In this paper, the liquid sloshing problem in an upright circular tank undergoing an oscillation in a single degree of freedom is considered. A fully nonlinear time-domain harmonic polynomial cell (HPC) method based on overset mesh is developed to delve into the flow physics, and the comparison is made with the weakly nonlinear multimodal theory. Both time-harmonic (or periodic) and transient-type oscillations are considered. For the time-harmonic oscillation, planar and swirling waves (including time-harmonic and periodically modulated swirling waves) occur when the excitation frequency is close to the lowest natural frequency. The swirling direction is dependent on initial conditions. The periodically modulated swirling waves switch back and forth between swirling waves and planar waves. The occurrence of swirling waves results in lateral hydrodynamic force and roll moment on top of in-line force and pitch moment components acting on the tank. The sloshing response in terms of surface elevations contains higher harmonic components, while the hydrodynamic forces and moments on the tank are remarkably linear. A NewWave type of excitation is imposed which represents on average the most probable maximum excitation to be expected for a given sea state, and narrow-banded sloshing responses are observed. This allows application of a designer-wave type of excitation which would excite the most probable maximum response in sloshing. A focused-wave-type excitation is also considered, and an impulselike feature is observed in the in-line force and pitch moment components. The total in-line force and pitch moment are further decomposed into inertial component, which is induced by the acceleration of the external motion, and residual component, which is closely associated with the liquid sloshing. It is found that under a focused-wave-type excitation the inertial component contribution is more dominant, while under a designer-wave-type excitation the residual component dominates instead.