G.F.Zolotenko Computer simulation on the basis of Hamilton's type equations of nonlinear sloshing in a rectangular tank |
Applied hydromechanics, Vol. 4 (76) ¹ 1, (2002) |
| The nonlinear systems of the ordinary integro-differential equations arising in dynamics of the relative motions of an inviscid homogeneous incompressible liquid with respect to the variational method by Bateman - Luke - Whitham and having a structural similarity to the Hamiltonian equations are considered. The properties of this systems of equations and the known method of their solution by means of the elimination of the liquid quasivelocities and the reduction to a certain systems of the second order equations relative to the liquid coordinates are analyzed. In the case of a rectangular tank partially filled with a liquid it is developed the alternative approach that bases on an idea of the direct integration of the exact equations by means of the Runge - Kutta method. It is proposed an algorithm of the numerical solution of the initial exact equations the capabilities of which are demonstrated in the problem of the liquid nonlinear free oscillations in the inclined rectangular tank after its acceleration. |
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| TEXT LANGUAGE: Russian |