Hostname: page-component-848d4c4894-2xdlg Total loading time: 0 Render date: 2024-07-08T03:00:03.312Z Has data issue: false hasContentIssue false
  • English
  • Français

Open-boundary spectral and flux-balance Vlasov simulation

Published online by Cambridge University Press:  10 December 2019

Alexander J. Klimas Open the ORCID record for Alexander J. Klimas [Opens in a new window]  and
Adolfo F. Viñas
Alexander J. Klimas*
Affiliation:
GPHI/UMBC, NASA/Goddard Space Flight Center, Greenbelt, MD  20770, USA
Adolfo F. Viñas
Affiliation:
Department of Physics, Catholic University of America, Washington, DC  20064, USA NASA/Goddard Space Flight Center, Greenbelt, MD  20770, USA
*
†Email address for correspondence: alex.klimas@nasa.gov
Get access Rights & Permissions [Opens in a new window]

Abstract

Simulations of one-dimensional Vlasov–Maxwell solutions with non-periodic boundary conditions are discussed. Results obtained using a recently developed filtered flux-balance simulation system are compared to those obtained using a filtered, Fourier–Fourier transformed system. Excellent agreement is confirmed except for the appearance of the Gibbs phenomenon on the discontinuous simulated solutions of the transformed system. Recovery of the flux-balance results from the Fourier transformed results using the inverse polynomial reconstruction method is demonstrated.

Keywords

plasma dynamicsplasma nonlinear phenomenaplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 85 , Issue 6 , December 2019 , 905850610
Copyright
© Cambridge University Press 2019 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abbasi, H., Jenab, M. H. & Pajouh, H. H. 2011 Preventing the recurrence effect in the Vlasov simulation by randomizing phase-point velocities in phase space. Phys. Rev. E 84 (3), 036702.Google Scholar
Abdi, A. & Hosseini, S. M. 2008 An investigation of resolution of 2-variate Gibbs phenomenon. Appl. Math. Comput. 203 (2), 714–732.Google Scholar
Adcock, B., Hansen, A. C. & Shadrin, A. 2014 A stability barrier for reconstructions from Fourier samples. SIAM J. Numer. Anal. 52 (1), 125–139.Google Scholar
Bateman, H. 1954 Tables of Integral Transforms, vol. 1. McGraw-Hill Book Company, Inc.Google Scholar
Black, C., Germaschewski, K., Bhattacharjee, A. & Ng, C. S. 2013 Discrete kinetic eigenmode spectra of electron plasma oscillations in weakly collisional plasma: a numerical study. Phys. Plasmas 20 (1), 012125.Google Scholar
Briand, C., Mangeney, A. & Califano, F. 2007 Electrostatic coherent structures generation by local heating in a collisionless plasma. Phys. Lett. A 368 (1–2), 82–86.Google Scholar
Briand, C., Mangeney, A. & Califano, F. 2008 Coherent electric structures: Vlasov–Ampere simulations and observational consequences. J. Geophys. Res. 113 (A7), 07219.Google Scholar
Buchner, J. & Elkina, N. 2006 Anomalous resistivity of current-driven isothermal plasmas due to phase space structuring. Phys. Plasmas 13 (8), 082304.Google Scholar
Califano, F. & Lontano, M. 2005 Electron hole generation and propagation in an inhomogeneous collisionless plasma. Phys. Rev. Lett. 95 (24), 082102.Google Scholar
Cheng, C. Z. & Knorr, G. 1976 Integration of Vlasov equation in configuration space. J. Comput. Phys. 22 (3), 330–351.Google Scholar
Daughton, W., Scudder, J. & Karimabadi, H. 2006 Fully kinetic simulations of undriven magnetic reconnection with open boundary conditions. Phys. Plasmas 13 (072101), 072101.Google Scholar
Einkemmer, L. & Ostermann, A. 2014 A strategy to suppress recurrence in grid-based Vlasov solvers. Eur. Phys. J. D 68 (7), 197.Google Scholar
Eliasson, B. 2001 Outflow boundary conditions for the Fourier tranformed one-dimensional Vlasov–Poisson system. J. Sci. Comput. 61 (1), 1–28.Google Scholar
Eliasson, B. 2002 Outflow boundary conditions for the Fourier transformed two-dimensional Vlasov equation. J. Comput. Phys. 181 (1), 98–125.Google Scholar
Eliasson, B. 2003 Numerical modelling of the two-dimensional Fourier transformed Vlasov–Maxwell system. J. Comput. Phys. 190 (2), 501–522.Google Scholar
Eliasson, B. 2007 Outflow boundary conditions for the Fourier transformed three-dimensional Vlasov–Maxwell system. J. Comput. Phys. 225 (2), 1508–1532.Google Scholar
Figua, H., Bouchut, F., Feix, M. R. & Fijalkow, E. 2000 Instability of the filtering method for Vlasov’s equation. J. Comput. Phys. 159 (2), 440–447.Google Scholar
Fijalkow, E. 1999 A numerical solution to the Vlasov equation. Comput. Phys. Commun. 116 (2–3), 319–328.Google Scholar
Filbet, F., Sonnendrucker, E. & Bertrand, P. 2001 Conservative numerical schemes for the Vlasov equation. J. Comput. Phys. 172 (1), 166–187.Google Scholar
Gelb, A. & Tanner, J. 2006 Robust reprojection methods for the resolution of the Gibbs phenomenon. Appl. Comput. Harmon. Anal. 20 (1), 3–25.Google Scholar
Ghizzo, A. & Del Sarto, D. 2014 Nonlinear nature of kinetic undamped waves induced by electrostatic turbulence in stimulated Raman backscattering. Eur. Phys. J. D 68 (10), 275.Google Scholar
Gottlieb, D. & Shu, C. W. 1997 On the Gibbs phenomenon and its resolution. SIAM Rev. 39 (4), 644–668.Google Scholar
Gottlieb, D., Shu, C. W., Solomonoff, A. & Vandeven, H. 1992 On the Gibb’s phenomenon. 1. Recovering exponential accuracy from the Fourier partial sum of a nonperiodic analytic function. J. Comput. Appl. Maths 43 (1–2), 81–98.Google Scholar
Grant, F. C. & Feix, M. R. 1967a Fourier-Hermite solutions of Vlasov equations in linearized limit. Phys. Fluids 10 (4), 696–702.Google Scholar
Grant, F. C. & Feix, M. R. 1967b Transition between Landau and Van Kampen treatments of Vlasov equation. Phys. Fluids 10 (6), 1356.Google Scholar
Ishizawa, A., Horiuchi, R. & Ohtani, H. 2004 Two-scale structure of the current layer controlled by meandering motion during steady-state collisionless driven reconnection. Phys. Plasmas 11 (7), 3579–3585.Google Scholar
Joyce, G., Knorr, G. & Meier, H. K. 1971 Numerical integration methods of Vlasov Equation. J. Comput. Phys. 8 (1), 53–63.Google Scholar
Jung, J. H. & Shizgal, B. D. 2004 Generalization of the inverse polynomial reconstruction method in the resolution of the Gibbs phenomenon. J. Comput. Appl. Maths 172 (1), 131–151.Google Scholar
Jung, J. H. & Shizgal, B. D. 2005 Inverse polynomial reconstruction of two dimensional Fourier images. J. Sci. Comput. 25 (3), 367–399.Google Scholar
Jung, J. H. & Shizgal, B. D. 2007 On the numerical convergence with the inverse polynomial reconstruction method for the resolution of the Gibbs phenomenon. J. Comput. Phys. 224 (2), 477–488.Google Scholar
Juno, J., Hakim, A., Tenbarge, J., Shi, E. & Dorland, W. 2018 Discontinuous Galerkin algorithms for fully kinetic plasmas. J. Comput. Phys. 353, 110–147.Google Scholar
Karimabadi, H., Daughton, W. & Scudder, J. 2007 Multi-scale structure of the electron diffusion region. Geophys. Res. Lett. 34, L13104.Google Scholar
Klimas, A. 1979 Approximation method for electrostatic Vlasov turbulence. J. Math. Phys. 20 (10), 2131–2138.Google Scholar
Klimas, A. 1987 A method for overcoming the velocity space filamentation problem in collisionless plasma model solutions. J. Comput. Phys. 68 (1), 202–226.Google Scholar
Klimas, A. & Cooper, J. 1983 Vlasov–Maxwell and Vlasov–Poisson equations as models of a one-dimensional electron plasma. Phys. Fluids 26 (2), 478–479.Google Scholar
Klimas, A. & Farrell, W. M. 1994 A splitting algorithm for Vlasov simulation with filamentation filtration. J. Comput. Phys. 110 (1), 150–163.Google Scholar
Klimas, A. & Viñas, A. F. 2018 Absence of recurrence in Fourier–Fourier transformed Vlasov–Poisson simulations. J. Plasma Phys. 905840405.Google Scholar
Klimas, A., Hesse, M. & Zenitani, S. 2008 Particle-in-cell simulation of collisionless reconnection with open outflow boundaries. Phys. Plasmas 15, 082102.Google Scholar
Knorr, G. 1973 Plasma simulation with few particles. J. Comput. Phys. 13 (2), 165–180.Google Scholar
Newman, D. L., Sen, N. & Goldman, M. V. 2007 Reduced multidimensional Vlasov simulations, with applications to electrostatic structures in space plasmas. Phys. Plasmas 14 (5), 055907.Google Scholar
Ohtani, H. & Horiuchi, R. 2009 Open boundary condition for particle simulation in magnetic reconnection research. Plasma Fusion Res. 4 (024), 024.Google Scholar
Pezzi, O., Camporeale, E. & Valentini, F. 2016 Collisional effects on the numerical recurrence in Vlasov–Poisson simulations. Phys. Plasmas 23 (2), 022103.Google Scholar
Pusztai, I., Tenbarge, J. M., Csapo, A. N., Juno, J., Hakim, A., Yi, L. & Fulop, T. 2018 Low Mach-number collisionless electrostatic shocks and associated ion acceleration. Plasma Phys. Control. Fusion 60 (3), 035004.Google Scholar
Shizgal, B. D. & Jung, J. H. 2003 Towards the resolution of the Gibbs phenomena. J. Comput. Appl. Maths 161 (1), 41–65.Google Scholar
Umeda, T. 2007 Vlasov simulation of Langmuir wave packets. Nonlinear Process. Geophys. 14 (5), 671–679.Google Scholar
Viñas, A. F. & Klimas, A. 2018 Flux-balance Vlasov simulation with filamentation filtration. J. Comput. Phys. 375, 983–1004.Google Scholar
Supplementary material: File

Klimas and Viñas supplementary material

Klimas and Viñas supplementary material

Download Klimas and Viñas supplementary material(File)
File 64.5 MB