square-root conformation approach for other Constitutive Eqns

[Joe199999]

Dear developers
I read in the docs that the "square-root conformation approach" is applied only for the Oldroyd-B model. I want to know what I should do to apply it to other models, like PTT. Is it easy to do that?

[DanielFractal]

Same principle applies. For a derivation check the article "The Kernel-Conformation Constitutive Laws", which writes the general form of the equations including both model families. You only need to keep track of the jacobian.
Be mindful that in the case of the (non-simplified) PTT family, when the slip parameter is nonzero, the transformation for the conformation tensor is slightly different.
If you only need the formulas, the rheotool user guide shows all of those and the particular PTT case.

[Joe199999]

Dear Daniel
Thanks for your reply.
Do you know why the developers haven't added this method for other models?
Is there any technical or scientific reason?

[DanielFractal]

I suppose it is because there is no need. Log-conformation performs better than root-conformation (for any root) in pretty much all cases. They might have given this justification in the guide, but I do not recall.

[Joe199999]

Thank you!
I read this paper:
doi:10.1017/jfm.2023.92
, in which the authors mentioned that log-conformation cannot capture the upstream vortices of flow around cylinders:

In the numerical results based on the logarithmic reconstruction method, we do not observe the upstream recirculation found in the experiments of Qin et al. (2019a). Moreover, the logarithmic reconstruction method was also adopted by Mokhtari et al. (2022) and Kumar
& Ardekani (2022) and the upstream recirculation was not reported in their simulations. However, the square root reconstruction method can successfully predict the upstream recirculation, which is, therefore, adopted in the present simulation.

So, to do the validation, I need to have this approach.