Abstract
Free surface flow of incompressible liquids interacts with compressible gases and flexible structures in applications like liquid tanks or air chamber supported floating platforms. After briefly describing the physical modeling of the coupled system, we suggest a procedure for model order reduction based on the modal bases of the un-coupled domains. To again couple the different physical domains, one needs to assemble the coupling conditions on the interfaces between gas, liquid, and structure domains in terms of the modal coordinates. We demonstrate the effectiveness of the model order reduction by applying it to a geometrically simple but strongly coupled tank system, for which we compute the sloshing modes.
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Notes
- 1.
Using the relation \(\varvec{\nabla }\cdot {\varvec{(}{\delta }\cdot \varvec{\sigma }}) = ({\varvec{\nabla }\cdot \varvec{\sigma }})\cdot \varvec{\delta } +\varvec{\sigma }:({\varvec{\nabla }\varvec{\delta }})\), where ‘ : ’ denotes the double dot product, i.e. the sum of the products of conjugated tensor elements.
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Toth, F., Kaltenbacher, M. (2020). Coupling of Incompressible Free-Surface Flow, Acoustic Fluid and Flexible Structure Via a Modal Basis. In: Fehr, J., Haasdonk, B. (eds) IUTAM Symposium on Model Order Reduction of Coupled Systems, Stuttgart, Germany, May 22–25, 2018. IUTAM Bookseries, vol 36. Springer, Cham. https://doi.org/10.1007/978-3-030-21013-7_10
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