Volume 21, Issue 2
Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods

Matej Klima, Milan Kucharik & Mikhail Shashkov

Commun. Comput. Phys., 21 (2017), pp. 526-558.

Published online: 2018-04

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  • 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.

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@Article{CiCP-21-526, author = {}, title = {Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods}, journal = {Communications in Computational Physics}, year = {2018}, volume = {21}, number = {2}, pages = {526--558}, 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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2015-0021}, url = {http://global-sci.org/intro/article_detail/cicp/11249.html} }
TY - JOUR T1 - Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods JO - Communications in Computational Physics VL - 2 SP - 526 EP - 558 PY - 2018 DA - 2018/04 SN - 21 DO - http://doi.org/10.4208/cicp.OA-2015-0021 UR - https://global-sci.org/intro/article_detail/cicp/11249.html KW - AB -

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.

Matej Klima, Milan Kucharik & Mikhail Shashkov. (2020). Local Error Analysis and Comparison of the Swept- and Intersection-Based Remapping Methods. Communications in Computational Physics. 21 (2). 526-558. doi:10.4208/cicp.OA-2015-0021
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