricketson, Lee ^[2]; ^[2]

Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

As simulations of kinetic plasmas continue to increase in scope and complexity, a rigorous and straightforward method for verifying particle-in-cell (PIC) implementations is necessary to ensure their correctness. Here, in this paper, we present a deterministic method for the rigorous verification of multidimensional, multispecies, electrostatic particle-in-cell codes based on the method of manufactured solutions. Specifically, we prove that rigorous verification is possible through the exclusive examination of errors of grid quantities (i.e., moments and/or fields), allowing for a very light-weight and non-intrusive implementation in existing PIC codes. This is a marked improvement over earlier PIC verification approaches (only demonstrated with one species in 1D-1V), which rely on the comparison of cumulative distribution functions, and are invasive on the code base, introduce additional stochastic noise, are significantly more computationally expensive, and lack rigorous convergence properties. Interestingly, we show that different grid quantities feature different rates of convergence with the number of particles and mesh size, impacting the verification process. These theoretical results are confirmed numerically with a multi-species 2D-2V particle-in-cell code, including the ability of the method to detect order reduction due to an incorrect implementation.

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: AC02-05CH11231; AC52-07NA27344; AC52-06NA25396

OSTI ID:: 1906366

Alternate ID(s):: OSTI ID: 1826611

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 448; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (12)

A multi-dimensional, energy- and charge-conserving, nonlinearly implicit, electromagnetic Vlasov–Darwin particle-in-cell algorithm Chen, G.; Chacón, L. Computer Physics Communications, Vol. 197 https://doi.org/10.1016/j.cpc.2015.08.008	journal	December 2015
Electromagnetic gyrokinetic δf particle-in-cell turbulence simulation with realistic equilibrium profiles and geometry Chen, Yang; Parker, Scott E. Journal of Computational Physics, Vol. 220, Issue 2 https://doi.org/10.1016/j.jcp.2006.05.028	journal	January 2007
Pegasus: A new hybrid-kinetic particle-in-cell code for astrophysical plasma dynamics Kunz, Matthew W.; Stone, James M.; Bai, Xue-Ning Journal of Computational Physics, Vol. 259 https://doi.org/10.1016/j.jcp.2013.11.035	journal	February 2014
Warp-X: A new exascale computing platform for beam–plasma simulations Vay, J. -L.; Almgren, A.; Bell, J. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 909 https://doi.org/10.1016/j.nima.2018.01.035	journal	November 2018
Numerical study of neoclassical plasma pedestal in a tokamak geometry Chang, C. S.; Ku, Seunghoe; Weitzner, H. Physics of Plasmas, Vol. 11, Issue 5 https://doi.org/10.1063/1.1707024	journal	May 2004
A verification of the gyrokinetic microstability codes GEM, GYRO, and GS2 Bravenec, R. V.; Chen, Y.; Candy, J. Physics of Plasmas, Vol. 20, Issue 10 https://doi.org/10.1063/1.4826511	journal	October 2013
A methodology for the rigorous verification of Particle-in-Cell simulations Riva, Fabio; Beadle, Carrie F.; Ricci, Paolo Physics of Plasmas, Vol. 24, Issue 5 https://doi.org/10.1063/1.4977917	journal	March 2017
Cross-verification of the global gyrokinetic codes GENE and XGC Merlo, G.; Dominski, J.; Bhattacharjee, A. Physics of Plasmas, Vol. 25, Issue 6 https://doi.org/10.1063/1.5036563	journal	June 2018
Cross-verification of neoclassical transport solutions from XGCa against NEO Hager, R.; Dominski, J.; Chang, C. S. Physics of Plasmas, Vol. 26, Issue 10 https://doi.org/10.1063/1.5121308	journal	October 2019
Sparse grid techniques for particle-in-cell schemes Ricketson, L. F.; Cerfon, A. J. Plasma Physics and Controlled Fusion, Vol. 59, Issue 2 https://doi.org/10.1088/1361-6587/59/2/024002	journal	December 2016
Two-dimensional goodness-of-fit testing in astronomy Peacock, J. A. Monthly Notices of the Royal Astronomical Society, Vol. 202, Issue 3 https://doi.org/10.1093/mnras/202.3.615	journal	March 1983
Realistic simulations of a cyclotron spiral inflector within a particle-in-cell framework Winklehner, Daniel; Adelmann, Andreas; Gsell, Achim Physical Review Accelerators and Beams, Vol. 20, Issue 12 https://doi.org/10.1103/PhysRevAccelBeams.20.124201	journal	December 2017

Similar Records

Comparing 10 Methods for Solution Verification, and Linking to Model Validation

Technical Report · 2005 · OSTI ID:15015103

The Thermalization Verification Problem for EMPIRE-PIC and EMPIRE-Fluid

Technical Report · 2019 · OSTI ID:1763211

An Overview of Gemma FY20 Verification Activities

Technical Report · 2020 · OSTI ID:1821973

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Kinetic plasmas
Method of manufactured solutions
Particle-in-cell methods

A deterministic verification strategy for electrostatic particle-in-cell algorithms in arbitrary spatial dimensions using the method of manufactured solutions

Citation Formats

References (12)

Similar Records

Related Subjects