A Multigrid Algorithm for Nonlocal Collisional Electrostatic Drift-Wave Turbulence

Abstract

We have developed a three-dimensional anisotropic multigrid solver for simulating nonlocal collisional electrostatic drift-wave turbulence in a tokamak with magnetic shear. As an example, the solver has been used to obtain entire flux-surface solutions of the nonlocal Hasegawa–Wakatani equations in the absence of curvature effects. The implicit treatment of the parallel-gradient terms permits the use of a relatively large time step. Considerable effort was made in the design of the implicit solver to ensure that the presence of anisotropy does not lead to a significant degradation in performance. The multigrid algorithm has several advantages over a pseudospectral Poisson solver; most importantly, all nonlinear terms, including those in the Ohm's law, can be retained in a straightforward manner. Although in this work the solver is illustrated using straightened tokamak (sheared slab) geometry, the object-oriented construction of the code will facilitate the eventual inclusion of curvature terms and the complete nonlinear reduced Braginskii equations, including ion thermal dynamics.