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

Research output: Contribution to journalJournal articleResearchpeer-review

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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

Cite this

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title = "Streamline integration as a method for structured grid generation in X-point geometry",
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.",
keywords = "X-point, Monitor metric, Streamline integration, Structured grid",
author = "M. Wiesenberger and M. Held and L. Einkemmer and A. Kendl",
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language = "English",
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journal = "Journal of Computational Physics",
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Streamline integration as a method for structured grid generation in X-point geometry. / Wiesenberger, M.; Held, M.; Einkemmer, L.; Kendl, A.

In: Journal of Computational Physics, Vol. 373, 2018, p. 370-384.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Streamline integration as a method for structured grid generation in X-point geometry

AU - Wiesenberger, M.

AU - Held, M.

AU - Einkemmer, L.

AU - Kendl, A.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - X-point

KW - Monitor metric

KW - Streamline integration

KW - Structured grid

U2 - 10.1016/j.jcp.2018.07.007

DO - 10.1016/j.jcp.2018.07.007

M3 - Journal article

VL - 373

SP - 370

EP - 384

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

ER -