一种分区式流固耦合界面平衡方法及其在强附加质量问题中的应用
A PARTITIONED FLUID-STRUCTURE INTERACTION INTERFACE EQUILIBRIUM METHOD AND ITS APPLICATION IN STRONG ADDED MASS PROBLEMS
-
摘要: 隐式有限体积/显式有限元分区式流固耦合方法兼具隐式流体求解器在大时间步与数值稳定性方面的优势, 以及显式固体求解器在处理大变形、非线性动力学问题时的计算精度与鲁棒性, 因此在多物理场分区式耦合中具有广泛应用前景. 然而在强附加质量效应下, 传统分区式流固耦合方法常出现数值计算不稳定的问题, 尤其当固体采用显式有限元求解时, 其小时间步和速度高频振荡会显著放大界面误差, 导致计算难以收敛. 针对这一关键难题, 本文提出一种面向强附加质量场景的隐式有限体积/显式有限元分区式流固耦合计算框架. 该方法在界面条件中引入位移-速度-力三场一致性约束, 有效解决传统位移-力两场耦合无法保证界面速度平衡的问题; 同时结合耦合时间窗口控制机制与基于径向基函数的高精度映射, 提高了数据传递的准确性与耦合过程的稳定性. 通过压力驱动弹性圆管膨胀和 Turek-Hron FSI3 典型算例的验证, 结果表明, 该方法在强附加质量的条件下仍能获得稳定收敛的结果, 界面振荡显著减弱, 结构位移和振荡频率均与参考解高度一致. 此外, 基于上述算例, 对提出的改进算法进行耦合计算效率的分析, 结果表明, 改进算法完成计算所需的总耦合时间相比传统算法分别缩短了73.4%和89.0%. 因此, 本文提出的耦合策略能够有效克服显式求解器参与耦合时的不稳定性, 实现强附加质量效应下流固耦合问题的稳定、高精度计算.Abstract: The implicit finite volume/explicit finite element partitioned fluid-structure interaction (FSI) method combines the advantages of implicit fluid solvers in terms of large time steps and numerical stability with the computational accuracy and robustness of explicit solid solvers in handling large deformations and nonlinear dynamic problems, thereby holding broad application prospects in multi-physics partitioned coupling. However, under strong added mass effects, traditional partitioned FSI methods often suffer from numerical instability issues. Particularly when explicit finite element solvers are employed for the solid domain, their small time steps and high-frequency velocity oscillations significantly amplify interface errors, leading to difficulties in convergence. To address this critical challenge, this paper proposes a partitioned implicit finite volume/explicit finite element computational framework tailored for strong added-mass scenarios. The method introduces displacement-velocity-force three-field consistency constraints into the interface conditions, effectively resolving the issue of traditional displacement-force two-field coupling failing to ensure interface velocity balance. Simultaneously, by incorporating a coupled time window control mechanism and high-precision mapping based on radial basis functions, the accuracy of data transfer and the stability of the coupling process are enhanced. Validation through pressure-driven elastic tube expansion and the Turek-Hron FSI3 benchmark cases demonstrates that the proposed method achieves stable and convergent results even under strong added mass conditions, with significantly reduced interface oscillations. The structural displacements and oscillation frequencies show high consistency with reference solutions. In addition, based on the above benchmark cases, the coupled computational efficiency of the proposed improved algorithm is analyzed. The results indicate that, compared with the conventional algorithm, the total coupled time required by the improved algorithm to complete the calculations is reduced by 73.4% and 89.0%, respectively. Consequently, the coupling strategy presented in this paper effectively overcomes the instability associated with explicit solvers in coupled simulations, enabling stable and high-precision computation of FSI problems under strong added mass effects.
下载: