Are these rules by Patankar true?
Hi,
i was reading the book by Patankar called Numerical heat transfer and fluid flow. He stated some rules regarding the system of equations formed from the momentum equation (and poisson) which i wonder if they're true in all conditions: 1. all coefficients (a_p and neighbor a_nb) must always be positive. 2. a_p = summation of a_nb I'm now using FVM fractional step. Do these rules apply as well? thanks 
Re: Are these rules by Patankar true?
Oh btw, he also states that coarse grids during computation should still give a physically realistic solution, although it may not be an accurate one.
Is that true as well for all cases, assuming no errors in the programming and logic? thanks again 
Re: Are these rules by Patankar true?
These conditions are usually not true when using a high order scheme or in the presence of nonorthogonal terms. They are desirable because they will ensure that quantities remain bounded. That is, the value at P will lie somewhere between the maximum and minimum of its neighbours if there are no source terms.

Re: Are these rules by Patankar true?
I suspect it depends a bit on what is meant by physically realistic. For example, if the flow is close to a mode change, a coarse grid can predict the flow to be in in one mode whereas a fine grid can predict another.
In fact, this occurred in my first CFD prediction which was of a 2D swirling flow in a cylinder: the coarse grid predicted the jet to turn through 90 degrees and follow the head of the combustor whereas the fine grid predicted the jet to enter at an angle and form a closed recirculation between the jet and the head of the combustor. Of course, the coarse grid flow mode is correct for a slightly higher swirl number but not for the one specified. So is the coarse grid flow to be considered as realistic even though it is quite different from the fine grid flow? 
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