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

Chizari, Hossain 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: Engineering
Publisher: Springer Science Business Media
ISSN: 0126-6705
Date of Acceptance: 14 October 2015
Last Modified: 19 Oct 2021 01:22
URI: https://orca.cardiff.ac.uk/id/eprint/135202

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