A Numerical Method for the Analysis of Nonlinear Sloshing in Circular Cylindrical Containers

Summary

A new computational method has been developed for the analysis of three-dimensional large-amplitude motion of liquids with free surfaces in moving containers. The problem is formulated mathematically as a nonlinear initial-boundary value problem under the assumption of irrotational flow of an inviscid fluid. Basic equations of the problem are discretized spacewise by the boundary element method based on Green’s second identity and timewise by a forward-time Taylor series expansion. The size of a time increment is determined every time step so that the remainder of truncated Taylor series should be equal to a given small value. This variable time-stepping technique has made a great contribution to numerically stable computations. As a numerical example, swirl motion of a liquid free surface in a circular cylindrical container undergoing horizontal excitation has been analyzed.