Modeling and structure-preserving model reduction of a nonlinear flow problem on networks
Björn Liljegren-Sailer
Transfer Group
Structure-preserving discretization has been an active area of research for several decades. By preserving or
mimicking relevant geometric structures such as, e.g., conservation laws, passivity or symplecticities,
unphysical solution behavior and numerical instabilities can be avoided in many cases. The development of
structure-preserving model reduction methods is a more recent topic.
In this talk, we consider nonlinear partial differential equations on networks that are relevant for the
modeling of gas transportation systems. We aim for online-efficient surrogate models obtained by snapshot-
based model order reduction and complexity reduction methods. The Galerkin-type approximations
considered are motivated by energy-based modeling concepts, such as the port-Hamiltonian formalism and
the Legendre transformation. They are mass-conservative and energy-dissipative under certain compatibility
conditions, and a well-posedness result can be derived for them.
A special focus of the talk is on the implementation of the snapshot-based reduction steps. We face
constrained data approximation problems as opposed to the unconstrained training problems in most
conventional model reduction methods.