An equilibrium-preserving discretization for the nonlinear Rosenbluth–Fokker–Planck operator in arbitrary multi-dimensional geometry
Abstract
Here, the Fokker–Planck collision operator is an advection-diffusion operator which describe dynamical systems such as weakly coupled plasmas, photonics in high temperature environment biological, and even social systems. For plasmas in the continuum, the Fokker–Planck collision operator supports such important physical properties as conservation of number, momentum, and energy, as well as positivity. It also obeys the Boltzmann's H-theorem, i.e., the operator increases the system entropy while simultaneously driving the distribution function towards a Maxwellian. In the discrete, when these properties are not ensured, numerical simulations can either fail catastrophically or suffer from significant numerical pollution. There is strong emphasis in the literature on developing numerical techniques to solve the Fokker–Planck equation while preserving these properties. In this short note, we focus on the analytical equilibrium preserving property, meaning that the Fokker–Planck collision operator vanishes when acting on an analytical Maxwellian distribution function. The equilibrium preservation property is especially important, for example, when one is attempting to capture subtle transport physics. Since transport arises from small Ο(ϵ) corrections to the equilibrium (where ϵ is a small expansion parameter), numerical truncation error present in the equilibrium solution may dominate, overwhelming transport dynamics.
- Publication Date:
- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1460628
- Alternate Identifier(s):
- OSTI ID: 1396735
- Report Number(s):
- LA-UR-16-28802
Journal ID: ISSN 0021-9991; TRN: US1901882
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Journal of Computational Physics
- Additional Journal Information:
- Journal Volume: 339; Journal Issue: C; Journal ID: ISSN 0021-9991
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics; Conservative discretization; Exact analytical equilibrium preserving; Multiple dimensions; Fokker–Planck; Rosenbluth potentials
Citation Formats
Taitano, William T., Chacon, Luis, and Simakov, Andrei Nikolaevich. An equilibrium-preserving discretization for the nonlinear Rosenbluth–Fokker–Planck operator in arbitrary multi-dimensional geometry. United States: N. p., 2017.
Web. doi:10.1016/j.jcp.2017.03.032.
Taitano, William T., Chacon, Luis, & Simakov, Andrei Nikolaevich. An equilibrium-preserving discretization for the nonlinear Rosenbluth–Fokker–Planck operator in arbitrary multi-dimensional geometry. United States. https://doi.org/10.1016/j.jcp.2017.03.032
Taitano, William T., Chacon, Luis, and Simakov, Andrei Nikolaevich. Thu .
"An equilibrium-preserving discretization for the nonlinear Rosenbluth–Fokker–Planck operator in arbitrary multi-dimensional geometry". United States. https://doi.org/10.1016/j.jcp.2017.03.032. https://www.osti.gov/servlets/purl/1460628.
@article{osti_1460628,
title = {An equilibrium-preserving discretization for the nonlinear Rosenbluth–Fokker–Planck operator in arbitrary multi-dimensional geometry},
author = {Taitano, William T. and Chacon, Luis and Simakov, Andrei Nikolaevich},
abstractNote = {Here, the Fokker–Planck collision operator is an advection-diffusion operator which describe dynamical systems such as weakly coupled plasmas, photonics in high temperature environment biological, and even social systems. For plasmas in the continuum, the Fokker–Planck collision operator supports such important physical properties as conservation of number, momentum, and energy, as well as positivity. It also obeys the Boltzmann's H-theorem, i.e., the operator increases the system entropy while simultaneously driving the distribution function towards a Maxwellian. In the discrete, when these properties are not ensured, numerical simulations can either fail catastrophically or suffer from significant numerical pollution. There is strong emphasis in the literature on developing numerical techniques to solve the Fokker–Planck equation while preserving these properties. In this short note, we focus on the analytical equilibrium preserving property, meaning that the Fokker–Planck collision operator vanishes when acting on an analytical Maxwellian distribution function. The equilibrium preservation property is especially important, for example, when one is attempting to capture subtle transport physics. Since transport arises from small Ο(ϵ) corrections to the equilibrium (where ϵ is a small expansion parameter), numerical truncation error present in the equilibrium solution may dominate, overwhelming transport dynamics.},
doi = {10.1016/j.jcp.2017.03.032},
journal = {Journal of Computational Physics},
number = C,
volume = 339,
place = {United States},
year = {Thu Apr 06 00:00:00 EDT 2017},
month = {Thu Apr 06 00:00:00 EDT 2017}
}
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Works referencing / citing this record:
Diffusion-driven fluid dynamics in ideal gases and plasmas
journal, June 2018
- Vold, E. L.; Yin, L.; Taitano, W.
- Physics of Plasmas, Vol. 25, Issue 6
Kinetic physics in ICF: present understanding and future directions
journal, April 2018
- Rinderknecht, Hans G.; Amendt, P. A.; Wilks, S. C.
- Plasma Physics and Controlled Fusion, Vol. 60, Issue 6
Yield degradation in inertial-confinement-fusion implosions due to shock-driven kinetic fuel-species stratification and viscous heating
journal, May 2018
- Taitano, W. T.; Simakov, A. N.; Chacón, L.
- Physics of Plasmas, Vol. 25, Issue 5
Ion species stratification within strong shocks in two-ion plasmas
journal, March 2018
- Keenan, Brett D.; Simakov, Andrei N.; Taitano, William T.
- Physics of Plasmas, Vol. 25, Issue 3
Conservative discrete-velocity method for the ellipsoidal Fokker-Planck equation in gas-kinetic theory
journal, September 2019
- Liu, Sha; Yuan, Ruifeng; Javid, Usman
- Physical Review E, Vol. 100, Issue 3
Plasma ion stratification by weak planar shocks
journal, September 2017
- Simakov, Andrei N.; Keenan, Brett D.; Taitano, William T.
- Physics of Plasmas, Vol. 24, Issue 9
Deciphering the Kinetic Structure of Multi-Ion Plasma Shocks
text, January 2017
- Keenan, Brett D.; Simakov, Andrei N.; Chacon, Luis
- arXiv
Ion Species Stratification Within Strong Shocks in Two-Ion Plasmas
text, January 2017
- Keenan, Brett D.; Simakov, Andrei N.; Taitano, William T.
- arXiv