Immersed Boundary-Finite Difference Lattice Boltzmann method through fluid–structure interaction for viscoplastic fluids

In this paper, an immersed boundary-finite difference lattice Boltzmann is proposed to simulate fluid–structure interaction of viscoplastic fluids. For simulation of the viscoplastic fluids, the Bingham model without any regularization of the constitutive law was applied. This method is the combination of Finite Difference Lattice Boltzmann for modeling the fluid motion and the effect of the solid structure is studied by the immersed boundary method (IBM). The accuracy of the method for the simulation of viscoplastic fluids has been validated in a lid-driven cavity. In addition, the fluid–structure interaction part was validated by a lid-driven cavity with an elastic bottom wall. The fluid–structure interaction in the presence of viscoplastic fluids for rigid and elastic cases have been studied in two different examples. To study the fluid–structure interaction for a rigid body with the viscoplastic fluid, a rosette-shaped in a lid-driven cavity has been studied. In the case of the elastic bodies, the lid-driven cavity filled with viscoplastic fluids by the elastic bottom wall is simulated. In these studies, the yielded/unyielded sections and streamlines have been depicted for high Rayleigh numbers. The effects of the unyielded development on the elastic/deformable parts are presented.