## High-order 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 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 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) (SC-21)

- OSTI Identifier:
- 1532566

- Alternate Identifier(s):
- OSTI ID: 1526551

- Grant/Contract Number:
- AC02-05CH11231; AC52-07NA27344

- Resource Type:
- Publisher's Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 373; Journal Issue: C; Journal ID: ISSN 0021-9991

- 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. High-order 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. High-order 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 .
"High-order discretization of a gyrokinetic Vlasov model in edge plasma geometry". United States. doi:10.1016/j.jcp.2018.07.008.
```

```
@article{osti_1532566,
```

title = {High-order 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 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.},

doi = {10.1016/j.jcp.2018.07.008},

journal = {Journal of Computational Physics},

number = C,

volume = 373,

place = {United States},

year = {2018},

month = {11}

}

DOI: 10.1016/j.jcp.2018.07.008

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