Adding Least Squares for Skewed Cells

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Motivation

The current Green-Gauss gradient scheme performs poorly in skewed cells. The reason for this is that the face values in cells with high skewness have significant errors, which leads to large errors in the gradient computation.

Below is an example for the PB-FHR case, which is supposed to have a flat velocity profile in its lower part. The oscillations shown by the Green-Gauss interpolation are quite substantial and interfere with the physics of the system.

Design

• The least-squares interpolation should follow the weighted scheme proposed in this article
• For now, we will only use least-square corrections for skewed meshes

Impact

The proposed modification will allow us to have much more accurate results in skewed meshes

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Can someone add a more general label than NavierStokes please, this will benefit any application using FVs, e.g., P1 thermal radiation transport? Thanks!