The simulation of gas transportation networks becomes increasingly more important as its
use-cases broaden to more complex applications. Classically, the purpose of the gas …

To counter the volatile nature of renewable energy sources, gas networks take a vital role.
But, to ensure fulfillment of contracts under these circumstances, a vast number of possible …

We study the modeling and simulation of gas pipeline networks, with a focus on fast
numerical methods for the simulation of transient dynamics. The obtained mathematical …

The question of what conditions should be set at the nodes of a discrete graph for the wave
equation with discrete time is investigated. The variational method for the derivation of these …

The Riemann problem for coupled Euler equations is analysed. The coupling conditions at a
steady interface impose continuous pressure and temperature while momentum differs. The …

Differential equations on metric graphs can describe many phenomena in the physical world
but also the spread of information on social media. To efficiently compute the optimal setup …

We extend the index-aware model order reduction method (IMOR) to differential-algebraic
equations (DAEs) arising from gas transport networks, which have a tractability index of one …

We propose a novel deep learning (DL) approach to solve one-dimensional non-linear
elliptic, parabolic, and hyperbolic problems on graphs. A system of physics-informed neural …

This thesis is devoted to the study of analytic properties of solutions to coupled conservation
laws and associated numerical methods. The focus is put on two particular problems:(i) a …

To counter the volatile nature of renewable energy sources, gas networks take a vital role.
But, to ensure fulfillment of contracts under these circumstances, a vast number of possible …