A symplectic integrator for dynamic coupling between nonlinear vessel motion with variable cross-section and bottom topography and interior shallow-water sloshing |
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| Institution: | 1. Univ. Grenoble Alpes, Inria, CNRS, Grenoble INP*, LJK, 38000 Grenoble, France;2. Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43, blvd du 11 novembre 1918, 69622 Villeurbanne Cedex, France;1. Bioinformatics Research Center, North Carolina State University, Raleigh, NC, USA;2. Department of Biological Sciences, Center for Human Health and the Environment, North Carolina State University, Raleigh, NC, USA;3. Department of Environmental and Molecular Toxicology, Sinnhuber Aquatic Research Laboratory, Oregon State University, Corvallis, OR, USA;1. School of Interdisciplinary Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan;2. Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan;1. Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, 25068 Řež near Prague, Czechia;2. Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University, Břehová 7, 11519 Prague, Czechia |
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| Abstract: | The coupled motion between shallow-water sloshing in a moving vessel with variable cross-section and bottom topography, and the vessel dynamics is considered, with the vessel dynamics restricted to horizontal motion governed by a nonlinear spring. The coupled fluid and vessel equations in Eulerian coordinates are transformed to the Lagrangian particle path setting which leads to a formulation with nice properties for numerical simulation. In the Lagrangian representation, a simple and fast numerical algorithm based on the Störmer–Verlet method, is implemented. The numerical scheme conserves the total energy in the system, as well as giving the partition of energy between the fluid and vessel. Numerical simulations of the coupled nonlinear dynamics are presented. |
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| Keywords: | Shallow-water sloshing Lagrangian particle path Störmer–Verlet algorithm Symplecticity Dynamic coupling |
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