Partitioned water hammer modeling using the block Gauss-Seidel algorithm

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.