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

Abstract

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 sometime claimed in the literature. An- * other 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.

Flow modulation by a few fixed spherical particles in a turbulent channel flow

“…It is worth mentioning that Xu & Subramaniam (2010) suggested two points were necessary to resolve a boundary layer around a particle for the immersed boundary method. However, it is reasonable to relax this criterion for the boundary treatment scheme used in the present simulations, which has a second-order accuracy (see Peng, Ayala & Wang 2019a). A validation test will be given in § 3 for the case of a uniform flow passing a fixed particle to justify this point.…”

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

“…The major problem of IBM, as we already indicated in a series of laminar flow tests (see part I of this study in Ref. [1]), is its inaccuracy in computing the local velocity gradients inside the diffused surface. This usually results in significantly underestimated local dissipation rate and viscous diffusion near the solid surface.…”

“…In the first part of this study [1], we compared the performances of several representative interpolated bounce-back schemes and immersed boundary algorithms in several laminar flow configurations. In general, for the no-slip boundary treatment in the lattice Boltzmann method (LBM), the interpolated bounce-back (IBB) schemes can result in more accurate velocity, hydrodynamic force/torque, and dissipation rate calculations than the immersed boundary method (IBM).…”

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In the first part of this study [1], we compared the performances of two categories of no-slip boundary treatments, i.e., the interpolated bounce-back schemes and the immersed boundary methods in a series of laminar flow simulations within the lattice Boltzmann method. In this second part, these boundary treatments are further compared in the simulations of turbulent flows with complex geometry to provide a next-level assessment of these schemes.

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Enhanced single-node lattice Boltzmann boundary condition for fluid flows

“…A subset of the linkwise group consists of techniques inspired by the half-way bounce-back (HW) rule [6,7] and commonly referred to as interpolated bounceback in recent literature [15,[22][23][24]. The most common HW extension to treat curved boundary conditions is the Bouzidi, Firdaouss, and Lallemand method (BFL) [25].…”