Non-linear reduced order modeling for transport dominated fuid systems

Reduced order modeling aims to approximate large and complex dynamical systems with smaller ones to reduce simulation costs in the design or control processes of these systems. Standard linear mode-based model order reduction (MOR) can fail for transport dominated fluid systems (TDFS), because the underlying transport is often inherently non-linear. However, given that, in case of TDFS, the transported quantity changes slowly with respect to the advection speed, only few degrees of freedom (DOF) are required if the system is parametrized in a reference frame that moves with the transported quantity. This thesis aims to improve MOR of TDFS by implementing well adapted non-linear coordinate transformations that take the transport of the systems into account. The first part of this thesis addresses non-linear adaptive wavelet-filtering of flow systems to adjust the computational resources to the co-moving reference frame, already when generating the data. To enable MOR with the utilized adaptive data structure, a wavelet-based adaptive version of the proper orthogonal decomposition (POD) is proposed that balances error contributions of wavelet compression and POD truncation. The second part addresses non-linear reduction methods that compensate the transport by a shift or with help of an auxiliary field parametrizing the transport. Compared to the POD, the new methods allow for efficient decomposition of TDFS with only few DOF, while providing better physical insight into the system compared to neural autoencoder networks. The presented methodology enables the decomposition of reactive systems with topologically changing front structure, such as splitting or merging reaction fronts, that pose difficulties for many non-linear reduction methods. The last part studies the ability of the non-linear reduction methods to predict new system states using intrusive and non-intrusive reduced order models. In the case of the latter, manifold Galerkin projections with a tailored hyper-reduction strategy are utilized, enabling rapid simulations of reactive flows. Given that reactive systems are considered challenging for classical MOR applications, this contribution is an essential building block for future applications.

Author dc:creator

• Krah, Philipp Louis

Advisors dc:contributor.advisor

• Reiss, Julius
• Mehrmann, Volker

Licence dc:rights.uri

• https://creativecommons.org/licenses/by/4.0/

Language dc:language.iso

en

Identifier URI

https://doi.org/10.14279/depositonce-16974

OAI identifier oai:identifier

oai:depositonce.tu-berlin.de:11303/18181