In coastal and ocean engineering applications, a computational domain with a limited size and open boundaries is often used to simulate periodic wave propagation in open water. When a wave train moving through the domain reaches an open boundary, a proper boundary condition must be used to minimize wave reflection. Otherwise, incorrect wave shape, severe water volume change and unphysical wave-structure interaction may occur. In general, two types of methods exist to reduce wave reflection at open boundaries: the radiation boundary condition and the sponge, or wave-absorbing, layer method.
The radiation boundary condition was originally proposed by Sommerfeld (1912) for mathematical physics and later revised by Orlanski (1976) for hydraulic flow. It was implemented in FLOW-3D as “the outflow boundary condition” (Hirt, 1999) and has been used for many successful applications since then. The idea is to allow continuous wave propagation through an open boundary.
The radiation boundary condition has its limitations, however. Equation (1) is obtained from the assumption of a linear wave, and is numerically evaluated at the open boundary. Theoretically, this method is not suitable for nonlinear wave and dispersive wave conditions. Although short-term wave reflection from an open boundary can be reduced to a small amount by the radiation boundary condition, an accumulation of the wave reflections over long periods can become significant and affect the wave motion inside the computational domain. Figure 1 shows wave profiles at different times for a 2D nonlinear wave with waves generated at the left side and an outflow boundary placed at the right side of the domain. The wavelength is 10.43 m, wave period 2.8 s, wave height 0.4 m, and the undisturbed water depth is 2 m. The wave takes 13.42 s to travel from the one side to the other side of the domain. It can be seen that the calculated wave profile becomes more irregular with time. Figure 2 shows that the calculated water volume in the domain increases significantly with time. At 75 s, the computational domain is completely filled with fluid.
Gengsheng Wei, “The Sponge Layer Method in FLOW-3D,” Flow Science Report 07-15, October 2015, Copyright Flow Science