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Topological solvability analysis and its application to liquid flow networks coupled to Functional Mock‐up Units
Author(s) -
Baum Ann-Kristin,
Kolmbauer Michael,
Offner Günter,
Pöchtrager Bernhard
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900054
Subject(s) - uniqueness , black box , topology (electrical circuits) , flow (mathematics) , mathematics , class (philosophy) , extension (predicate logic) , unit (ring theory) , graph , computer science , differential (mechanical device) , theoretical computer science , mathematical analysis , physics , combinatorics , artificial intelligence , geometry , mathematics education , thermodynamics , programming language
We present a unified topological analysis for physical networks coupled to black‐box models. While the governing equations of the physical network are derived by representing the network as a linear graph, the equations of the black‐box model are characterized as an abstract class of Differential‐Algebraic equations (DAEs) of a specific form (Functional Mock‐up Unit). Combining those two representations, existence and uniqueness results can be formulated based on the connectivity of the physical network and a concrete classification of the black‐box models. This is the natural extension of the approach derived in [3].