### 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.

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 language | English |
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Journal | Journal of Computational Physics |

Volume | 373 |

Pages (from-to) | 370-384 |

Number of pages | 15 |

ISSN | 0021-9991 |

DOIs | |

Publication status | Published - 2018 |

### Keywords

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

### Cite this

Wiesenberger, M., Held, M., Einkemmer, L., & Kendl, A. (2018). Streamline integration as a method for structured grid generation in X-point geometry.

*Journal of Computational Physics*,*373*, 370-384. https://doi.org/10.1016/j.jcp.2018.07.007