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On third-order limiter functions for finite volume methods


Schmidtmann, Birte; Abgrall, Rémi; Torrilhon, Manuel (2016). On third-order limiter functions for finite volume methods. Bulletin of the Brazilian Mathematical Society, N.S., 47(2):753-764.

Abstract

In this article, we propose a finite volume limiter function for a reconstruction on the three-point stencil. Compared to classical limiter functions in the MUSCL framework, which yield 2$^{rd}$-order accuracy, the new limiter is 3$^{rd}$-order accurate for smooth solution. In an earlier work, such a 3$^{rd}$-order limiter function was proposed and showed successful results [2]. However, it came with unspecified parameters. We close this gap by giving information on these parameters.

Abstract

In this article, we propose a finite volume limiter function for a reconstruction on the three-point stencil. Compared to classical limiter functions in the MUSCL framework, which yield 2$^{rd}$-order accuracy, the new limiter is 3$^{rd}$-order accurate for smooth solution. In an earlier work, such a 3$^{rd}$-order limiter function was proposed and showed successful results [2]. However, it came with unspecified parameters. We close this gap by giving information on these parameters.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:June 2016
Deposited On:19 May 2017 13:47
Last Modified:28 May 2017 05:14
Publisher:Springer
ISSN:1678-7544
Publisher DOI:https://doi.org/10.1007/s00574-016-0183-5

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