Streamline integration as a method for structured grid generation in X-point geometry

M. Wiesenberger*, M. Held, L. Einkemmer, A. Kendl

*Corresponding author for this work

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Abstract

We investigate structured grids aligned to the contours of a two-dimensional flux-function with an X-point (saddle point). Our theoretical analysis finds that orthogonal grids exist if and only if the Laplacian of the flux-function vanishes at the X-point. In general, this condition is sufficient for the existence of a structured aligned grid with an X-point. With the help of streamline integration we then propose a numerical grid construction algorithm. In a suitably chosen monitor metric the Laplacian of the flux-function vanishes at the X-point such that a grid construction is possible.

We study the convergence of the solution to elliptic equations on the proposed grid. The diverging volume element and cell sizes at the X-point reduce the convergence rate. As a consequence, the proposed grid should be used with grid refinement around the X-point in practical applications. We show that grid refinement in the cells neighbouring the X-point restores the expected convergence rate.
Original languageEnglish
JournalJournal of Computational Physics
Volume373
Pages (from-to)370-384
Number of pages15
ISSN0021-9991
DOIs
Publication statusPublished - 2018

Keywords

  • X-point
  • Monitor metric
  • Streamline integration
  • Structured grid

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