A new gyrokinetic hyperbolic solver with discontinuous Galerkin method in tokamak geometry

Abstract

We develop a hyperbolic solver for the gyrokinetic equation in tokamak geometry. The new solver is based on the discontinuous Galerkin approach on a finite element mesh composed of irregular spatial and regular velocity elements together with a strong-stability-preserving time discretization method. We investigate the effects of the basis function on the conservation properties of physical quantities such as mass, kinetic energy, and toroidal canonical angular momentum in an axisymmetric configuration of toroidal plasma. It is shown that if the proper basis function is chosen, the new solver has a good conservation property of the key physical quantities in the simplified circular magnetic geometry and realistic tokamak geometry. The invariance of the canonical Maxwellian distribution function in time is confirmed. We also investigate the effect of weighting functions for the polynomial basis. The weighted basis functions show a similar conservation property to the polynomial basis; the canonical Maxwellian weighted basis shows better invariance with the lower order polynomials. The performance tests of MPI parallelization are also carried out. The results indicate that the new solve solver performs well up to a few thousand CPU cores. [1] G. Jo, J.-M. Kwon, J. Seo, E. Yoon, Comput. Phys. Commun. 273 (2022) 108265