Boundary induced non linearities at small Reynolds Numbers

We investigate the influence of boundary slip velocity in Newtonian fluids at finite Reynolds numbers. Numerical simulations with Lattice Boltzmann method (LBM) and Finite Differences method (FDM) are performed to quantify the effect of heterogeneous boundary conditions on the integral and local properties of the flow. Non linear effects are induced by the non homogeneity of the boundary condition and change the symmetry properties of the flow inducing an overall mean flow reduction. To explain the observed drag modification, reciprocal relations for stationary ensembles are used, predicting a reduction of the mean flow rate from the creeping flow to be proportional to the fourth power of the friction Reynolds number. Both numerical schemes are then validated within the theoretical predictions and reveal a pronounced numerical efficiency of the LBM with respect to FDM.