by M. Barnyak, I. Gavrilyuk, M. Hermann, A. Timokha
Preprint series: 10-01, Reports on Numerical Mathematics
Abstract: By using Kelvin's inversion, we construct analytical harmonic functions satisfying the zero-Neumann condition on the inner spherical wall everywhere except a single point where the velocity is infinite. This set of functions can be used to construct approximate velocity potentials associated with liquid sloshing in a spherical tank, and in other related hydrodynamic problems.
Keywords: Sloshing, spherical tank, variational methods, modal system