Structure-preserving algorithm for fluid-solid coupling dynamic responses of saturated poroelastic rods

Based on the momentum balance equations for 3D fluid-solid mixture, the momentum balance equations for pore fluid and the balance equations of volume fraction, the fluid-solid coupling axial vibration equations for saturated poroelastic rods were established. With the orthogonal variables, a 1st-order multi-symplectic structure-preserving form of the axial vibration equations was built firstly, then the generalized multi-symplectic conservation law and the errors of the modified local momentum were derived. The axial displacement profile of the solid skeleton and the seepage velocity profile of the pore fluid were obtained, where the effect of the dissipation constant on the axial dynamic responses was also revealed numerically. Compared with the analytical solution derived with the variable-separating method, this generalized multi-symplectic structure-preserving scheme has excellent validity and high accuracy. The generalized multi-symplectic conservation law and its corresponding conditions were presented. Meanwhile, the numerical errors of the generalized multi-symplectic conservation law and the generalized multi-symplectic local momentum were both investigated for different dimensionless parameters. The results show that the proposed generalized multi-symplectic structure-preserving scheme has long-time numerical stability and good conservation properties.