Polynomial in cellLimited<cubic> seems dodgy
Hello :)
After having some convergence problems in a Godunovtype scheme I programmed in OpenFOAM, I have been investigating the source code for the gradScheme cellLimited<cubic> in src/finiteVolume/finiteVolume/gradSchemes/limitedGradSchemes/cellLimitedGrad/gradientLimiters/cubicGradientLimiter.H The paper it is based on (Michalak and OllivierGooch, 2008) says that the limiter function should be a cubic polynomial P(r) with P(r = 0) = 0, P(r = t) = 1, P'(r = 0) = 1, P'(r = t) = 0. By my calculations, this should be: P(r) = ar^3 + br^2 + r a = (t  2)/(t^3) b =  (3at^2 + 1)/(2t) https://www.wolframalpha.com/input/?...+and+t+%3D+1.5 But the source code says: P(r) = ar^3 + br^2 + r a = 2/t^2  2/t^3 b =  (3/2)at https://www.wolframalpha.com/input/?...+and+t+%3D+1.5 The WolframAlpha graphs (shown for t = 1.5) suggest that P'(r = t) is definitely not zero for the polynomial that is in the OpenFOAM code. Coincidentally, I initially ended up with the same coefficients as in the OpenFOAM code when I accidentally said the derivative of r with respect to r was 0 and not 1 when incorporating the constraint P'(r = t), then I plotted the graphs and realised something was wrong. Is this a mistake in the code or do I just not understand it properly? :o Thanks, Shannon 
Perhaps worth dropping a bug report?

I submitted a bug report https://develop.openfoam.com/Develop...//issues/2113 and it is getting fixed :)

Well done  the system works! Thanks for putting the effort in to get this fixed for us all.

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