VARIATIONAL BOUNDARY-ELEMENT ANALYSIS OF SMALL-AMPLITUDE FLUID OSCILLATION IN A LOW-GRAVITY ENVIRONMENT

A variational boundary element technique is developed to analyse the small-amplitude oscillation of an incompressible, inviscid fluid contained in a rigid tank of arbitrary geometry under low-gravity conditions. Due to the influence of surface tension, the fluid usually oscillates about a curved free surface, which must first be determined by the solution of a nonlinear equilibrium problem. All of the energy expressions for the linear vibration problem are derived in terms of the normal displacement of the fluid boundary, which leads to a generalized eigenproblem. Numerical results are presented for several two- and three-dimensional evaluation problems; whenever possible, comparisons are made with known analytical solutions. The results indicate that the boundary element technique is robust and accurate.