[Feng]

I am using Large eddy simulation to simulate flow over a three-dimensional hill with a terrain following coordinate system. I need to calculate area-averaged (horizontal plane averaged) total stress (resolved+sgs) in the xz direction (x is the streamwise direction).

I have <uw> <u> <w> <txz> (txz is sgs stress) values for every grid points (<> means time-avergaed here). For the area-averaged stress, should I calculate tao=<uw>-<u><w>+<txz> for every grid point first, then interpolate tao to horizontal planes, and then take the average to get the stress I wanted or I should first interpolate <uw>,<u>,<w>,<txz> to horizontal planes respectively, then area average these four and then calculate calculate [<uw>]-[<u>][<w>]+[<txz>] to get the stress I need ([] means horizontally averaged values).

Results from these two methods are very different, I am confused which one is correct

Thanks a lot