Numerical study of interactions between Bingham fluids and flexible structures using the immersed boundary-lattice Boltzmann method

This paper studies the interactions between Bingham fluids and flexible structures under an immersed boundary lattice-Boltzmann framework. The objective of this paper is to understand the rheology effects of Bingham fluids on the structure responses and the flow characteristics within Bingham fluids-structure interactions. To this end, a numerical algorithm that integrates the lattice Boltzmann method and the smoothed point interpolation method is proposed. Alongside this, a hybrid multiple relaxation time scheme in the framework of the immersed boundary-lattice Boltzmann method is used to improve the numerical accuracy and stability. Then, the numerical algorithm is applied to three typical fluid-structure interactions cases in both Newtonian and Bingham fluids regarding an elastic beam, a self-induced elastic beam attached to a circular cylinder and a self-propelled fishlike body. Numerical results highlight that the yield stress of Bingham fluids influences predominantly on the structure responses, such as the solid deformation, the oscillation amplitude, the oscillation period, and the swimming velocity. In addition, the yielded/unyielded zones' evolution process of the Bingham fluids-structure interaction is also identified in this paper.