Highorder discretization of a gyrokinetic Vlasov model in edge plasma geometry
Abstract
We describe a new spatial discretization of a continuum gyrokinetic Vlasov model in axisymmetric tokamak edge plasma geometries. The geometries are represented using a multiblock decomposition in which logically distinct blocks are smoothly mapped from rectangular computational domains and are aligned with magnetic flux surfaces to accommodate strong anisotropy induced by the magnetic field. We employ a fourthorder, finitevolume discretization in mapped coordinates to mitigate the computational expense associated with discretization on 4D phase space grids. Applied to a conservative formulation of the gyrokinetic system, a finitevolume approach expresses local conservation discretely in a natural manner involving the calculation of normal fluxes at cell faces. In the approach presented here, the normal fluxes are computed in terms of faceaveraged velocity normals in such a way that (i) the divergencefree property of the gyrokinetic velocity is preserved discretely to machine precision, (ii) the configuration space normal velocities are independent of mapping metrics, and (iii) the configuration space normal velocities are computed from exact pointwise evaluation of magnetic field data except for one term. The algorithms described in this paper form the foundation of a continuum gyrokinetic edge code named COGENT, which is used here to perform a convergence study verifying themore »
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Applied Numerical Algorithms Group
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Fusion Energy Program
 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:
 1526551
 DOE Contract Number:
 AC0205CH11231
 Resource Type:
 Journal Article
 Journal Name:
 Journal of Computational Physics
 Additional Journal Information:
 Journal Volume: 373; Journal Issue: C; Journal ID: ISSN 00219991
 Publisher:
 Elsevier
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Citation Formats
Dorr, Milo R., Colella, Phillip, Dorf, Mikhail A., Ghosh, Debojyoti, Hittinger, Jeffrey A. F., and Schwartz, Peter O. Highorder discretization of a gyrokinetic Vlasov model in edge plasma geometry. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.07.008.
Dorr, Milo R., Colella, Phillip, Dorf, Mikhail A., Ghosh, Debojyoti, Hittinger, Jeffrey A. F., & Schwartz, Peter O. Highorder discretization of a gyrokinetic Vlasov model in edge plasma geometry. United States. doi:10.1016/j.jcp.2018.07.008.
Dorr, Milo R., Colella, Phillip, Dorf, Mikhail A., Ghosh, Debojyoti, Hittinger, Jeffrey A. F., and Schwartz, Peter O. Thu .
"Highorder discretization of a gyrokinetic Vlasov model in edge plasma geometry". United States. doi:10.1016/j.jcp.2018.07.008.
@article{osti_1526551,
title = {Highorder discretization of a gyrokinetic Vlasov model in edge plasma geometry},
author = {Dorr, Milo R. and Colella, Phillip and Dorf, Mikhail A. and Ghosh, Debojyoti and Hittinger, Jeffrey A. F. and Schwartz, Peter O.},
abstractNote = {We describe a new spatial discretization of a continuum gyrokinetic Vlasov model in axisymmetric tokamak edge plasma geometries. The geometries are represented using a multiblock decomposition in which logically distinct blocks are smoothly mapped from rectangular computational domains and are aligned with magnetic flux surfaces to accommodate strong anisotropy induced by the magnetic field. We employ a fourthorder, finitevolume discretization in mapped coordinates to mitigate the computational expense associated with discretization on 4D phase space grids. Applied to a conservative formulation of the gyrokinetic system, a finitevolume approach expresses local conservation discretely in a natural manner involving the calculation of normal fluxes at cell faces. In the approach presented here, the normal fluxes are computed in terms of faceaveraged velocity normals in such a way that (i) the divergencefree property of the gyrokinetic velocity is preserved discretely to machine precision, (ii) the configuration space normal velocities are independent of mapping metrics, and (iii) the configuration space normal velocities are computed from exact pointwise evaluation of magnetic field data except for one term. The algorithms described in this paper form the foundation of a continuum gyrokinetic edge code named COGENT, which is used here to perform a convergence study verifying the accuracy of the spatial discretization.},
doi = {10.1016/j.jcp.2018.07.008},
journal = {Journal of Computational Physics},
issn = {00219991},
number = C,
volume = 373,
place = {United States},
year = {2018},
month = {11}
}