TP C02: Hierarchische PDAE-Surrogate-Modellierung und stabile PDAE-Diskretisierung zur Simulation großer instationärer Gasnetzwerke

Third Party Funds Group - Sub project

Overall project details

Overall project: TRR 154: Mathematical Modelling, Simulation and Optimisation Using the Example of Gas Networks


Project Details

Project leader:
Prof. Dr. Nicole Marheineke

Project members:
Björn Liljegren-Sailer

Contributing FAU Organisations:
Professur für Angewandte Mathematik (Mathematische Modellierung)

Funding source: DFG / Sonderforschungsbereich / Transregio (SFB / TRR)
Start date: 01/04/2014
End date: 30/04/2018


Abstract (technical / expert description):

This subproject focuses on the development and analysis of models
and methods for a stable and fast simulation of huge transient
gasnetworks, which will also be used for an efficient parameter
optimization and control of the network. The main aspects are the
development of a numerical discretization in space and time that is
adjusted to the topology of the network as well as a hierarchical
modelling of several elements (pipes, compressors ect.) and
subnet-structures.

For the complete network as a coupled system of nonlinear partial
differential equations and algebraic equations (PDAE) we consider
approximations by a spatial semi-discretization. We strive for a
determination and classification of topology depending critera for the
index of the time dependend differential algebraic system. Topology- and
controldepending spatial discretizations will be determinded, that lead
to DAEs of index 1, in order to diminish the influence of perturbations
for the DAE system best possible. Moreover we want to establish a
perturbationanalysis as well as existence and uniquness results for die
PDAE-model. Here, the time and pressure/flow-depending control-states
that can change the variable structure (dynamic as well as static) for
certain points in time and for certain states of the network will be a
major challange.

As a method, we focus on a Galerkin-Approach in space followed by a
discretization in time of the resulting DAE with implicit or
semi-implicit methods respectively, such that the algebraic constraints
hold for the current point in time. Continuationmethods and
space-mapping techniques are used for the initialisation to guarantee
good convergence behaviour. Furthermore, to satisfy the control
requirements of the systems and to enable the handling of huge networks,
this subproject aims at the enhancement of the simulation speed. It is
planed to detect characteristic subnetstructures and derive parameter
dependen transient surrogate models with suitable error estimators by
applying model order reduction methods. These input-ouput models as
dynamic systems of ODEs will be coupled with die complete PDAE model in
one model hierarchy.


External Partners

Humboldt-Universität zu Berlin

Last updated on 2019-01-08 at 15:48