Accuracy Variations in Residual Distribution and F

Authors: Hossain Chizari Farzad Ismail

Publish Date: 2015/12/14

Volume: 40, Issue: 3, Pages: 1231-1264

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Abstract

This paper presents an analytical and numerical approach in studying accuracy deterioration of residual distribution and cellvertex finite volume methods on triangular grids Results herein demonstrate that both methods preserve the orderofaccuracy reasonably well for uniformly skewed triangular grids and the L 2 errors of both secondorder accurate methods behave similarly with values of the same magnitude On the other hand the firstorder finite volume method has an L 2 error of about an order of magnitude higher than its residual distribution counterpart Both firstorder methods are unable to preserve the orderofaccuracy for highfrequency data when the grids are highly skewed although the residual distribution approach has a slightly better performance Both secondorder methods perform quite decently for highfrequency data on uniformly skewed grids However the orderofaccuracy of finite volume methods excessively deteriorate when the grids are skewed nonuniformly unlike the residual distribution methods which preserve the orderofaccuracySince the scaling and rotation of the whole triangle do not affect the skewness and aspect ratio in this analysis the longest length of the triangle considered 1 Fig 23 The shaded part would be the domain of x y for a general triangle because firstly if xfrac12 or y0 that triangle could be replaced with the completely similar one in which x y are in the shadeddomain by flipping Second if the x2+y21 then there will be a similar triangle such that the longest edge will be scaled into 1 Consequently by analyzing this prototype the relation between skewness and aspect ratio with x y will be determined

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