# Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods

## Abstract

Abstract In this paper, the numerical error of two widely used methods for remapping of discrete quantities from one computational mesh to another is investigated. We compare the intuitive, but resource intensive method utilizing intersections of computational cells with the faster and simpler swept-region-based method. Both algorithms are formally second order accurate, however, they are known to produce slightly different quantity profiles in practical applications. The second-order estimate of the error formula is constructed algebraically for both algorithms so that their local accuracy can be evaluated. This general estimate is then used to assess the dependence of the performance of both methods on parameters such as the second derivatives of the remapped distribution, mesh geometry or mesh movement. Due to the complexity of such analysis, it is performed on a set of simplified elementary mesh patterns such as cell corner expansion, rotation or shear. On selected numerical tests it is demonstrated that the swept-based method can distort a symmetric quantity distribution more substantially than the intersection-based approach when the computational mesh moves in an unsuitable direction.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1492652

- Report Number(s):
- LA-UR-15-24666

Journal ID: ISSN 1815-2406; applab

- DOE Contract Number:
- 89233218CNA000001

- Resource Type:
- Journal Article

- Journal Name:
- Communications in Computational Physics

- Additional Journal Information:
- Journal Volume: 21; Journal Issue: 02; Journal ID: ISSN 1815-2406

- Publisher:
- Global Science Press

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Klima, Matej, Kucharik, Milan, and Shashkov, Mikhail.
```*Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods*. United States: N. p., 2017.
Web. doi:10.4208/cicp.OA-2015-0021.

```
Klima, Matej, Kucharik, Milan, & Shashkov, Mikhail.
```*Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods*. United States. doi:10.4208/cicp.OA-2015-0021.

```
Klima, Matej, Kucharik, Milan, and Shashkov, Mikhail. Wed .
"Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods". United States. doi:10.4208/cicp.OA-2015-0021.
```

```
@article{osti_1492652,
```

title = {Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods},

author = {Klima, Matej and Kucharik, Milan and Shashkov, Mikhail},

abstractNote = {Abstract In this paper, the numerical error of two widely used methods for remapping of discrete quantities from one computational mesh to another is investigated. We compare the intuitive, but resource intensive method utilizing intersections of computational cells with the faster and simpler swept-region-based method. Both algorithms are formally second order accurate, however, they are known to produce slightly different quantity profiles in practical applications. The second-order estimate of the error formula is constructed algebraically for both algorithms so that their local accuracy can be evaluated. This general estimate is then used to assess the dependence of the performance of both methods on parameters such as the second derivatives of the remapped distribution, mesh geometry or mesh movement. Due to the complexity of such analysis, it is performed on a set of simplified elementary mesh patterns such as cell corner expansion, rotation or shear. On selected numerical tests it is demonstrated that the swept-based method can distort a symmetric quantity distribution more substantially than the intersection-based approach when the computational mesh moves in an unsuitable direction.},

doi = {10.4208/cicp.OA-2015-0021},

journal = {Communications in Computational Physics},

issn = {1815-2406},

number = 02,

volume = 21,

place = {United States},

year = {2017},

month = {2}

}