Computational cost  Re ^3
Hi,
I just started reading a textbook on cfd and found this statement The computational cost for a DNS increases as the cube of the Reynold number. Can someone please explain how this order of magnitude estimate was arrived at. Thanks 
a very quick (and brutal) estimation can be done assuming that you have to work with a cell Reynolds number = O(1). Therefore, for each direction, you have
Reh = u h /ni = ReL h/L = ReL / N = O(1) 
From the michujo estimate, the exact Re^3 scaling is then reached when considering an unitary Courant number (as most DNS methods rely on explicit convection schemes). As a result, the time step also scales like the grid step and the final estimate is reached.

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