Journal
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
Volume 40, Issue 3, Pages 1231-1264Publisher
SPRINGER
DOI: 10.1007/s40840-015-0292-0
Keywords
Residual distribution; Cell-vertex finite volume; Order-of-accuracy; Triangular grid; Skewness
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Funding
- Universiti Sains Malaysia [1001/PAERO/814152]
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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 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 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.
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