An extrapolated version of a time-dependent nonreflecting boundary condition is developed for use at artificial boundaries to truncate infinite/semi-infinite domains for transient water wave problems. Test examples include single- and multiple-frequency flap wavemaker problems and free vibrations of a floating circular cylinder. The finite element results compare favorably to analytical solutions. It is shown that with the proposed boundary condition the numerical simulations have little reflections from the artificial boundaries.
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