A coupled lattice boltzmann - immersed boundary method to model the behaviour of thin flexible structures in fluids

Abstract

This article presents a computational model to simulate the fluid interaction with moving flexible thin structures. The model is based on a combination of three numerical approaches, (i) a Lattice-Boltzmann solver for the flow equations, (ii) a finite difference method to solve the solid equation, and (iii) an Immersed Boundary Method (IBM) to model the coupling between the fluid and the solid. The present IBM, based on a direct-forcing approach, preserves the no-slip boundary condition at the interface fluid-solid, and allows using Cartesian uniform lattice encompassing both fluid and solid domains. The flexible solid is modelled as an elastic structure. The resulting governing equation involves thus tension and bending forces as internal forces, the inertial and gravity forces and finally the action of the fluid represented by the IBM forcing. The method is first validated with reference to an academic test case dealing with numerical simulations of a flapping flag in a free stream. The model shows results in good agreement with the published academic test case. The validation extends to the free motion of rag in a water tunnel and a qualitative comparison is available against experimental data performed with Digital Image Correlation (DIC). Finally, the present method is used to simulate the behaviour of flexible rags in the presence of highly rotating flows at high Reynolds number, as it is the case in stirred tanks.