Direct-forcing immersed-boundary method: A simple correction preventing boundary slip error

The boundary slip error resulting from the interpolation/spreading non-reciprocity of direct-forcing immersed-boundary method is analyzed based on a simple and generic theoretical framework. In explicit implementations, scales with Courant number, as predicted by analysis confirmed lattice-Boltzmann simulation results. Using an analytical approximation error, force can be corrected in order to prevent flow penetration. This priori correction leads major improvement no-slip condition while avoiding any additional computational time or implementation effort.