An immersed boundary-lattice Boltzmann method with hybrid multiple relaxation times for viscoplastic fluid-structure interaction problems

Existing studies of fluid-structure interaction (FSI) in ocean engineering mainly focus on the interaction between Newtonian fluids and structure. The FSI problems involving non-Newtonian fluids, especially viscoplastic fluids, have rarely been studied while the inherent dynamic behavior is not clear. In this paper, an immersed boundary-lattice Boltzmann method (IB-LBM) is developed for numerical investigations on FSI problems involving viscoplastic fluids. The present IB-LBM is integrated with a hybrid multiple relaxation times (MRT) scheme where different diagonal relaxation matrices are used for modeling Newtonian and non-Newtonian fluids, and are combined in a hybrid manner using a step function to achieve smooth transition for Newtonian to non-Newtonian fluid behavior at the FSI area. Four benchmark problems are used to validate the IB-LBM with hybrid MRT scheme. It is demonstrated that the numerical model can avoid numerical instability when modeling viscoplastic fluid flow and reduce the numerical boundary slip in the IB-LBM. The numerical model is further used to study the viscoplastic fluid flow around a fixed and moving cylinder (or particle). We show that the present IB-LBM with the hybrid MRT scheme is effective in modeling FSI involving viscoplastic fluids while the obtained phenomena are quite different from those with Newtonian fluids.