Construction of solutions for the problem of free oscillations of an ideal liquid in cavities of complex geometric form - Barnyak, M. Ya. (Ukrains’kyi Matematychnyi Zhurnal, 2005)
We consider the problem of free oscillations of an ideal incompressible liquid in cavities of complex geometric form. The domain filled with liquid is divided into subdomains of simpler geometric form. The original problem is reduced to the spectral problem for a part of the domain filled with liquid. To this end, we use solutions of auxiliary boundary-value problems in subdomains. We construct approximate solutions of the problem obtained using the variational method. We also consider the problem of the rational choice of a system of coordinate functions. Results of the numerical realization of the proposed method are presented.