On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods
We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allow...
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| Published in: | Computer physics communications Vol. 198; no. C; pp. 47 - 58 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01-01-2016
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| Abstract | We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier–Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC. |
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| AbstractList | We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier–Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC. We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and the configuration space is discretized via a Fourier decomposition. The novelty of our approach is an implicit time discretization that allows exact conservation of charge, momentum and energy. The computational efficiency and the cost-effectiveness of this method are compared to the fully-implicit PIC method recently introduced by Markidis and Lapenta (2011) and Chen et al. (2011). The following examples are discussed: Langmuir wave, Landau damping, ion-acoustic wave, two-stream instability. The Fourier-Hermite spectral method can achieve solutions that are several orders of magnitude more accurate at a fraction of the cost with respect to PIC. |
| Author | Camporeale, E. Moulton, J.D. Delzanno, G.L. Bergen, B.K. |
| Author_xml | – sequence: 1 givenname: E. orcidid: 0000-0002-7862-6383 surname: Camporeale fullname: Camporeale, E. email: e.camporeale@cwi.nl organization: Center for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands – sequence: 2 givenname: G.L. surname: Delzanno fullname: Delzanno, G.L. organization: T-5 Applied Mathematics and Plasma Physics, Los Alamos National Laboratory, 87545 Los Alamos, NM, USA – sequence: 3 givenname: B.K. surname: Bergen fullname: Bergen, B.K. organization: CCS-7 Applied Computer Science, Los Alamos National Laboratory, 87545 Los Alamos, NM, USA – sequence: 4 givenname: J.D. surname: Moulton fullname: Moulton, J.D. organization: T-5 Applied Mathematics and Plasma Physics, Los Alamos National Laboratory, 87545 Los Alamos, NM, USA |
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| Snippet | We describe a spectral method for the numerical solution of the Vlasov–Poisson system where the velocity space is decomposed by means of an Hermite basis, and... We describe a spectral method for the numerical solution of the Vlasov-Poisson system where the velocity space is decomposed by means of an Hermite basis, and... |
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| SubjectTerms | Computational efficiency Decomposition Discretization Fourier analysis Mathematical models Multiscale simulations Particle in cell technique Plasma physics Spectra Spectral methods Vlasov equation |
| Title | On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods |
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