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

## Abstract

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. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines 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. - Graphical abstract: - Highlights: • Construct structured, elliptic numerical grids with elementary numerical methods. • Align coordinate lines with or make them orthogonal to the domain boundary. • Compute grid points and metric elements upmore »

- Authors:

- Institute for Ion Physics and Applied Physics, Universität Innsbruck, A-6020 Innsbruck (Austria)
- Numerical Analysis group, Universität Innsbruck, A-6020 Innsbruck (Austria)

- Publication Date:

- OSTI Identifier:
- 22622303

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 340; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ACCURACY; ALGORITHMS; COMPUTERIZED SIMULATION; CONTROL; COORDINATES; DISTRIBUTION; MATHEMATICAL SOLUTIONS; NUMERICAL ANALYSIS; TWO-DIMENSIONAL CALCULATIONS; TWO-DIMENSIONAL SYSTEMS; WEIGHT

### Citation Formats

```
Wiesenberger, M., E-mail: Matthias.Wiesenberger@uibk.ac.at, Held, M., and Einkemmer, L..
```*Streamline integration as a method for two-dimensional elliptic grid generation*. United States: N. p., 2017.
Web. doi:10.1016/J.JCP.2017.03.056.

```
Wiesenberger, M., E-mail: Matthias.Wiesenberger@uibk.ac.at, Held, M., & Einkemmer, L..
```*Streamline integration as a method for two-dimensional elliptic grid generation*. United States. doi:10.1016/J.JCP.2017.03.056.

```
Wiesenberger, M., E-mail: Matthias.Wiesenberger@uibk.ac.at, Held, M., and Einkemmer, L.. Sat .
"Streamline integration as a method for two-dimensional elliptic grid generation". United States.
doi:10.1016/J.JCP.2017.03.056.
```

```
@article{osti_22622303,
```

title = {Streamline integration as a method for two-dimensional elliptic grid generation},

author = {Wiesenberger, M., E-mail: Matthias.Wiesenberger@uibk.ac.at and Held, M. and Einkemmer, L.},

abstractNote = {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. Furthermore, we can adapt any analytically given boundary aligned structured grid, which specifically includes polar and Cartesian grids. The resulting coordinate lines 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. - Graphical abstract: - Highlights: • Construct structured, elliptic numerical grids with elementary numerical methods. • Align coordinate lines with or make them orthogonal to the domain boundary. • Compute grid points and metric elements up to machine precision. • Control cell distribution by adaption functions or monitor metrics.},

doi = {10.1016/J.JCP.2017.03.056},

journal = {Journal of Computational Physics},

number = ,

volume = 340,

place = {United States},

year = {Sat Jul 01 00:00:00 EDT 2017},

month = {Sat Jul 01 00:00:00 EDT 2017}

}