Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space
Abstract
We propose a spectral method for the 1D-1V Vlasov–Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling α and shifting u of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of α and u based on the numerical solution of the discrete Vlasov–Poisson system obtained at that time step. Once the new values of the Hermite parameters α and u are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update α and u based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion aremore »
- Authors:
-
- Eindhoven University of Technology (Netherlands)
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- KTH Royal Institute of Technology, Stockholm (Sweden)
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1983856
- Report Number(s):
- LA-UR-22-28459
Journal ID: ISSN 0021-9991; TRN: US2402999
- Grant/Contract Number:
- 89233218CNA000001
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 488; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; Vlasov–Poisson equations; spectral method; AW Hermite discretization; adaptive coefficients
Citation Formats
Pagliantini, Cecilia, Delzanno, Gian Luca, and Markidis, Stefano. Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space. United States: N. p., 2023.
Web. doi:10.1016/j.jcp.2023.112252.
Pagliantini, Cecilia, Delzanno, Gian Luca, & Markidis, Stefano. Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space. United States. https://doi.org/10.1016/j.jcp.2023.112252
Pagliantini, Cecilia, Delzanno, Gian Luca, and Markidis, Stefano. Tue .
"Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space". United States. https://doi.org/10.1016/j.jcp.2023.112252. https://www.osti.gov/servlets/purl/1983856.
@article{osti_1983856,
title = {Physics-based adaptivity of a spectral method for the Vlasov–Poisson equations based on the asymmetrically-weighted Hermite expansion in velocity space},
author = {Pagliantini, Cecilia and Delzanno, Gian Luca and Markidis, Stefano},
abstractNote = {We propose a spectral method for the 1D-1V Vlasov–Poisson system where the discretization in velocity space is based on asymmetrically-weighted Hermite functions, dynamically adapted via a scaling α and shifting u of the velocity variable. Specifically, at each time instant an adaptivity criterion selects new values of α and u based on the numerical solution of the discrete Vlasov–Poisson system obtained at that time step. Once the new values of the Hermite parameters α and u are fixed, the Hermite expansion is updated and the discrete system is further evolved for the next time step. The procedure is applied iteratively over the desired temporal interval. The key aspects of the adaptive algorithm are: the map between approximation spaces associated with different values of the Hermite parameters that preserves total mass, momentum and energy; and the adaptivity criterion to update α and u based on physics considerations relating the Hermite parameters to the average velocity and temperature of each plasma species. For the discretization of the spatial coordinate, we rely on Fourier functions and use the implicit midpoint rule for time stepping. The resulting numerical method possesses intrinsically the property of fluid-kinetic coupling, where the low-order terms of the expansion are akin to the fluid moments of a macroscopic description of the plasma, while kinetic physics is retained by adding more spectral terms. Moreover, the scheme features conservation of total mass, momentum and energy associated in the discrete, for periodic boundary conditions. A set of numerical experiments confirms that the adaptive method outperforms the non-adaptive one in terms of accuracy and stability of the numerical solution.},
doi = {10.1016/j.jcp.2023.112252},
journal = {Journal of Computational Physics},
number = ,
volume = 488,
place = {United States},
year = {Tue Jun 06 00:00:00 EDT 2023},
month = {Tue Jun 06 00:00:00 EDT 2023}
}
Figures / Tables:
Works referenced in this record:
A Decision-Making Machine Learning Approach in Hermite Spectral Approximations of Partial Differential Equations
journal, May 2022
- Fatone, L.; Funaro, D.; Manzini, G.
- Journal of Scientific Computing, Vol. 92, Issue 1
On the velocity space discretization for the Vlasov–Poisson system: Comparison between implicit Hermite spectral and Particle-in-Cell methods
journal, January 2016
- Camporeale, E.; Delzanno, G. L.; Bergen, B. K.
- Computer Physics Communications, Vol. 198
Convergence of Spectral Discretizations of the Vlasov--Poisson System
journal, January 2017
- Manzini, G.; Funaro, D.; Delzanno, G. L.
- SIAM Journal on Numerical Analysis, Vol. 55, Issue 5
Vlasov Simulations Using Velocity-Scaled Hermite Representations
journal, August 1998
- Schumer, Joseph W.; Holloway, James Paul
- Journal of Computational Physics, Vol. 144, Issue 2
Suppression of Recurrence in the Hermite-Spectral Method for Transport Equations
journal, January 2018
- Cai, Zhenning; Wang, Yanli
- SIAM Journal on Numerical Analysis, Vol. 56, Issue 5
Multi-dimensional, fully-implicit, spectral method for the Vlasov–Maxwell equations with exact conservation laws in discrete form
journal, November 2015
- Delzanno, G. L.
- Journal of Computational Physics, Vol. 301
Numerical integration methods of the Vlasov equation
journal, August 1971
- Joyce, Glenn; Knorr, Georg; Meier, Homer K.
- Journal of Computational Physics, Vol. 8, Issue 1
Arbitrary-order time-accurate semi-Lagrangian spectral approximations of the Vlasov–Poisson system
journal, May 2019
- Fatone, L.; Funaro, D.; Manzini, G.
- Journal of Computational Physics, Vol. 384
High‐Frequency Plasma Waves and Pitch Angle Scattering Induced by Pulsed Electron Beams
journal, September 2019
- Delzanno, G. L.; Roytershteyn, V.
- Journal of Geophysical Research: Space Physics, Vol. 124, Issue 9
New approach for the study of linear Vlasov stability of inhomogeneous systems
journal, September 2006
- Camporeale, Enrico; Delzanno, Gian Luca; Lapenta, Giovanni
- Physics of Plasmas, Vol. 13, Issue 9
A numerical method based on the Fourier-Fourier transform approach for modeling 1-D electron plasma evolution
journal, May 1983
- Klimas, Alexander J.
- Journal of Computational Physics, Vol. 50, Issue 2
On Stable Wall Boundary Conditions for the Hermite Discretization of the Linearised Boltzmann Equation
journal, November 2017
- Sarna, Neeraj; Torrilhon, Manuel
- Journal of Statistical Physics, Vol. 170, Issue 1
Note onN-dimensional hermite polynomials
journal, December 1949
- Grad, Harold
- Communications on Pure and Applied Mathematics, Vol. 2, Issue 4
On the kinetic theory of rarefied gases
journal, December 1949
- Grad, Harold
- Communications on Pure and Applied Mathematics, Vol. 2, Issue 4
Locally refined discrete velocity grids for stationary rarefied flow simulations
journal, January 2014
- Baranger, C.; Claudel, J.; Hérouard, N.
- Journal of Computational Physics, Vol. 257
A rescaling velocity method for dissipative kinetic equations. Applications to granular media
journal, September 2013
- Filbet, Francis; Rey, Thomas
- Journal of Computational Physics, Vol. 248
The recurrence of the initial state in the numerical solution of the Vlasov equation
journal, May 1974
- Canosa, José; Gazdag, Jenö; Fromm, J. E.
- Journal of Computational Physics, Vol. 15, Issue 1
Fourier–Hermite spectral representation for the Vlasov–Poisson system in the weakly collisional limit
journal, February 2015
- Parker, Joseph T.; Dellar, Paul J.
- Journal of Plasma Physics, Vol. 81, Issue 2
A Legendre–Fourier spectral method with exact conservation laws for the Vlasov–Poisson system
journal, July 2016
- Manzini, G.; Delzanno, G. L.; Vencels, J.
- Journal of Computational Physics, Vol. 317
On the convergence of the Fourier-Hermite transformation method for the Vlasov equation with an artificial collision term
journal, December 1977
- Gajewski, Herbert; Zacharias, Klaus
- Journal of Mathematical Analysis and Applications, Vol. 61, Issue 3
Filtered Hyperbolic Moment Method for the Vlasov Equation
journal, December 2018
- Di, Yana; Fan, Yuwei; Kou, Zhenzhong
- Journal of Scientific Computing, Vol. 79, Issue 2
Fourier–Hermite decomposition of the collisional Vlasov–Maxwell system: implications for the velocity-space cascade
journal, March 2019
- Pezzi, O.; Valentini, F.; Servidio, S.
- Plasma Physics and Controlled Fusion, Vol. 61, Issue 5
Electron Acceleration in the Heart of the Van Allen Radiation Belts
journal, July 2013
- Reeves, G. D.; Spence, H. E.; Henderson, M. G.
- Science, Vol. 341, Issue 6149
On the stability of conservative discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system
journal, February 2022
- Bessemoulin-Chatard, Marianne; Filbet, Francis
- Journal of Computational Physics, Vol. 451
Spectral velocity discretizations for the Vlasov-Maxwell equations
journal, January 1996
- Holloway, James Paul
- Transport Theory and Statistical Physics, Vol. 25, Issue 1
The integration of the vlasov equation in configuration space
journal, November 1976
- Cheng, C. Z.; Knorr, Georg
- Journal of Computational Physics, Vol. 22, Issue 3
Conservative Discontinuous Galerkin/Hermite Spectral Method for the Vlasov–Poisson System
journal, September 2020
- Filbet, Francis; Xiong, Tao
- Communications on Applied Mathematics and Computation, Vol. 4, Issue 1
Viriato : A Fourier–Hermite spectral code for strongly magnetized fluid–kinetic plasma dynamics
journal, September 2016
- Loureiro, N. F.; Dorland, W.; Fazendeiro, L.
- Computer Physics Communications, Vol. 206
Plasma Oscillations with Diffusion in Velocity Space
journal, December 1958
- Lenard, A.; Bernstein, Ira B.
- Physical Review, Vol. 112, Issue 5
Nonlinear Effects from Vlasov's Equation
journal, January 1963
- Engelmann, F.; Feix, M.; Minardi, E.
- Physics of Fluids, Vol. 6, Issue 2
A generalized Fourier–Hermite method for the Vlasov–Poisson system
journal, April 2021
- Kormann, Katharina; Yurova, Anna
- BIT Numerical Mathematics, Vol. 61, Issue 3
Solving Vlasov Equations Using NR$xx$ Method
journal, January 2013
- Cai, Zhenning; Li, Ruo; Wang, Yanli
- SIAM Journal on Scientific Computing, Vol. 35, Issue 6
Numerical Study of Inertial Kinetic-Alfvén Turbulence
journal, January 2019
- Roytershteyn, Vadim; Boldyrev, Stanislav; Delzanno, Gian Luca
- The Astrophysical Journal, Vol. 870, Issue 2
Figures / Tables found in this record: