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The interpolated bounce-back scheme and the immersed boundary method are thetwo most popular algorithms in treating a no-slip boundary on curved surfacesin the lattice Boltzmann method. While those algorithms are frequentlyimplemented in the numerical simulations involving complex geometries, such asparticle-laden flows, their performances are seldom compared systematicallyover the same local quantities within the same context. In this paper, wepresent a systematic comparative investigation on some frequently used and moststate-of-the-art interpolated bounce-back schemes and immersed boundarymethods, based on both theoretical analyses and numerical simulations of fourselected 2D and 3D laminar flow problems. Our analyses show that immersedboundary methods (IBM) typically yield a first-order accuracy when theregularized delta-function is employed to interpolate velocity from theEulerian to Lagrangian mesh, and the resulting boundary force back to theEulerian mesh. This first order in accuracy for IBM is observed for both thelocal velocity and hydrodynamic force/torque, apparently different from thesecond-order accuracy sometimes claimed in the literature. Another seriousproblem of immersed boundary methods is that the local stress within thediffused fluid-solid interface tends to be significantly underestimated. On theother hand, the interpolated bounce-back generally possesses a second-orderaccuracy for velocity, hydrodynamic force/torque, and local stress field. Themain disadvantage of the interpolated bounce-back schemes is its higher levelof fluctuations in the calculated hydrodynamic force/torque when a solid objectmoves across the grid lines. General guidelines are also provided for thenecessary grid resolutions in the two approaches in order to accuratelysimulate flows over a solid particle.

computers and fluids

A comparative study of immersed boundary method and interpolated  bounce-back scheme for no-slip boundary treatment in the lattice Boltzmann  method: Part I, laminar flows