High-order discretization of a gyrokinetic Vlasov model in edge plasma geometry

Journal Article · 14 November 2018 · Journal of Computational Physics

DOI: https://doi.org/10.1016/j.jcp.2018.07.008 · OSTI ID:1526551

Dorr, Milo R. ^[1]; Colella, Phillip ^[2]; Dorf, Mikhail A. ^[3]; Ghosh, Debojyoti ^[1]; Hittinger, Jeffrey A. F. ^[1]; Schwartz, Peter O. ^[2]

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1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
2. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Applied Numerical Algorithms Group
3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Fusion Energy Program

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 fourth-order, finite-volume 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 finite-volume 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 face-averaged velocity normals in such a way that (i) the divergence-free 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.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
• Grant/Contract Number: AC02-05CH11231; AC52-07NA27344
• OSTI ID: 1526551
• Report Number(s): LLNL-JRNL--741095; ark:/13030/qt9ph360bz
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 373; ISSN 0021-9991
• Publisher: ElsevierCopyright Statement
• Country of Publication: United States
• Language: English