Transregio/CRC 154: Mathematical Modelling, Simulation and Optimization on the Example of Gas Networks
Subproject A01: Global Methods for Stationary and Instationary Gastransport
This project will develop methods for the global solution of nonlinear integer optimization problemes with ODEs or PDEs, on the example of stationary and instationary gastransport. In addition this is performed for topology planing problems. Main issue is the derivation of convex relaxations of instationary problems, based on Riemann invariants or first-discretize-then-optimize models. On basis of the stationary case the mixing of different gases is incorporated, e.g., of hydrogen into natural gas, for gas transport as well as topology optimization. Acyclicity of flows can be exploited in several contexts in this subproject.
Contact: Pascal Börner, Marc Pfetsch, Stefan Ulbrich
Subproject A02: Analysis and consistent numerical approximation of optimization problems for hyperbolic PDE models of gas networks
The project A02 develops a detailed mathematical analysis and consistent numerical discretization of optimal control problems for systems of hyperbolic balance laws. The results will be used for the computation of convergent discrete gradients for derivative-based optimization methods. Here, results for scalar equations from the previous phases of the project are extended to the case of systems. In a further step, higher order schemes and a-priori error estimators for the optimal control of entropy solutions will be analyzed.
Contact: Jannik Breitkopf, Stefan Ulbrich
Subproject A09: Online optimization of potential-based flow networks
Contact: Annette Lutz, Yann Disser
