Development of a tokamak magnetohydrodynamic code with the discontinuous Galerkin and Weighted Essentially Non-Oscillatory methods

Abstract

In this study, we present the development of a new initial-value magnetohydrodynamic (MHD) code for toroidal geometry using discontinuous Galerkin (DG) and Weighted Essentially Non-Oscillatory (WENO) methods. The code utilizes a triangular mesh based on the flux of the fixed boundary equilibrium in the poloidal plane, which is uniformly divided in the toroidal direction. By solving the conservative perturbed generalized Lagrange multiplier (GLM) MHD model, the code can simulate both ideal and resistive toroidal plasmas. We validate the code by performing the linear calculations of the internal kink mode and tearing mode, and our results show good agreement with calculations conducted using an eigen-value MHD code. Furthermore, nonlinear simulations of the resistive internal kink mode and tearing mode are also carried out. We discuss the challenges and limitations of the code, as well as the future efforts to improve its performance. The development of this new initial-value MHD code opens up new possibilities for studying and understanding the dynamics of toroidal plasmas, contributing to the advancement of fusion research.