An efficient multiscale method for 2D dynamic analysis of the coupling system of fluid and heterogeneous structure

The two-dimensional dynamic analysis of the coupling system of fluid and heterogeneous structure is investigated by using an efficient multiscale computational method. The macroscopic equations of the coupling system are deduced. The liquid pressure-based and solid displacement-based coarse elements are employed for the numerical simulation. In addition, the piecewise oscillating boundary condition and the Lagrange polynomial boundary condition are used to construct the displacement base function of the solid coarse element and the pressure base function of the liquid coarse element, respectively. Furthermore, the generalized mode base functions are introduced into the multiscale base functions of both the fluid and structure coarse elements to capture the dynamic effect of the coarse element and improve the computational accuracy effectively. The predictor–corrector scheme is applied to solve the macroscopic transient response equation of the coupling system. Finally, several numerical examples are carried out to verify the validity and high efficiency of the proposed multiscale method by comparison with the fine-scale reference solutions.