A VOS based Immersed Boundary-Lattice Boltzmann method for incompressible fluid flows with complex and moving boundaries

Abstract

A Volume of Solid (VOS) based Immersed Boundary-Lattice Boltzmann Method (IB-LBM) in the framework of the direct forcing based IB-LBM model has been developed in this work to simulate the fluid flow with complex and moving boundaries efficiently. In the present model, the concept of VOS is introduced to achieve the field extension to the solid phase, and a unified Lattice Boltzmann Equation (LBE) has been obtained to describe the fluid flow and the solid body motion consistently. To solve the resulting unified LBE, an efficient direct forcing model has been developed. Compared with the traditional surface based IB model with the direct forcing strategy, in the present work, the dependency of the Lagrangian grid to describe the body profile on the background Cartesian grid is removed by modelling the solid body with a Level-Set function. With such Level-Set description about the body surface, the VOS function can be obtained for the further field extension. With the present IB-LBM algorithm, the motion of the solid body can be enforced effectively without iterations about the forcing term compared with the implicit velocity correction or multiple velocity correction based IB algorithm, and flow penetration, which has been observed in the explicit velocity correction based IB model, can be reduced considerably. To achieve the velocity adjustment in the solid phase, an optimal forcing factor is recommended. With such optimal factor, the unphysical oscillation during force prediction can be well controlled. To verify the performance of the present model, a series of typical benchmarks, including the fluid flow caused by general shaped fixed or moving structures, hydrodynamic characteristics of thin-wall bodies undergoing specified motions and even more complex vortex induced vibrations, are conducted and the good agreements between the present results and the well-validated previous ones confirm the reliability and robustness of the present model.