  A novel smooth immersed boundary method (IBM) based on a direct-forcing
formulation is proposed to simulate incompressible dense particle-laden flows.
This IBM relies on a regularization of the transfer function between the
Eulerian grid points (to discretise the fluid governing equations) and
Lagrangian markers (to represent the particle surface) to fulfill the no-slip
condition at the surfaces of the particles, allowing both symmetrical and
non-symmetrical interpolation and spreading supports to be used. This enables
that local source term contributions to the Eulerian grid, accounting for the
boundary condition enforced at a Lagrangian marker on the surface of a
particle, can be present on the inside of the particle only when this is
beneficial, for instance when the Lagrangian marker is near another particle
surface or near a domain boundary. However, when the Lagrangian marker is not
near another particle surface or a domain boundary, the interpolation and
spreading operators are locally symmetrical, meaning a ``classic'' IBM scheme
is adopted. This approach, named hybrid IBM (HyBM), is validated with a number
of test-cases from the literature. These results show that the HyBM achieves
more accurate results compared to a classical IBM framework, especially at
coarser mesh resolutions, when there are Lagrangian markers close to a particle
surface or a domain wall.
