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

## TL;DR

This paper demonstrates that the spectral element method provides highly accurate and computationally efficient transient simulations of hydraulic systems, enabling real-time control and optimization in engineering applications.

## Contribution

It introduces the use of the spectral element method for hydraulic system simulations, highlighting its accuracy, efficiency, and suitability for real-time control applications.

## Key findings

- SEM yields highly accurate approximations at modest computational costs.
- Boundary conditions are imposed weakly using a stable upwind discretization.
- The method effectively simulates water hammer effects and pressure wave evolution.

## 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.