Numerical simulation of magnetically confined plasmas is uniquely challenging because of its high degree of anisotropy. Parallel flows are typically orders of magnitude larger than transverse flows. Corruption of small transverse flows by large parallel flows due to discretization errors can destroy numerical accuracy. A principal method for avoiding such corruption is the use of flux coordinate grids, in which at least one coordinate approximately satisfies B = 0. In previous work, such a flux coordinate system is based on a static, axisymmetric equilibrium. If the simulation is followed far enough into the nonlinear regime, the magnetic field can evolve away from this initial configuration, causing the coordinate system to lose its field-aligned properties. We have developed a new differential geometry approach to adaptive grid generation using Beltrami’s equation, a generalization of Laplace’s equation for curvilinear surfaces, in which the metric tensor g is chosen to provide the necessary grid properties for alignment as well as adaptation to specified quantities with strong gradients. The method provides independence of initial representation and guarantees a well-posed grid.
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