AN APPLICATION OF THE CBS SCHEME IN THE FLUID-MEMBRANE INTERACTION
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摘要: 提出了一种不可压缩流体与弹性薄膜耦合问题的特征线分裂有限元解法. 首先, 给出了流场和结构的控制方程. 然后, 对流场、结构以及流固耦合的具体求解过程进行了描述. 其中, 流场求解采用改进特征线分裂方法和双时间步方法相结合的隐式求解方式, 并利用艾特肯加速法对每个时间步的迭代收敛过程进行了加速处理;结构部分的空间离散和时间积分分别采用伽辽金有限元方法和广义方法, 并通过牛顿迭代法对所得非线性代数方程组进行了求解;流场网格的更新采用弹簧近似法;流场、结构两求解模块之间采用松耦合方式.最后, 采用该方法对具有弹性底面的方腔顶盖驱动流问题进行了求解, 验证了算法的准确性和稳定性.此外, 计算结果表明艾特肯加速法可以显著地提高双时间步方法迭代求解过程的收敛速度.Abstract: A finite element scheme for the fluid-membrane interaction is proposed. First, governing equations for the incompressible flow and the elastic membrane are presented. Then, the proposed algorithm is discussed in detail. By this method, an improved characteristic-based split (CBS) scheme is combined with the dual-time stepping method and taken as the flow solver, and the Aitken method is applied to accelerate the convergence of the iteration. The governing equation of the structure is discretized by the Galerkin finite element method and the Generalized-α method, and the obtained nonlinear algebraic equations are solved by the Newton-Raphson method. Moreover, the spring analogy method is used for mesh moving, and the flow and structure solvers are loosely coupled. Finally, the proposed method is applied to a benchmark problem, namely, the driven cavity with flexible bottom, and the stability and accuracy of the proposed method are verified. In addition, it is found that the convergence rate of the flow solver can be increased significantly by the Aitken method.
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Key words:
- CBS /
- finite element method /
- fluid-structure interaction /
- dual-time stepping /
- Aitken method /
- generalized-α method
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