An equilibrium-preserving discretization for the nonlinear Rosenbluth–Fokker–Planck operator in arbitrary multi-dimensional geometry

Journal Article · Thu Apr 06 00:00:00 EDT 2017 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2017.03.032· OSTI ID:1460628

Taitano, William T.  ^[1]; Chacon, Luis  ^[1]; Simakov, Andrei Nikolaevich  ^[1]

---

1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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.

• Research Organization: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1460628
• Alternate ID(s): OSTI ID: 1396735
• Report Number(s): LA-UR-16-28802; TRN: US1901882
• Journal Information: Journal of Computational Physics, Vol. 339, Issue C; ISSN 0021-9991
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Mathematics
Conservative discretization
Exact analytical equilibrium preserving
Multiple dimensions
Fokker–Planck
Rosenbluth potentials