[Nek5000-users] Clarification on PN-PN formulation with IFCHAR=T

[nek5000-users at lists.mcs.anl.gov]

Dear all,


I am doing DNS of an incompressible flow using the PN-PN formulation with IFCHAR=T. We chose the PN-PN formulation because we wanted to ensure continuous pressure field. We chose the characteristics based time-stepping for stability.


More than a question, I would like to see if I am understanding the solution process correctly. I've read the "NEK_doc.pdf" file dated from July 2015 which contains information on the PN-PN formulation, and Dr. Fischer's notes on implementation of the OIFS/characteristics approach. I've also looked at the code.


>From what I can tell, the main difference when using PN-PN with IFCHAR=T vs. IFCHAR=F is that instead of having the non-linear terms on the RHS (IFCHAR=F) (see Eq. 7.7 from NEK_doc.pdf), we have the \tilde{u}^n-q (q=1,...,k) terms from the material derivative which act as an explicit forcing term. Then, the pressure field is solved, decoupled from velocity, using Eq. 7.13 from NEK_doc.pdf. The computed pressure is then used to solve the Helmholtz system for the velocity field.

Does this seem correct? Specially the part of the pressure solve being decoupled from velocity. From the code, it definitely seems that way. Also, if the flow is incompressible, that means Q_T in eq 7.13 is zero, but shouldn't grad(Q_T) be zero as well?


Thanks for your attention,


Juan Diego



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