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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:373

Article

Wiesenberger, M.¹  Held, M.²  Einkemmer, L.^3,4  Kendl, A.² 

[1] Tech Univ Denmark, Dept Phys, DK-2800 Lyngby, Denmark

[2] Univ Innsbruck, Inst Ion Phys & Appl Phys, A-6020 Innsbruck, Austria

[3] Univ Tubingen, Dept Math, D-72076 Tubingen, Germany

[4] Univ Innsbruck, Dept Math, A-6020 Innsbruck, Austria

关键词: X-Point;    Monitor metric;    Streamline integration;    Structured grid;   

DOI  :  10.1016/j.jcp.2018.07.007

来源: Elsevier

【 摘 要 】

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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free