strange observations: 2
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 the my explanation, could be wrongk
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. |
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