A field-aligned gyrokinetic solver based on discontinuous Galerkin in tokamak geometry

Abstract

This paper presents the development of a hyperbolic solver for the gyrokinetic equation in tokamak geometry. The discontinuous Galerkin method discretizes the gyrokinetic equation on the field-aligned mesh composed of twisted prism-shaped elements in the tokamak domain. The elements are generated by extending the vertices of unstructured triangular elements on a poloidal plane following the equilibrium magnetic field lines. A sub-triangulation is employed to transfer information between nonconforming meshes, which is inevitable when implementing the field-aligned mesh. The numerical integrations of elements in the field-aligned mesh are performed by transforming the numerical integrations of reference elements in a reference element. We investigate the impact of field-aligned mesh on the numerical interpolation of synthetic plasma fluctuation data generated by a ballooning function. The numerical tests show that the field-aligned mesh can significantly improve computational efficiencies. Additionally, we estimate a sufficient condition for a stable temporal discretization of the hyperbolic solver based on a Runge-Kutta method. The estimation indicates that the field-aligned mesh can allow a notable increase of the time step size for stable simulation. In the numerical experiments, the solver shows good conservations of physical quantities such as mass, kinetic energy, and toroidal canonical angular momentum.