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Three‐dimensional arbitrary Lagrangian–Eulerian numerical prediction method for non‐linear free surface oscillation
Author(s) -
Ushijima Satoru
Publication year - 1998
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/(sici)1097-0363(19980315)26:5<605::aid-fld668>3.0.co;2-w
Subject(s) - slosh dynamics , free surface , curvilinear coordinates , discretization , inviscid flow , oscillation (cell signaling) , numerical analysis , eulerian path , mathematics , mathematical analysis , surface (topology) , classical mechanics , computational fluid dynamics , volume of fluid method , mechanics , physics , flow (mathematics) , geometry , lagrangian , biology , genetics
A numerical prediction method has been proposed to predict non‐linear free surface oscillation in an arbitrarily‐shaped three‐dimensional container. The liquid motions are described with Navier–Stokes equations rather than Laplace equations which are derived by assuming the velocity potential. The profile of a liquid surface is precisely represented with the three‐dimensional curvilinear co‐ordinates which are regenerated in each computational step on the basis of the arbitrary Lagrangian–Eulerian (ALE) formulation. In the transformed space, the governing equations are discretized on a Lagrangian scheme with sufficient numerical accuracy and the boundary conditions near the liquid surface are implemented in a complete manner. In order to confirm the applicability of the present computational technique, numerical simulations are conducted for the free oscillations of viscid and inviscid liquids and for highly non‐linear oscillation. In addition, non‐linear sloshing motions caused by horizontal and vertical excitations and a transition from non‐linear sloshing to swirling are numerically predicted in three‐dimensional cylindrical containers. Conclusively, it is shown that these sloshing motions associated with high non‐linearity are reasonably predicted with the present numerical technique. © 1998 John Wiley & Sons, Ltd.