I.A.Lukovsky, G.F.Zolotenko, A.M.Pilkevich A comparative analysis of two variational models in the nonlinear theory of relative fluid motion |
Applied hydromechanics, Vol. 5 (77) ¹ 4, (2003) |
| Two fluid dynamics models constructed on the base of the variational Bateman-Luke-Whithem\ principle are compared. As a test problem, it is considered the problem of the nonlinear sloshing of an inviscid homogeneous incompressible liquid that partially fills a vertical circular cylinder performing an arbitrary translational movement. One of the model named Hamiltonian is based on the exact ordinary integro-differential Hamiltonian type equations and the other named 5-modal is based on the ordinary differential equations with the polinomial coefficients. The input models equations are ahalyzed and compared and the relations between them are established. A detailed derivation of the 5-modal equations actively used at the present time are carried out. Numerically it is solved a problem of the liquid free surface vibrations inside the uniformly accelerated tank which was in the state position initially. The numerical results for the generalized fluid coordinates and the free surface ordinates are compared. The estimates of the weighted mean square errors and relative errors of the calculations according to Hamiltonian model with respect to 5-model are given. The cases of the essential discrepancies in the calculations according to this model are noted. |
|
KEY WORDS: *** |
| TEXT LANGUAGE: Russian |