[FMDenaro]

Originally Posted by moshe

I agree with what you say. Though, I have found a paper that does an incremental PM method (with a staggered grid) and they( use one sided approximations for P^{n} in the intermediate velocity field.

For a collocated grid, the one-sided does not work (I tried it for the sake of curiosity), and it would make sense.

* Calculating three-dimensional flows around structures and over rough terrain, C.W. Hirt, J.L Cook, JCP, 1972

I don’know this paper, maybe the correction step uses the one-sided gradient from the opposite direction? But owing to the staggering v^n+1 and v* are on the same nodes but pressure is not. Thus, the gradient is automatically centered.