Dear Xu Yang,
thanks for your question.
For wet-node boundary approaches in general, please see the evergreen book by Krüger et al. ‘The Lattice Boltzmann Method: Principles and Practice’ from 2017.
As far as I know, there’s no explicit reference for the procedure labeled as ‘fneqMethod=2’.
Anyway, I’ll try to explain its name term by term:
(1) regularization (in the sense of the regularized lattice Boltzmann collision scheme) means that we reconstruct the fneq’s from the non-equilibrium momentum flux (named ‘Pi’) which in turn can be approximated via the rate of strain tensor according to CE analysis.
(2) second order finite differences are used for computing the velocity gradient which is necessary for the strain rate in (1).
For implementational details, please see https://www.openlb.net/DoxyGen/html/dc/dbc/wallFunctionBoundaryPostProcessors3D_8hh_source.html from line 760 onwards.