Multimodal method in sloshing
The multimodal method reduces the free-surface sloshing problem to a (modal) system of nonlinear ordinary differential equations. The method was originally proposed for nonimpulsive hydrodynamic loads but, recently, it was successfully extended to the sloshing-induced slamming. In the 50 – 60’s, the...
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| Date: | 2015 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2015
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| Series: | Нелінійні коливання |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Multimodal method in sloshing / I.O. Lukovsky, O.M. Tymokha // Нелінійні коливання. — 2015. — Т. 18, № 3. — С. 295-312 — Бібліогр.: 228 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | The multimodal method reduces the free-surface sloshing problem to a (modal) system of nonlinear ordinary differential equations. The method was originally proposed for nonimpulsive hydrodynamic loads but, recently, it was successfully extended to the sloshing-induced slamming. In the 50 – 60’s, the method was employed in the Computational Fluid Dynamics (CFD) but has lost the contest the algorithms of the 90-00’s. Nowadays, the method plays the dual role: firstly, as a unique analytical tool for studying nonlinear sloshing regimes, their stability, and chaos as well as for simulations when traditional CFD fails (e.g., containers with a perforated screen) and, secondly, as a source of the modal systems which are analogies of the Kordeweg – de Vries, Boussinesq etc. equations but for the contained liquid. The paper surveys the state-of-the-art and existing modal systems, specifies open problems. |
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