An IB-LBM implementation for fluid-solid interactions with an MLS approximation for implicit coupling

This paper presents a combination of the implicit immersed boundary (IB) method and the lattice Boltzmann method (LBM) for a fluid-solid interaction involving an immersed body with moving boundaries and complex geometries. In the implicit IB-LBM method, the flow is computed using LBM. The body force caused by the immersed body is not pre-calculated, but implicitly determined using a corrected velocity field that accurately satisfies the no-slip and no-penetration conditions on the interface between the fluid and solid. The information transfer is not using the traditional Dirac delta function and moving-least-square (MLS). But an improved MLS (IMLS) approximation has been developed to combined the implicit IB-LBM method, where the orthogonal function system with a weight function is used as the basis function and overcome these disadvantages of traditional MLS, in which it may cause numerical instabilities because the matrix inversion must be solved and the final equations system is easily ill-conditioned or singular. Several different flow problems (a two-dimensional flow past a static, rotating and oscillating cylinder, and the vortex-induced vibration of a cylinder as well as the free movement of flapping foil) are simulated to validate the accuracy and efficiency of the present implicit IB-LBM method. The simulation results show good agreement with previous numerical and experimental results. It is found that the present IB-LBM is efficient and reliable in dealing with fluid-solid interaction problems.