High-order Discretization of a Gyrokinetic Vlasov Model in Edge Plasma Geometry

TL;DR

This paper develops a high-order spatial discretization method for a gyrokinetic Vlasov model in tokamak edge plasma geometries, improving accuracy and efficiency in high-dimensional phase space simulations.

Contribution

It introduces a high-order finite-volume discretization on mapped multiblock grids that preserves divergence-free properties for gyrokinetic phase space velocity.

Findings

Achieves higher accuracy with fewer grid points compared to lower-order methods.

Maintains divergence-free phase space velocity discretely to prevent error accumulation.

Effectively handles complex edge plasma geometries with multiple mapped blocks.

Abstract

We present a high-order spatial discretization of a continuum gyrokinetic Vlasov model in axisymmetric tokamak edge plasma geometries. Such models describe the phase space advection of plasma species distribution functions in the absence of collisions. The gyrokinetic model is posed in a four-dimensional phase space, upon which a grid is imposed when discretized. To mitigate the computational cost associated with high-dimensional grids, we employ a high-order discretization to reduce the grid size needed to achieve a given level of accuracy relative to lower-order methods. Strong anisotropy induced by the magnetic field motivates the use of mapped coordinate grids aligned with magnetic flux surfaces. The natural partitioning of the edge geometry by the separatrix between the closed and open field line regions leads to the consideration of multiple mapped blocks, in what is known as a mapped multiblock (MMB) approach. We describe the specialization of a more general formalism that we have developed for the construction of high-order, finite-volume discretizations on MMB grids, yielding the accurate evaluation of the gyrokinetic Vlasov operator, the metric factors resulting from the MMB coordinate mappings, and the interaction of blocks at adjacent boundaries. Our conservative formulation of the gyrokinetic Vlasov model incorporates the fact that the phase space velocity has zero divergence, which must be preserved discretely to avoid truncation error accumulation. We describe an approach for the discrete evaluation of the gyrokinetic phase space velocity that preserves the divergence-free property to machine precision.