Hi, I wrote a small 2-D code using projection finite difference on staggered mesh for a N-S problem in a periodic square--means a square with periodic BC and periodic body force. I wrote the first version three years ago in Matlab and based on classnotes which were carefully examined by the intructor, classmates and me. now,I wrote a C++ version almost independent from the previous version but based on the same trustable formulation.

as we know, when delaing with a high Re, upwinding or something like is needed unless mesh resolution is resolved.

however, I use forward time and central difference and very course mesh for any Re situations, and I didn't observe what people claim(and I also believe). instead, both version of codes always give me at least qualitative convincing results.

I am pretty puzzled, does anyone want to shed a light?

here is my explanation which could be nonsense.

in the pivotal idea under upwinding is: when the convection wins over diffusion, the downstream point should not involve to interpolate the upstream point.

if such a rule is violated, the lesser we get inaccurate solutions, the more severely we could end up with a qualitatively wrong solution.

however, the periodic is a spacial situation. the downstream is also upstream somewhere.