In computational plasma physics, one often faces problems with extremely high transport anisotropy, 1e6 and more, since transport along the magnetic field is much faster than across. To deal with this in numerical simulations, the common practice is to align the computational grid with the magnetic field, i.e., using grid (b) rather than grid (a) in this Figure. enter image description here

A well known technique for optimizing the grid in simulations is Adaptive Mesh Refinement (AMR) which amounts to splitting some of grid cells to achieve adequate resolution. Are there techniques for automatically adjusting the grid by rotating and/or reshaping grid cells to achieve alignment with a desired direction? Anything like that described in the literature?

  • $\begingroup$ Is the B-Field constant and known? $\endgroup$
    – MPIchael
    Jul 28, 2023 at 8:33
  • $\begingroup$ In the simplest case (that is common and very important), yes - the B field is constant and known. $\endgroup$ Jul 28, 2023 at 15:01
  • $\begingroup$ hm, in the static case it might be possible to adapt the winslow equations for this. See e.g. "High-order unstructured curved mesh generation using the Winslow equations" by Fortunato and Persson or the original "Numerical solution of the quasilinear poisson equation in a nonuniform triangle mesh" by Winslow. There exists variants where you additionally introduce right hand sides to the equations to shape the interior to your liking. $\endgroup$
    – Bort
    Jul 28, 2023 at 15:49
  • $\begingroup$ Never heard of the Winslow equations, very interesting, thanks! $\endgroup$ Jul 28, 2023 at 16:16
  • $\begingroup$ Just going by the pictures, this could be of interest to you: arxiv.org/pdf/1503.04709.pdf $\endgroup$
    – Bort
    Jul 28, 2023 at 16:33


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