The effects of nonlinearity on a train of linear water waves in deep water interacting with underlying currents are investigated numerically via a boundary-integral method. The current is assumed to be two-dimensional and stationary, being induced by a distribution of singularities located beneath the free surface, which impose sharp and gentle surface velocity gradients. For ‘slowly’ varying currents, the fully nonlinear results confirm that opposing currents induce wave steepening and breaking within the region where a high convergence of rays occurs. For ‘rapidly’ varying currents, wave blocking and breaking are more prominent. In this case reflection was observed when sufficiently strong adverse currents are imposed, confirming that at least part of the wave energy that builds up within the caustic can be released in the form of partial reflection and wave breaking. For bichromatic waves, the fully nonlinear results show that partial wave blocking occurs at the individual wave components in the wave groups and that waves become almost monochromatic upstream of the blocking region.

The effects of uniform vorticity on a train of 'gentle' and 'steep' deep-water waves interacting with underlying flows are investigated through a fully nonlinear boundary integral method. It is shown that wave blocking and breaking can be more prominent depending on the magnitude and direction of the shear flow. Reflection continues to occur when sufficiently strong adverse currents are imposed on 'gentle' deep-water waves, though now affected by vorticity. For increasingly positive values of vorticity, the induced shear flow reduces the speed of right-going progressive waves, introducing significant changes to the free-surface profile until waves are completely blocked by the underlying current. A plunging breaker is formed at the blocking point when 'steep' deep-water waves interact with strong adverse currents. Conversely negative vorticities augment the speed of right-going progressive waves, with wave breaking being detected for strong opposing currents. The time of breaking is sensitive to the vorticity's sign and magnitude, with wave breaking occurring later for negative values of vorticity. Stopping velocities according to nonlinear wave theory proved to be sufficient to cause wave blocking and breaking.

A submerged cylinder in a uniform stream flow is approximated by a horizontal doublet, following Lamb's classical method. A linear steady solution including surface tension effects is derived, showing that under certain conditions small-scale ripples are formed ahead of the cylinder, while a train of ‘gravity-like’ waves appear downstream. Surface tension effects and a dipole are included in the fully nonlinear unsteady non-periodic boundary-integral solver described by Tanaka et al. (J. Fluid Mech., vol. 185, 1987, pp. 235–248). Nonlinear effects are modelled by considering a flat free surface or the linear stationary solution as an initial condition for the fully nonlinear irrotational flow programme. Long-run computations show that these unsteady flows approach a steady solution for some parameters after waves have radiated away. In other cases the flow does not approach a steady solution. Interesting features at the free surface such as the appearance of ‘parasitic capillaries’ near the crest of gravity waves and the formation of capillary–gravity waves upstream of the cylinder are found.

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Acoustic waves are modeled using a 2D frequency-domain finite-difference scheme with three different artificial damping boundaries: the absorbing boundary condition (ABC), perfectly matched layer (PML), and a hybrid strategy combining PML and ABC. We evaluated the features of each simulation for a given artificial boundary condition for homogeneous and heterogeneous media. For shorter PML layers, the hybrid absorbing scheme gave better results when compared with the traditional PML technique, with a significant reduction of the spurious reflections and a shorter computational run time.

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