  A boundary thickening-based direct forcing (BTDF) immersed boundary (IB)
method is proposed for fully resolved simulation of incompressible viscous
flows laden with finite size particles. By slightly thickening the boundary
thickness, the local communication between the Lagrangian points on the solid
boundary and their neighboring fluid Eulerian grids is improved, based on an
implicit direct forcing (IDF) approach and a partition-of-unity condition for
the regularized delta function. This strategy yields a simple, yet much better
imposition of the no-slip and no-penetration boundary conditions than the
conventional direct forcing (DF) technique. In particular, the present BTDF
method can achieve a numerical accuracy comparable with other representative
improved methods, such as multi-direct forcing (MDF), implicit velocity
correction (IVC) and the reproducing kernel particle method (RKPM), while its
computation cost remains much lower and nearly equivalent to the conventional
DF scheme. The dependence of the optimum thickness value of boundary thickening
on the form of the regularized delta functions is also revealed. By coupling
the lattice Boltzmann method (LBM) with BTDF-IB, the robustness of the present
BTDF IB method is demonstrated using numerical simulations of creeping flow
(Re=0.1), steady vortex separating flow (Re=40) and unsteady vortex shedding
flow (Re=200) around a circular cylinder.
