New unconditionally stable and high-accuracy finite element procedures for high-frequency solid-fluid coupled dynamic systems

To achieve high-precision computation of the dynamic response of saturated poroelastic media under high-frequency loads, this paper develops new, unconditionally stable and high-accuracy finite element procedures based on the u-w and u-U solid-fluid coupled dynamic systems. In the procedures the solution domain is spatially discretized using the standard finite element method, while a precise time step integration method is introduced for temporal domain computations. A matrix-based spectral analysis is conducted to validate the stability of the proposed procedures. Subsequently, an error estimation and convergence analysis of the procedures are performed. Four classical examples involving different load types with varying time dependences are used to validate the numerical performance of the proposed procedures. Through rigorous comparison with analytical/reference solutions, the proposed procedures have been convincingly demonstrated to accurately capture the relative motion between the solid skeleton and the pore fluid under high-frequency loads. Furthermore, the procedures have remarkable advantages in both accuracy and efficiency compared to the commonly employed Newmark schemes.