Proceeding from balanced truncation-based parametric reduced order
models (BT-pROM) a matrix interpolation strategy is presented that allows the
cheap evaluation of reduced order models at new parameter sets. The method ex-
tends the framework of model order reduction (MOR) for high-order parameter-
dependent linear time invariant systems in descriptor form by Geuss (2013) by
treating not only permutations and rotations but also distortions of reduced order
basis vectors. The applicability of the interpolation strategy and different variants is
shown on BT-pROMs for gas transport in pipeline-networks
This work deals with the model order reduction (MOR) of a nonlinear-
parametric system of partial differential equations (PDEs). Applying a semidis-
cretization in space and replacing the nonlinearities by introducing new state vari-
ables, we set up quadratic-linear differential algebraic systems (QLDAE) and use a
Krylov-subspace MOR. The approach is investigated for gas pipeline modeling
Optimization and control of large transient gas networks require the fast
simulation of the underlying parametric partial differential algebraic systems. Sur-
rogate modeling techniques based on linearization around specific stationary states,
spatial semi-discretization and model order reduction allow for the set-up of para-
metric reduced order models that can act as basis sample to cover a wide parameter
range by means of matrix interpolations. However, the interpolated models are often
not stable. In this paper, we develop a stability-preserving interpolation method.
This paper provides a first contribution to port-Hamiltonian modeling of district heating networks. By introducing a model hierarchy of flow equations on the network, this work aims at a thermodynamically consistent port-Hamiltonian embedding of the partial differential-algebraic systems. We show that a spatially discretized network model describing the advection of the internal energy density with respect to an underlying incompressible stationary Euler-type hydrodynamics can be considered as a parameter-dependent finite-dimensional port-Hamiltonian system. Moreover, we present an infinite-dimensional port-Hamiltonian formulation for a compressible instationary thermodynamic fluid flow in a pipe. Based on these first promising results, we raise open questions and point out research perspectives concerning structure-preserving discretization, model reduction, and optimization.