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Abstract
We investigate structured grids aligned to the contours of a twodimensional fluxfunction with an Xpoint (saddle point). Our theoretical analysis finds that orthogonal grids exist if and only if the Laplacian of the fluxfunction vanishes at the Xpoint. In general, this condition is sufficient for the existence of a structured aligned grid with an Xpoint. With the help of streamline integration we then propose a numerical grid construction algorithm. In a suitably chosen monitor metric the Laplacian of the fluxfunction vanishes at the Xpoint 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 Xpoint reduce the convergence rate. As a consequence, the proposed grid should be used with grid refinement around the Xpoint in practical applications. We show that grid refinement in the cells neighbouring the Xpoint 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 Xpoint reduce the convergence rate. As a consequence, the proposed grid should be used with grid refinement around the Xpoint in practical applications. We show that grid refinement in the cells neighbouring the Xpoint restores the expected convergence rate.
Original language  English 

Journal  Journal of Computational Physics 
Volume  373 
Pages (fromto)  370384 
Number of pages  15 
ISSN  00219991 
DOIs  
Publication status  Published  2018 
Keywords
 Xpoint
 Monitor metric
 Streamline integration
 Structured grid
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Projects
 1 Active

COFUNDfellowsDTU: COFUNDfellowsDTU
Brodersen, S. W. & Præstrud, M. R.
01/01/2017 → 31/12/2022
Project: Research