A comparative study of direct‐forcing immersed boundary‐lattice Boltzmann methods for stationary complex boundaries

Abstract

SUMMARYIn this study, we assess several interface schemes for stationary complex boundary flows under the direct-forcing immersed boundary-lattice Boltzmann methods (IB-LBM) based on a split-forcing lattice Boltzmann equation (LBE). Our strategy is to couple various interface schemes, which were adopted in the previous direct-forcing immersed boundary methods (IBM), with the split-forcing LBE, which enables us to directly use the direct-forcing concept in the lattice Boltzmann calculation algorithm with a second-order accuracy without involving the Navier-Stokes equation. In this study, we investigate not only common diffuse interface schemes but also a sharp interface scheme. For the diffuse interface scheme, we consider explicit and implicit interface schemes. In the calculation of velocity interpolation and force distribution, we use the 2-and 4-point discrete delta functions, which give the second-order approximation. For the sharp interface scheme, we deal with the exterior sharp interface scheme, where we impose the force density on exterior (solid) nodes nearest to the boundary. All tested schemes show a second-order overall accuracy when the simulation results of the Taylor-Green decaying vortex are compared with the analytical solutions. It is also confirmed that for stationary complex boundary flows, the sharper the interface scheme, the more accurate the results are. In the simulation of flows past a circular cylinder, the results from each interface scheme are comparable to those from other corresponding numerical schemes.

PROTEUS: A coupled iterative force-correction immersed-boundary cascaded lattice Boltzmann solver for moving and deformable boundary applications

“…Therefore, as shown in our previous study [40], the overall accuracy of the surrounding flow field rather deteriorates as the number of iterations in the IBM increases. A similar result has been reported by Kang [34].…”

“…The apparent order of convergence is p = 1.992 for the CLBM, p = 1.998 for the BGK-LBM, p = 1.986 for the IDF-CLBM between the refining region (D = 20 − 80) and p = 1.958 for the IDF-CLBM between the refining region (D = 10 − 40). The L 2 -error is slightly lower for the BGK LBM and in agreement with the values reported in [34]. Wu and Shu [38] reported a convergence rate of 1.9 and Kang and Hassan [34] a convergence rate of 1.98.…”

“…The L 2 -error is slightly lower for the BGK LBM and in agreement with the values reported in [34]. Wu and Shu [38] reported a convergence rate of 1.9 and Kang and Hassan [34] a convergence rate of 1.98. Fig.…”

“…The iterative force correction IB scheme proposed by Zhang et al [36] is coupled with the CLBM. A few iterative IB schemes exist in the literature [34,35], where the velocity term in Eq. (9) is explicitly modified in order to account for the presence of external forces.…”

“…However, the non-slip boundary condition cannot be satisfied exactly by those methods. A few iterative IB schemes exist in the literature [34,35] that improve the accuracy of the prescribed boundary conditions. Zhang et al [36] proposed an iterative force correction scheme based on Cheng's external forcing term [37].…”