I am solving turbulent pipe flow with an explicit MacCormack scheme and Wilcox k-omega model. The laminar version of the code had three distinct stability criteria which worked fine after implementation.

Now, the turbulent version seems to have stability problem. I tried to upgrade the stability criteria for the new set of equations, but it seems that solution eventually blows up. I have noticed the omega values grow very large through all the domain.

Does anybody know if there are new stability conditions with k-omega model, or I should merely extend MacCormack stability to the new equations?

Also I appreciate it if anyone can introduce a paper or book that discusses two-equation models stability.

  • $\begingroup$ In general, I don't recommend explicit timestepping for complicated flows, such as those requiring a turbulence model. If a coupled solver is infeasible, you should use a segregated solver (e.g. PISO). Also, which Wilcox k-omega model are you using? 2006? $\endgroup$
    – Paul
    Dec 10 '16 at 3:23
  • $\begingroup$ Thanks Paul. I understand that implicit may be a better option but at this point I cannot really change the whole scheme. I am using the older version of Wilcox model (1993) but it can be updated to the most recent one without much complication. Do you think the newer model is more stable? $\endgroup$ Dec 12 '16 at 15:43

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