Conservative discretization of the Landau collision integral
Abstract
Here we describe a density, momentum, and energyconserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finiteelement and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finiteelement implementation.
 Authors:
 Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC21)
 OSTI Identifier:
 1379746
 Alternate Identifier(s):
 OSTI ID: 1373960
 Grant/Contract Number:
 AC0205CH11231; AC0209CH11466
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 24; Journal Issue: 3; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; Tensor methods; Polynomials; Galerkin methods; Plasma collisions; Conservation of momentum
Citation Formats
Hirvijoki, E., and Adams, M. F.. Conservative discretization of the Landau collision integral. United States: N. p., 2017.
Web. doi:10.1063/1.4979122.
Hirvijoki, E., & Adams, M. F.. Conservative discretization of the Landau collision integral. United States. doi:10.1063/1.4979122.
Hirvijoki, E., and Adams, M. F.. Tue .
"Conservative discretization of the Landau collision integral". United States.
doi:10.1063/1.4979122. https://www.osti.gov/servlets/purl/1379746.
@article{osti_1379746,
title = {Conservative discretization of the Landau collision integral},
author = {Hirvijoki, E. and Adams, M. F.},
abstractNote = {Here we describe a density, momentum, and energyconserving discretization of the nonlinear Landau collision integral. The method is suitable for both the finiteelement and discontinuous Galerkin methods and does not require structured meshes. The conservation laws for the discretization are proven algebraically and demonstrated numerically for an axially symmetric nonlinear relaxation problem using a finiteelement implementation.},
doi = {10.1063/1.4979122},
journal = {Physics of Plasmas},
number = 3,
volume = 24,
place = {United States},
year = {Tue Mar 28 00:00:00 EDT 2017},
month = {Tue Mar 28 00:00:00 EDT 2017}
}
Other availability
Cited by: 2works
Citation information provided by
Web of Science
Web of Science
Save to My Library
You must Sign In or Create an Account in order to save documents to your library.

Expansion of the Boltzmann collision integral in a Landau series
The problem of expansion of the Boltzmann collision integral for arbitrary interaction potential is considered in the form of a power series in the momentum transferred in a collision. Such a series is termed a Landau series. An exact (without divergence) expansion of the collision integral in a Landau series is performed, the explicit form of the general term of this series is found, and its properties analyzed. (JFP) 
Fast algorithms for numerical, conservative, and entropy approximations of the FokkerPlanckLandau equation
We present fast numerical algorithms to solve the nonlinear FokkerPlanckLandau equation in 3D velocity space. The discretization of the collision operator preserves the properties required by the physical nature of the FokkerPlanckLandau equation, such as the conservation of mass, momentum, and energy, the decay of the entropy, and the fact that the steady states are Maxwellians. At the end of this paper, we give numerical results illustrating the efficiency of these fast algorithms in terms of accuracy and CPU time. 20 refs., 7 figs. 
Discretization of the inducedcharge boundary integral equation.
Boundaryelement methods (BEMs) for solving integral equations numerically have been used in many fields to compute the induced charges at dielectric boundaries. In this paper, we consider a more accurate implementation of BEM in the context of ions in aqueous solution near proteins, but our results are applicable more generally. The ions that modulate protein function are often within a few angstroms of the protein, which leads to the significant accumulation of polarization charge at the proteinsolvent interface. Computing the induced charge accurately and quickly poses a numerical challenge in solving a popular integral equation using BEM. In particular, themore »