A Lagrangian Point Approximation-Based Immersed Boundary–Lattice Boltzmann Method for FSI Problems Involving Deformable Body

Abstract

The proposed immersed boundary-lattice Boltzmann method (IB-LBM) with smoothed point interpolation method (S-PIM) has been verified to be an effective tool for simulating complex fluid–structure interaction (FSI) problems in previous works. LBM is employed as fluid solver with a simple solution process, S-PIM is used for largely deformable solids on the basis of gradient smoothing technique, and their combinations for FSI problems are achieved under the framework of immersed boundary method (IBM). IBM allows the coupling method to use a fixed fluid Euler mesh to avoid frequent mesh updates due to the movement or deformation of solids, whereas the introduction of fictitious fluid causes the internal mass effect and yields numerical errors. An extended Lagrangian point approximation approach has been proposed and introduced in IB-LBM with S-PIM to tackle this issue, and numerical experiments for FSI problems associated with rigid movement and large deformation of solids are investigated. It is verified that the accuracy and convergency properties of the present method are significantly improved compared with the original one in which the mass effect was not considered.