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Partitioned water hammer modeling using the block Gauss–Seidel algorithm
Journal of Fluids and Structures ( IF 3.4 ) Pub Date : 2021-03-18 , DOI: 10.1016/j.jfluidstructs.2021.103260
Huade Cao , Magdi Mohareb , Ioan Nistor

The monolithic classical and extended fluid-structural interaction water hammer models are based on the simplified ring hypothesis to characterize the structural radial response of the pipe under pressure. Recent work has shown that this approach predicts an unrealistic discontinuity in the pipe wall in the neighborhood of the pressure wave front. In order to remedy this limitation, the present study adopts a partitioned approach which couples a continuous shell-based finite element model with a water hammer fluid model based on the method of characteristics, within the context of the partitioned block Gauss–Seidel iterative algorithm. In order to demonstrate the validity of the block Gauss–Seidel implementation, the classical and extended water hammer models, normally solved using a monolithic approach, are solved under the present partitioned model and shown to predict pressure histories identical to those based on the monolithic solution. Comparisons are then conducted for the pressure histories as predicted by the classical, extended, and shell-based approaches. The study shows that the accuracy is optimized for integer values of the Courant number. By adopting either an optimal constant relaxation factor or the Aitken relaxation factor, the number of iterations needed for convergence was significantly reduced. The accuracy and computational efficiency are shown to highly depend on the number of subdivisions in the fluid model. In contrast, the number of subdivisions in the structural model, while influencing the computational efficiency, is shown not to influence the accuracy of the predictions. When applying the partitioned approach to the classical and shell-based models, the predicted pressure histories are found to be independent of the specified tolerance. In contrast, when applied to the extended model, the chosen tolerance has implications on the stability and accuracy of the solution.



中文翻译:

使用块高斯-赛德尔算法对水锤进行分区建模

整体式经典和扩展的流固耦合水锤模型基于简化的环假设,以表征压力下管道的结构径向响应。最近的工作表明,这种方法可以预测压力波前附近管壁的不连续性。为了弥补这一局限性,本研究采用了一种分区方法,该方法将基于壳的连续有限元模型与基于特征方法的水锤流体模型耦合,并在分区块高斯-赛德尔迭代算法的背景下进行。为了证明区块高斯-赛德尔(Gauss-Seidel)实施的有效性,通常使用整体方法求解的经典和扩展水锤模型,在当前的分区模型下求解,并显示出与基于整体解决方案的压力历史相同的压力历史。然后对经典,扩展和基于壳的方法所预测的压力历史进行比较。研究表明,对于Courant数的整数值,精度进行了优化。通过采用最佳常数松弛因子或Aitken松弛因子,收敛所需的迭代次数显着减少。结果表明,精度和计算效率高度依赖于流体模型中细分的数量。相反,结构模型中的细分数量虽然会影响计算效率,但不会影响预测的准确性。将分区方法应用于经典模型和基于壳的模型时,发现预测的压力历史与指定的公差无关。相反,当将其应用于扩展模型时,选择的公差会影响解决方案的稳定性和准确性。

更新日期:2021-03-18
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