Title: The spectral element method as an efficient tool for transient simulations of hydraulic systems,
Abstract: This paper presents transient numerical simulations of hydraulic systems in
engineering applications using the spectral element method (SEM). Along with a
detailed description of the underlying numerical method, it is shown that the
SEM yields highly accurate numerical approximations at modest computational
costs, which is in particular useful for optimization-based control
applications. In order to enable fast explicit time stepping methods, the
boundary conditions are imposed weakly using a numerically stable upwind
discretization. The benefits of the SEM in the area of hydraulic system
simulations are demonstrated in various examples including several simulations
of strong water hammer effects. Due to its exceptional convergence
characteristics, the SEM is particularly well suited to be used in real-time
capable control applications. As an example, it is shown that the time
evolution of pressure waves in a large scale pumped-storage power plant can be
well approximated using a low-dimensional system representation utilizing a
minimum number of dynamical states.