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Lagrangian finite element modelling of dam-fluid interaction: Accurate absorbing boundary conditions

机译：大坝与流体相互作用的拉格朗日有限元建模：精确的吸收边界条件

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摘要

The dynamic dam-fluid interaction is considered via a Lagrangian approach, based on a fluid finite element (FE) model under the assumption of small displacement and inviscid fluid. The fluid domain is discretized by enhanced displacement-based finite elements, which can be considered an evolution of those derived from the pioneering works of Bathe and Hahn [Bathe KJ, Hahn WF. On transient analysis of fluid-structure system. Comp Struct 1979;10:383-93] and of Wilson and Khalvati [Wilson EL, Khalvati M. Finite element for the dynamic analysis of fluid-solid system. Int J Numer Methods Eng 1983; 19:1657-68]. The irrotational condition for inviscid fluids is imposed by the penalty method and consequentially leads to a type of micropolar media. The model is implemented using a FE code, and the numerical results of a rectangular bidimensional basin (subjected to horizontal sinusoidal acceleration) are compared with the analytical solution. It is demonstrated that the Lagrangian model is able to perform pressure and gravity wave propagation analysis, even if the gravity (or surface) waves are dispersive. The dispersion nature of surface waves indicates that the wave propagation velocity is dependent on the wave frequency. For the practical analysis of the coupled dam-fluid problem the analysed region of the basin must be reduced and the use of suitable asymptotic boundary conditions must be investigated. The classical Sommerfeld condition is implemented by means of a boundary layer of dampers and the analysis results are shown for the cases of sinusoidal forcing. The classical Sommerfeld condition is highly efficient for pressure-based FE modelling, but may not be considered fully adequate for the displacement-based FE approach. In the present paper a high-order boundary condition proposed by Higdom [Higdom RL. Radiation boundary condition for dispersive waves. SIAM J Numer Anal 1994;31:64-100] is considered. Its implementation requires the resolution of a multifreedom constraint problem, defined in terms of incremental displacements, in the ambit of dynamic time integration problems. The first- and second-order Higdon conditions are developed and implemented. The results are compared with the Sommerfeld condition results, and with the analytical unbounded problem results. Finally, a number of finite element results are presented and their related features are discussed and critically compared.
机译：在小位移和无粘性流体的假设下，基于流体有限元（FE）模型，通过拉格朗日方法考虑了动态坝-流体相互作用。流体域通过基于位移的增强有限元离散化，可以认为是有限元的演化，这些有限元是从Bathe和Hahn [Bathe KJ，Hahn WF。关于流体结构系统的瞬态分析。 Comp Struct 1979; 10：383-93]和Wilson和Khalvati [Wilson EL，Khalvati M.用于流固系统动力学分析的有限元。 Int J Numer Methods Eng 1983； 19：1657-68]。粘性流体的不旋转条件是由罚分法施加的，因此导致了一种微极性介质。该模型使用FE代码实现，并将矩形二维盆地的数值结果（受水平正弦加速度影响）与解析解进行了比较。结果表明，即使重力（或表面）波是分散的，拉格朗日模型也能够执行压力和重力波传播分析。表面波的色散特性表明，波的传播速度取决于波的频率。为了对耦合的水坝问题进行实际分析，必须减少盆地的分析区域，并且必须研究使用合适的渐近边界条件。经典的Sommerfeld条件是通过阻尼器的边界层实现的，并给出了正弦强迫情况下的分析结果。经典的Sommerfeld条件对于基于压力的有限元建模非常有效，但对于基于位移的有限元方法可能并不足够。在本文中，Higdom提出了一个高阶边界条件[Higdom RL。色散波的辐射边界条件。 SIAM J Numer Anal 1994； 31：64-100]。它的实现要求解决多自由约束问题，该问题以动态时间积分问题为范围，以增量位移来定义。一阶和二阶希格登条件被开发和实现。将结果与Sommerfeld条件结​​果以及解析的无穷问题结果进行比较。最后，给出了一些有限元结果，并对它们的相关特征进行了讨论和严格比较。

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