Streamline integration as a method for two-dimensional elliptic grid generation

We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. The resulting grids are orthogonal to the boundary. Grid points as well...

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Bibliographic Details
Published inarXiv.org
Main Authors Wiesenberger, Matthias, Held, Markus, Einkemmer, Lukas
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 27.01.2017
Subjects
Algorithms
Domains
Grid generation (mathematics)
Jacobi matrix method
Jacobian matrix
Mathematics - Numerical Analysis
Nonlinear programming
Numerical analysis
Numerical methods
Parallel processing
Physics - Computational Physics
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Summary:We propose a new numerical algorithm to construct a structured numerical elliptic grid of a doubly connected domain. Our method is applicable to domains with boundaries defined by two contour lines of a two-dimensional function. The resulting grids are orthogonal to the boundary. Grid points as well as the elements of the Jacobian matrix can be computed efficiently and up to machine precision. In the simplest case we construct conformal grids, yet with the help of weight functions and monitor metrics we can control the distribution of cells across the domain. Our algorithm is parallelizable and easy to implement with elementary numerical methods. We assess the quality of grids by considering both the distribution of cell sizes and the accuracy of the solution to elliptic problems. Among the tested grids these key properties are best fulfilled by the grid constructed with the monitor metric approach.
ISSN:2331-8422
DOI:10.48550/arxiv.1610.07939