non linear terms in OF
Dear OpenFoamers
I understand that nonorthogonality is handled through deferred correction that solves the same equation repeatedly with different source term. But how are other sorts of nonlinearity such as those from higher order convection schemes as QUICK, explicit boundary conditions such as slip, turbulence models etc handled? I do not see a loop like the case for nonorthogonality for momentum prediction equation or ke turbulence models for instance. Are all of them handled implicitly? For steady state problems it seems to me that the outer loop takes care of all nonlinearity but for transient problems shouldn't there be another loop to make sure that we have a converged solution at each time step before going to the next. I appreciate it if someone can shed a light on this. Thanks 
Hi, the non linearities are treated by using the previous timestep information. This is the case for momentum predictor equation, TVD, schemes, etc.
Regards. 
Hi,
I still don't understand how the new equation with improved corrections are iteratively solved just like the case of non orthogonal corrections in pressure. I give the outline of icoFoam below without nonorthogonal loop. I appreciate if you can point out the code takes care of other deffered corrections due to TVD schemes for instance. Code:
icoFoam() { For steady state solution I can understand that the timesteps loop will take care of corrections in div(phi,U) but for transient solutions I just don't see it. I am definately missing something so I appreciate if anyone can point it out. 
Hi, much of this nonlinearities are treated but by the timestep, which must be such that Co<1. Nevertheless, you have solvers with "outer corrections" based in the pimple loop like pimpleFoam. In these solvers in each timestep you have an outer loop over all the equations as you want to find.
Regards. 
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Sorry to bother you. Why we need Co < 1 to get nonortho correction?

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From what I understood, all explicit terms (including tvd shemes and nonorthogonality) are treated using deferred correction. For icoFoam and simpleFoam, the iteration over a timestep is done only once by default. Therefore if you use large time step, you accept inaccurate solutions at each time step. OTOH PimpleFOAM has an outer loop that does corrections multiple times. I guess that with Co<1, one deferred correction step is enough probably because time discretization term swamp the secondary corrections. I do not think there is a theory similar to why we need to specify Co<1 when use explicit time discretization schemes such as crankNicholson. Someone can correct if I am wrong as I am not knowledgeable in OF. Hope this helps. 
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