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

• Published in: Applied Mathematical Modelling Vol. 54; pp. 627 - 647
• Main Authors: Mennemann, J.-F., Marko, L., Schmidt, J., Kemmetmüller, W., Kugi, A.
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.02.2018; Elsevier BV
• Subjects: Approximation; Boundary conditions; Computer simulation; Control applications; Efficiency; Elastic waves; Electric power generation; Hydraulic equipment; Hydraulics; Hyperbolic differential equations; Low-dimensional numerical approximations; Method of characteristics; Numerical analysis; Optimization; Pressure waves; Pumped-storage power plant; Real-time capable model; Simulation; Spectral element method; Spectrum analysis; Upwind discretization; Water hammer; Water hammer simulations; Method of characteristics; Low-dimensional numerical approximations; Real-time capable model; Pumped-storage power plant; Water hammer simulations; Spectral element method; Upwind discretization; Pressure waves; Hyperbolic differential equations; Control applications
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2017.10.010

•Application of the spectral element method to transient hydraulic system simulations.•Derivation of the numerical method and discussion of important boundary conditions.•Careful numerical convergence analysis and simulations of water hammer effects.•Simulation of pressure waves in a large-scale pumped-storage power plant.•Low-dimensional semi-discretization suitable for optimal and model predictive control. 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.