饱和多孔弹性杆流固耦合动力响应的保结构算法

Structure-Preserving Algorithm for Fluid-Solid Coupling Dynamic Responses of Saturated Poroelastic Rods

研究了不可压饱和多孔弹性杆的流固耦合动力响应问题.基于多孔介质理论,根据多孔介质流固混合物动量方程、孔隙流体动量方程及体积分数方程,建立流固耦合不可压饱和多孔弹性杆的轴向振动方程;引入正则变量,构造饱和多孔弹性杆轴向振动方程的广义多辛保结构形式、广义多辛守恒律及广义多辛局部动量误差;采用中点Box离散方法得到轴向振动方程的广义多辛离散格式、广义多辛守恒律数值误差及局部动量数值误差;数值模拟不可压饱和多孔弹性杆的轴向振动过程及流相渗流速度分布,考察了流固两相耦合系数对轴向振动过程及广义多辛守恒律误差和局部动量误差的影响.结果表明,已构造的广义多辛保结构算法具有很高的精确性和长时间的数值稳定性.

Based on the momentum balance equations for 3D fluid-solid mixture, the momen- tum 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. Com- pared 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 muiti-symplectic conservation law and its corresponding conditions were presented. Meanwhile, the numerical errors of the generalized multi-symplectic conservation law and the generalized muiti-symplectic local momentum were both investigated for different dimensionless parameters. The results show that the proposed generalized multi-symplectic structure-preser- ving scheme has long-time numerical stability and good conservation properties.