Dynamic coupling between horizontal vessel motion and two-layer shallow-water sloshing |
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Institution: | 1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John׳s, NL, Canada A1C 5S7;2. Department of Mathematics, Middle East Technical University, Ankara, Turkey;1. Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Canada;2. Department of Mechanical and Aerospace Engineering, New York University Polytechnic School of Engineering, Brooklyn, NY, USA |
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Abstract: | Numerical and analytical results are presented for fluid sloshing, of a two-layer inviscid, incompressible and immiscible fluid with thin layers and a rigid lid, coupled to a vessel which is free to undergo horizontal motion governed by a nonlinear spring. Exact analytical results are obtained for the linear problem, giving the natural frequencies and the resonance structure, particularly between the fluid and vessel. A numerical method for the linear and nonlinear equations is developed based on the high-resolution f-wave-propagation finite volume methods due to Bale et al. (2002) SIAM Journal on Scientific Computing 24, 955–978], adapted to include the pressure gradient at the rigid-lid, and coupled to a Runge–Kutta solver for the vessel motion. The numerical simulations in the linear limit are compared with the exact analytical solutions. The coupled nonlinear numerical solutions with simulations near the internal 1:1 resonance are presented. Of particular interest is the partition of energy between the vessel and fluid motion. |
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Keywords: | Dynamic coupling Shallow-water sloshing Two-layer flow f-Wave-propagation Resonance |
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