KINTORA: a semi-Lagrangian discontinuous Galerkin drift-kinetic, unstructured mesh tokamak solver
Abstract
Continuum gyrokinetic codes use structured, field-aligned grids on nested flux surfaces; particle-in-cell codes support unstructured meshes and open field lines but carry a statistical noise floor. We present a continuum drift-kinetic solver that occupies neither position: a semi-Lagrangian discontinuous Galerkin discretization on unstructured triangular poloidal planes extruded toroidally, whose parallel advance is a map along the exact field line in the flux-coordinate independent manner, so the mesh is never aligned with the field, with adiabatic electrons and a long-wavelength polarization field solve. Every operator is verified against an independently computed reference, from Landau damping to the geodesic-acoustic root and a linear ion-temperature-gradient eigenvalue problem, every measured rate within 4% except the geodesic-acoustic damping, within 12%. A linear toroidal ion-temperature-gradient demonstration on a canonical-Maxwellian equilibrium recovers a radially coherent mode whose growth rate, 0.065 c_s/a, is stationary in time. The collisionless zonal-flow residual is the one measurement still moving: it rises with poloidal refinement from 0.72 to 0.87 of the model's own orbit-quadrature prediction for the measured observable and has not converged. The solver is fully device resident, and every result is reproduced between CPU and GPU builds and across MPI process counts. The code, the data behind every table and an artifact description are in a public repository.
Related
- Positivity-preserving semi-Lagrangian discontinuous Galerkin methods for multi-species Vlasov-Ampère models of plasma
- Parallel Design of a GPU-Resident Semi-Lagrangian Drift-Kinetic Solver on Unstructured Extruded Tokamak Meshes
- A new formulation of Discontinuous Galerkin method for interface capturing approaches
- A class of high-order discontinuous-Galerkin methods satisfying infinitely many entropy conditions with provable error estimates and strong convergence for general nonlinear conservation laws
- Entropy-Stable and Well-Balanced Discontinuous Galerkin Methods for the Compressible Euler Equations in Vector-Invariant Form
BibTeX
@misc{adams2026kintora,
title = {{KINTORA: a semi-Lagrangian discontinuous Galerkin drift-kinetic, unstructured mesh tokamak solver}},
author = {Mark F. Adams},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17428},
eprint = {2610.17428},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17428},
}
RIS
TY - UNPB
TI - KINTORA: a semi-Lagrangian discontinuous Galerkin drift-kinetic, unstructured mesh tokamak solver
AU - Mark F. Adams
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.17428
UR - https://arxiv.org/abs/2610.17428
AB - Continuum gyrokinetic codes use structured, field-aligned grids on nested flux surfaces; particle-in-cell codes support unstructured meshes and open field lines but carry a statistical noise floor. We present a continuum drift-kinetic solver that occupies neither position: a semi-Lagrangian discontinuous Galerkin discretization on unstructured triangular poloidal planes extruded toroidally, whose parallel advance is a map along the exact field line in the flux-coordinate independent manner, so the mesh is never aligned with the field, with adiabatic electrons and a long-wavelength polarization field solve. Every operator is verified against an independently computed reference, from Landau damping to the geodesic-acoustic root and a linear ion-temperature-gradient eigenvalue problem, every measured rate within 4% except the geodesic-acoustic damping, within 12%. A linear toroidal ion-temperature-gradient demonstration on a canonical-Maxwellian equilibrium recovers a radially coherent mode whose growth rate, 0.065 c_s/a, is stationary in time. The collisionless zonal-flow residual is the one measurement still moving: it rises with poloidal refinement from 0.72 to 0.87 of the model's own orbit-quadrature prediction for the measured observable and has not converged. The solver is fully device resident, and every result is reproduced between CPU and GPU builds and across MPI process counts. The code, the data behind every table and an artifact description are in a public repository.
ER -