What boundary conditions should one use for CFD simulations of free-surface phenomena?

It is sometimes required to simulate free-surface flows in which progressive or standing surface waves enter the domain and interact with various features of the region which is being considered. These waves may or may not co-exist with currents in the bulk of the fluid. In reality, the waves will be reflected, scattered or refracted in the domain, and usually these processes will be complex and mult-dimensional. Indeed the background wave environment may involve wave trains propagating in multiple directions, as happens at ocean surfaces. The attached note is principally written to support simulations in which the background waves are uni-directional, and in which linear approximations to the boundary conditions are considered to be adequate. The linear approximations provided here ignore the effects of currents. It should be noted that the directions of waves and currents may not coincide.

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