Stephan GersterInstitut für Geometrie und Praktische Mathematik
phone:+49 241 80-94 559
TeachingMathematik I & II (für Bau-, Umwelt-, Wirtschafts-, Verkehrsingenieurwesen)
- Stochastic Galerkin Formulations for Hyperbolic Balance Laws Stochastic Galerkin methods reformulate a stochastic system as a deterministic one that describes the evolution of polynomial chaos modes. So far, results for general hyperbolic systems are not available. A problem is posed by the fact that the deterministic Jacobian of the projected system differs from the random Jacobian of the original system and hence hyperbolicity is not guaranteed. We show for some fluid-dynamic equations that hyperbolicity can be guaranteed.
- Feedback Control for Hyperbolic Systems Physical systems such as water and gas networks are usually operated in a state of equilibrium and feedback control is employed to damp small perturbations over time. We consider flow problems on networks, described by hyperbolic balance laws, and analyze their stability.
- Stochastic Fluctuations in Energy Networks The ability of gas-fired power plants to ramp quickly is used to balance fluctuations in the power grid caused by renewable energy sources, which in turn leads to time-varying gas consumption and fluctuations in the gas network. Since gas system operators assume nearly constant gas consumption, there is a need to assess the risk of these stochastic fluctuations. We discuss control policies to damp fluctuations in the network.
Publication: Stephan Gerster, Michael Herty, Aleksey Sikstel, Hyperbolic Stochastic Galerkin Formulation for the p-System, preprint, 2018
Publication: Stephan Gerster, Michael Herty, Discretized Feedback Control for Hyperbolic Balance Laws, preprint, 2017
Conferences and Research Stays
- SIAM Conference on Computational Science and Engineering, Spokane, USA, 2019
- IFIP Conference on System Modelling and Optimization, Essen, Germany 2018
- 20th European Conference on Mathematics for Industry, Budapest, Hungary, 2018
- GAMM Annual Meeting, Munich, Germany 2018
- Research stay at Los Alamos National Laboratory, Los Alamos, USA, 2018
- 2nd Physics Informed Machine Learning Conference, Santa Fe, USA, 2018
- Conference on Computational Engineering Science, Aachen, Germany, 2017
- Grid Science Winter School and Conference, Santa Fe, USA, 2017