A momentum exchange-based immersed boundary-lattice Boltzmann method for simulating a flexible filament in an incompressible flow

A momentum exchange-based immersed boundary-lattice Boltzmann method, which is used to solve the fluid–flexible-structure-interaction problem, is introduced in this paper. The present method, overcoming the drawback of the conventional penalty method employing a user-defined spring parameter for calculating the interaction force induced by the immersed boundary, uses a concept of momentum exchange on the boundary to calculate the interaction force. Numerical examples, including a laminar flow past a circular cylinder, a filament flapping in the wake of the cylinder, a single filament with the upstream end fixed flapping in a uniform flow field and the interaction of two filaments flapping in the flow, are provided to validate the present method and to illustrate its capability of dealing with the fluid–flexible-structure-interaction problem. Particularly, with considering the filament mass effects, a single filament with a fixed centre point undergoing a bending transition in the flow is firstly studied in the present paper. Our numerical results compare qualitatively well to experimental results. For a single filament with a fixed centre point, it is found that the flexure modulus has a significant effect on the final state of the filament: for a larger flexure modulus, the filament reaches the ‘quasi-steady’ state finally; for a small flexure modulus, the filaments will be flapping like two filaments.