Accuracy improvement of immersed boundary-lattice Boltzmann and finite element method by iterative velocity correction

Abstract

In an analysis of the fluid–structure interaction (FSI) problem, the non-slip boundary condition at solid walls cannot be accurately satisfied by the conventional immersed boundary-lattice Boltzmann coupling schemes due to insufficient interpolation accuracy. To solve this problem, an improved iterative velocity correction procedure for the immersed boundary-lattice Boltzmann coupling scheme is proposed by introducing a modified velocity operator. The particle distribution function was modified at each time step, and the evolution governing equation of the multiple relaxation time-lattice Boltzmann method was performed. A numerical framework for coupling lattice Boltzmann and finite element methods for transient problems involving FSI was established, and the iterative velocity correction immersed boundary method was used for the partitioned approach. The solid structure was discretized with the finite element method, while the single-component fluid flows were simulated with the lattice Boltzmann method. An FSI benchmark model was employed to verify the efficiency of the proposed coupling method. The results show that the developed method guarantees the non-slip boundary condition and maintains the convergence rate of the conventional immersed boundary method. In viscous flow and strong shearing flow, the accuracy of both stationary and moving solid boundaries is obviously improved.