An adaptive, conservative 0D2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes
Abstract
In this paper, we propose an adaptive velocityspace discretization scheme for the multispecies, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass, momentum, and energyconserving. Unlike most earlier studies, our approach normalizes the velocityspace coordinate to the temporally varying individual plasma species' local thermal velocity, v_{th} (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic v_{th} ratiobased expansion of the Rosenbluth potentials that only requires the computation of several velocityspace integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocitygrid adaptivity and asymptotic expansions delivers many ordersofmagnitude savings in mesh resolution requirements compared to a single, static uniform mesh.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA)
 OSTI Identifier:
 1457268
 Alternate Identifier(s):
 OSTI ID: 1347623
 Report Number(s):
 LAUR1527477
Journal ID: ISSN 00219991; TRN: US1901341
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 318; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICS AND COMPUTING; Conservative discretization; thermal velocity based adaptive grid; FokkerPlanck; Rosenbluth potentials; asymptotics
Citation Formats
Taitano, William, Chacon, Luis, and Simakov, Andrei Nikolaevich. An adaptive, conservative 0D2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes. United States: N. p., 2016.
Web. doi:10.1016/j.jcp.2016.03.071.
Taitano, William, Chacon, Luis, & Simakov, Andrei Nikolaevich. An adaptive, conservative 0D2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes. United States. doi:10.1016/j.jcp.2016.03.071.
Taitano, William, Chacon, Luis, and Simakov, Andrei Nikolaevich. Mon .
"An adaptive, conservative 0D2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes". United States. doi:10.1016/j.jcp.2016.03.071. https://www.osti.gov/servlets/purl/1457268.
@article{osti_1457268,
title = {An adaptive, conservative 0D2V multispecies Rosenbluth–Fokker–Planck solver for arbitrarily disparate mass and temperature regimes},
author = {Taitano, William and Chacon, Luis and Simakov, Andrei Nikolaevich},
abstractNote = {In this paper, we propose an adaptive velocityspace discretization scheme for the multispecies, multidimensional Rosenbluth–Fokker–Planck (RFP) equation, which is exactly mass, momentum, and energyconserving. Unlike most earlier studies, our approach normalizes the velocityspace coordinate to the temporally varying individual plasma species' local thermal velocity, vth (t), and explicitly considers the resulting inertial terms in the Fokker–Planck equation. Our conservation strategy employs nonlinear constraints to enforce discretely the conservation properties of these inertial terms and the Fokker–Planck collision operator. To deal with situations of extreme thermal velocity disparities among different species, we employ an asymptotic vth ratiobased expansion of the Rosenbluth potentials that only requires the computation of several velocityspace integrals. Numerical examples demonstrate the favorable efficiency and accuracy properties of the scheme. Specifically, we show that the combined use of the velocitygrid adaptivity and asymptotic expansions delivers many ordersofmagnitude savings in mesh resolution requirements compared to a single, static uniform mesh.},
doi = {10.1016/j.jcp.2016.03.071},
journal = {Journal of Computational Physics},
number = C,
volume = 318,
place = {United States},
year = {2016},
month = {4}
}
Web of Science