A time-domain Higher-Order Boundary Element Method (HOBEM) based on cubic shape functions for second-order wave-current-body interaction developed by Shao & Faltinsen [1] is further refined by investigating the feasibility of adopting the unstructured meshes on the free surface and body surfaces from an open source mesh generator [2]. When the steady local flow effect is considered in the time-domain boundary-value-problem formulation, the advection terms in the free surface are part of the sources of numerical instability. In this paper, the advection terms are taken care of in an implicit way in a 4th order Runge-Kutta scheme with much better stability. Some numerical examples extensively studied in the literature are studied in order to validate the present numerical model.

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