### Abstract

We formulate and test a hybrid fluid-Monte Carlo scheme for the treatment of elastic collisions in gases and plasmas. While our primary focus and demonstrations of applicability are for moderately collisional plasmas, as described by the Landau-Fokker-Planck equation, the method is expected to be applicable also to collision processes described by the Boltzmann equation. This scheme is similar to the previously discussed velocity-based scheme (R. Caflisch, et al., (2008) [7]) and the scattering-angle-based scheme (A.M. Dimits, et al., (2010) [14])], but with a firmer theoretical basis and without the inherent limitation to the Landau-Fokker-Planck case. It gives a significant performance improvement (e.g., error for a given computational effort) over the velocity-based scheme. These features are achieved by assigning passive scalars to each simulated particle and tracking their evolution through collisions. The method permits a formal error analysis that agrees with numerical results. The tests performed are for the evolution of an anisotropic Maxwellian and a bump-on-tail distribution.

Original language | English (US) |
---|---|

Pages (from-to) | 77-99 |

Number of pages | 23 |

Journal | Journal of Computational Physics |

Volume | 273 |

DOIs | |

State | Published - Sep 15 2014 |

### Fingerprint

### Keywords

- Coulomb collisions
- Entropy
- Hybrid
- Monte Carlo
- Particle collisions
- Plasma

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy (miscellaneous)

### Cite this

*Journal of Computational Physics*,

*273*, 77-99. https://doi.org/10.1016/j.jcp.2014.04.059

**An entropy based thermalization scheme for hybrid simulations of Coulomb collisions.** / Ricketson, L. F.; Rosin, M. S.; Caflisch, Russel; Dimits, A. M.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 273, pp. 77-99. https://doi.org/10.1016/j.jcp.2014.04.059

}

TY - JOUR

T1 - An entropy based thermalization scheme for hybrid simulations of Coulomb collisions

AU - Ricketson, L. F.

AU - Rosin, M. S.

AU - Caflisch, Russel

AU - Dimits, A. M.

PY - 2014/9/15

Y1 - 2014/9/15

N2 - We formulate and test a hybrid fluid-Monte Carlo scheme for the treatment of elastic collisions in gases and plasmas. While our primary focus and demonstrations of applicability are for moderately collisional plasmas, as described by the Landau-Fokker-Planck equation, the method is expected to be applicable also to collision processes described by the Boltzmann equation. This scheme is similar to the previously discussed velocity-based scheme (R. Caflisch, et al., (2008) [7]) and the scattering-angle-based scheme (A.M. Dimits, et al., (2010) [14])], but with a firmer theoretical basis and without the inherent limitation to the Landau-Fokker-Planck case. It gives a significant performance improvement (e.g., error for a given computational effort) over the velocity-based scheme. These features are achieved by assigning passive scalars to each simulated particle and tracking their evolution through collisions. The method permits a formal error analysis that agrees with numerical results. The tests performed are for the evolution of an anisotropic Maxwellian and a bump-on-tail distribution.

AB - We formulate and test a hybrid fluid-Monte Carlo scheme for the treatment of elastic collisions in gases and plasmas. While our primary focus and demonstrations of applicability are for moderately collisional plasmas, as described by the Landau-Fokker-Planck equation, the method is expected to be applicable also to collision processes described by the Boltzmann equation. This scheme is similar to the previously discussed velocity-based scheme (R. Caflisch, et al., (2008) [7]) and the scattering-angle-based scheme (A.M. Dimits, et al., (2010) [14])], but with a firmer theoretical basis and without the inherent limitation to the Landau-Fokker-Planck case. It gives a significant performance improvement (e.g., error for a given computational effort) over the velocity-based scheme. These features are achieved by assigning passive scalars to each simulated particle and tracking their evolution through collisions. The method permits a formal error analysis that agrees with numerical results. The tests performed are for the evolution of an anisotropic Maxwellian and a bump-on-tail distribution.

KW - Coulomb collisions

KW - Entropy

KW - Hybrid

KW - Monte Carlo

KW - Particle collisions

KW - Plasma

UR - http://www.scopus.com/inward/record.url?scp=84901361182&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84901361182&partnerID=8YFLogxK

U2 - 10.1016/j.jcp.2014.04.059

DO - 10.1016/j.jcp.2014.04.059

M3 - Article

AN - SCOPUS:84901361182

VL - 273

SP - 77

EP - 99

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -