Initialization Algorithms of a Rigid–Flexible Coupling Fluid–Structure Interaction System by Considering Length-and-Area Constraints

Rigid–flexible coupling fluid–structure interaction systems are expected to be future solutions for reducing energy lost in water. The dynamics of these systems is usually investigated via numerical simulations. However, in existing numerical works there is no accurate algorithm for the initialization of the flexible filament, which ensures both the length and area constraints, leading to inaccurate results or even severe numerical instabilities. We propose two alternative initialization algorithms, respectively, the “Trapezoidal arrangement” and the “Quartic curve arrangement”. The performances of both of these two algorithms are investigated in numerical simulations by using the immersed boundary method. The motion responses and force characteristics of the flexible filament are analyzed carefully, verifying the capability of the proposed algorithms. Specifically, “Quartic curve arrangement” is further recommended due to its good property of convergence.