Title: Conservative discontinuous Galerkin schemes for nonlinear Dougherty–Fokker–Planck collision operators

Abstract

Here, we present a novel discontinuous Galerkin algorithm for the solution of a class of Fokker–Planck collision operators. These operators arise in many fields of physics, and our particular application is for kinetic plasma simulations. In particular, we focus on an operator often known as the ‘Lenard–Bernstein’ or ‘Dougherty’ operator. Several novel algorithmic innovations, based on the concept of weak equality, are reported. These weak equalities are used to define weak operators that compute primitive moments, and are also used to determine a reconstruction procedure that allows an efficient and accurate discretization of the diffusion term. We show that when two integrations by parts are used to construct the discrete weak form, and finite velocity-space extents are accounted for, a scheme that conserves density, momentum and energy exactly is obtained. One novel feature is that the requirements of momentum and energy conservation lead to unique formulas to compute primitive moments. Careful definition of discretized moments also ensure that energy is conserved in the piecewise linear case, even though the kinetic-energy term, $v^2$ is not included in the basis set used in the discretization. A series of benchmark problems is presented and shows that the scheme conserves momentum and energy tomore » machine precision. Empirical evidence also indicates that entropy is a non-decreasing function. The collision terms are combined with the Vlasov equation to study collisional Landau damping and plasma heating via magnetic pumping.« less

Authors:

Hakim, Ammar  ^[1];

• Search DOE PAGES for author "Hakim, Ammar"
• Search DOE PAGES for ORCID "0000-0001-6603-8595"

Francisquez, Manaure  ^[2];

• Search DOE PAGES for author "Francisquez, Manaure"
• Search DOE PAGES for ORCID "0000-0002-8247-3770"

Juno, James  ^[3];

• Search DOE PAGES for author "Juno, James"
• Search DOE PAGES for ORCID "0000-0001-6835-273X"

Hammett, Gregory W. ^[1]

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+ Show Author Affiliations

1. Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center; Dartmouth College, Hanover, NH (United States)
3. Univ. of Maryland, College Park, MD (United States)

Publication Date:

Fri Jul 17 00:00:00 EDT 2020

Research Org.:

Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Org.:

USDOE Office of Science (SC); US Air Force Office of Scientific Research (AFOSR); National Aeronautics and Space Administration (NASA); National Science Foundation (NSF)

OSTI Identifier:

1668773

Grant/Contract Number:  

AC02-06CH11357; FG02-91-ER54109; AC02-09CH11466; SC-0010508; FC02-08ER54966; 80NSSC17K0428; ACI-1548562; FA9550-15-1-0193

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Plasma Physics

Additional Journal Information:

Journal Volume: 86; Journal Issue: 4; Journal ID: ISSN 0022-3778

Publisher:

Cambridge University Press

Country of Publication:

United States

Language:

English

Subject:

70 PLASMA PHYSICS AND FUSION TECHNOLOGY; plasma dynamics; plasma nonlinear phenomena; plasma simulation