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International Journal of Fluid Mechanics Research
ESCI SJR: 0.22 SNIP: 0.446 CiteScore™: 0.5

ISSN Imprimer: 2152-5102
ISSN En ligne: 2152-5110

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International Journal of Fluid Mechanics Research

DOI: 10.1615/InterJFluidMechRes.v32.i6.60
pages 718-741

Computer Simulation on the Basis of Hamilton-Type Equations of Nonlinear Fluid Oscillations in a Rectangular Tank

G. F. Zolotenko
Institute of Mathematics of National Academy of Sciences of Ukraine, Kyiv, Ukraine


The subject of consideration comprises nonlinear systems of ordinary integral-differential equations which appear in dynamics of relative motion of ideal homogeneous incompressible fluid in connection with a variational method by Bateman−Luke−Whitham; the equations are similar to Hamiltonian equations. The paper presents an analysis of properties of the said simultaneous equations and a known method for their approximate solution − by excluding quasi-velocities of the fluid and reducing the system to certain simultaneous equations of second order with respect to the coordinates of a free surface. An alternative approach is presented for a rectangular vessel partially filled with fluid. It is based on a direct integration of the original exact equations by the Runge-Kutta technique. An algorithm for numerical solution of the equations has been developed and is demonstrated by the example of nonlinear free oscillations (sloshing) of fluid in a tilted rectangular vessel after its being accelerated.

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