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

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 align...

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Bibliographic Details
Published in:Journal of computational physics 2018-11, Vol.373 (C), p.605-630
Main Authors: Dorr, Milo R., Colella, Phillip, Dorf, Mikhail A., Ghosh, Debojyoti, Hittinger, Jeffrey A.F., Schwartz, Peter O.
Format: Article
Language:English
Subjects:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY
Anisotropy
Computation
Computational physics
Configurations
Coordinates
Discretization
Divergence
Domains
Finite volume method
Finite-volume
Gyrokinetic
High-order
Magnetic fields
Magnetic flux
Mapped-multiblock
Plasma physics
Tokamak devices
Tokamak edge plasma
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Summary: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.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2018.07.008