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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?

Maxim Umansky
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  • Is the B-Field constant and known? – MPIchael Jul 28 '23 at 08:33
  • In the simplest case (that is common and very important), yes - the B field is constant and known. – Maxim Umansky Jul 28 '23 at 15:01
  • 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. – Bort Jul 28 '23 at 15:49
  • Never heard of the Winslow equations, very interesting, thanks! – Maxim Umansky Jul 28 '23 at 16:16
  • Just going by the pictures, this could be of interest to you: https://arxiv.org/pdf/1503.04709.pdf – Bort Jul 28 '23 at 16:33
  • @Bort Thanks, this looks very relevant too! – Maxim Umansky Jul 28 '23 at 21:01
  • Maybe the marching cubes algorithm is applicable too. When you interpret the isosurfaces of your |B| field you may subdivide a cubic grid via this algorithm. I am not sure if the resulting cells will be suitable for your application but it may be worth a read. https://en.wikipedia.org/wiki/Marching_cubes

    https://kogs-www.informatik.uni-hamburg.de/publikationen/pub-stelldinger/iciap07.pdf

    https://www.dune-project.org/modules/dune-tpmc/

     – MPIchael Jul 31 '23 at 09:32
  • @MPIchael Yes, that marching cubes algorithm looks very relevant for this problem, thanks a lot. – Maxim Umansky Jul 31 '23 at 15:12
  • I think that rewriting your governing equations in a different frame of reference could also be another alternative. – Sthavishtha Bhopalam Aug 28 '23 at 03:46

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