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arXiv · 1803.10507

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

M. Wiesenberger·M. Held·L. Einkemmer·A. Kendl
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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 neighboring the X-point restores the expected convergence rate.

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M. Wiesenberger, M. Held, L. Einkemmer, A. Kendl. 2018-03-28. Streamline integration as a method for structured grid generation in X-point geometry. https://doi.org/10.1016/j.jcp.2018.07.007

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