Boundary induced nonlinearities at small Reynolds numbers

We investigate the importance of boundary slip at finite Reynolds numbers for mixed boundary conditions. Nonlinear effects are induced by the non-homogeneity of the boundary condition and change the symmetry properties of the flow with an overall mean flow reduction. To explain the observed drag modification, exact reciprocal relations in the presence of heterogeneous boundary conditions are derived. The small-Reynolds-number limit predicts a reduction of the mean flow rate from the creeping flow to be proportional to the second power of the Reynolds number. To further support our theoretical analysis, numerical simulations with the lattice Boltzmann method (LBM) and finite difference method (FDM) are performed and reveal a pronounced numerical efficiency of LBM with respect to FDM.