Accuracy variations in residual distribution and finite volume methods on triangular grids

Chizari, Hossain ORCID: https://orcid.org/0000-0002-6630-1880 and Ismail, Farzad 2017. Accuracy variations in residual distribution and finite volume methods on triangular grids. Bulletin of the Malaysian Mathematical Sciences Society 40 (3) , pp. 1231-1264. 10.1007/s40840-015-0292-0

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Abstract

This paper presents an analytical and numerical approach in studying accuracy deterioration of residual distribution and cell-vertex finite volume methods on triangular grids. Results herein demonstrate that both methods preserve the order-of-accuracy reasonably well for uniformly skewed triangular grids and the L2 errors of both second-order accurate methods behave similarly with values of the same magnitude. On the other hand, the first-order finite volume method has an L2 error of about an order of magnitude higher than its residual distribution counterpart. Both first-order methods are unable to preserve the order-of-accuracy for high-frequency data when the grids are highly skewed although the residual distribution approach has a slightly better performance. Both second-order methods perform quite decently for high-frequency data on uniformly skewed grids. However, the order-of-accuracy of finite volume methods excessively deteriorate when the grids are skewed non-uniformly unlike the residual distribution methods which preserve the order-of-accuracy.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Schools > Engineering
Publisher:	Springer Science Business Media
ISSN:	0126-6705
Date of Acceptance:	14 October 2015
Last Modified:	05 Nov 2022 02:42
URI:	https://orca.cardiff.ac.uk/id/eprint/135202

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