  The interpolated bounce-back scheme and the immersed boundary method are the
two most popular algorithms in treating a no-slip boundary on curved surfaces
in the lattice Boltzmann method. While those algorithms are frequently
implemented in the numerical simulations involving complex geometries, such as
particle-laden flows, their performances are seldom compared systematically
over the same local quantities within the same context. In this paper, we
present a systematic comparative investigation on some frequently used and most
state-of-the-art interpolated bounce-back schemes and immersed boundary
methods, based on both theoretical analyses and numerical simulations of four
selected 2D and 3D laminar flow problems. Our analyses show that immersed
boundary methods (IBM) typically yield a first-order accuracy when the
regularized delta-function is employed to interpolate velocity from the
Eulerian to Lagrangian mesh, and the resulting boundary force back to the
Eulerian mesh. This first order in accuracy for IBM is observed for both the
local velocity and hydrodynamic force/torque, apparently different from the
second-order accuracy sometimes claimed in the literature. Another serious
problem of immersed boundary methods is that the local stress within the
diffused fluid-solid interface tends to be significantly underestimated. On the
other hand, the interpolated bounce-back generally possesses a second-order
accuracy for velocity, hydrodynamic force/torque, and local stress field. The
main disadvantage of the interpolated bounce-back schemes is its higher level
of fluctuations in the calculated hydrodynamic force/torque when a solid object
moves across the grid lines. General guidelines are also provided for the
necessary grid resolutions in the two approaches in order to accurately
simulate flows over a solid particle.
