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This paper presents transient numerical simulations of hydraulic systems inengineering applications using the spectral element method (SEM). Along with adetailed description of the underlying numerical method, it is shown that theSEM yields highly accurate numerical approximations at modest computationalcosts, which is in particular useful for optimization-based controlapplications. In order to enable fast explicit time stepping methods, theboundary conditions are imposed weakly using a numerically stable upwinddiscretization. The benefits of the SEM in the area of hydraulic systemsimulations are demonstrated in various examples including several simulationsof strong water hammer effects. Due to its exceptional convergencecharacteristics, the SEM is particularly well suited to be used in real-timecapable control applications. As an example, it is shown that the timeevolution of pressure waves in a large scale pumped-storage power plant can bewell approximated using a low-dimensional system representation utilizing aminimum number of dynamical states.

The spectral element method as an efficient tool for transient simulations of hydraulic systems