Abstract
In this paper, the formal order of accuracy of three commonly used gradient reconstruction methods is derived. The analysis showed that the Green–Gauss cell based (GGCB) method is intrinsically inconsistent, due to the leading error term that is independent of the mesh spacing. On the other hand, the Green–Gauss node based (GGNB) and the Least Squares cell based (LSCB) methods achieved a minimum of 1st order accuracy regardless of the mesh geometric properties. Implications of the former results were practically tested on four CFD applications to show that in three out of four cases, the LSCB method achieved the highest order of accuracy. In terms of the computational expenses, the GGNB method consumed 9–34% additional time when compared to the fastest converging method in each test case. Both the GGCB and the LSCB methods consumed nearly the same computational time to reach convergence.
Published Version
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