I am new to limiters in FVM CFD so pardon me if its a blunder. Was curious about Venkatakrishnan's limiter (first image) that is industry standard in many commercial CFD solvers. He came up with the final form as given below and further modified the Δ_ term in order to avoid division by numerical values close to zero. Why not eliminate Δ_ term by taking out one from the numerator(second image)? Any advantage of writing in this form(first image)? ref: 10.1006/jcph.1995.1084
ref: Conference Paper New Unstructured-Grid Limiter Functions
It’s to remove the application of the smoothing function where it’s not required. If we don’t have any large gradients in certain regions, we do not need to do any smoothing at these regions. So, the modification is applied in regions away from uniform flow regions.
Thanks. But my question was related to the form represented in Eq. (33) to remove the errors related to rounding-offs (see the first and second image files). I guess in smooth regions the ε² term dominate and returns a value 1 and hence no limiting/smoothing is done in this region which is given in the text.
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