Jiaqi,

the algorithm in step-35 is the one that is proposed in 
"L. Timmermans, P. Minev, and F. Van De Vosse, “An approximate projec-
tion scheme for incompressible flow using spectral elements”, International
journal for numerical methods in fluids, vol. 22, no. 7, pp. 673–688, 1996."

The velocity that is solved for is the auxiliary one. You can recover the 
"true"
weakly divergence-free velocity by the correction you mentioned.
Notice that the divergence-free velocity is eliminated from the equation 
for the
auxiliary velocity.

Best,
Daniel

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