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The Least Squares and Green-Gauss gradient schemes have been traditionally studied as two distinct techniques for gradient computation on unstructured meshes in literature. In this Letter, we show that the Green-Gauss gradient method can be interpreted as a Weighted Least Squares gradient scheme, and that therefore methods of the Green-Gauss family may be encompassed in the larger set of Least Squares based gradient schemes.

A comparative study on pressure and pressure-correction-based fractional-step methods for incompressible flows is presented. Implicit fractional-step methods are shown to give rise to a splitting error due to the implicit temporal discretization of the intermediate momentum equations. Through mathematical reasoning and a numerical example, a relative advantage of pressure-correction-based approaches over pressure-based approach for the computation of low Reynolds number flows using implicit fractional-step methods is demonstrated.

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