Transparent boundary condition for the momentum conservative scheme of the shallow water equations

In conducting water wave simulations, the correct implementation of boundary conditions is important to obtain accurate wave dynamics in the computational domain. For assessment of coastal structures such as breakwaters, where both transmitted and reflected waves are present in the computational domain, we often need to observe simulation behavior for a somewhat long period of time. In this case, applying a transparent boundary condition is necessary, a condition that allows transmitted wave propagates to the right, whereas reflected waves propagates to the left at all times. In this paper, we propose a transparent boundary condition which derives from the embedded wave generation method of Liam et al. [5]. In this paper, the method is implemented to the momentum conservative scheme of the shallow water equations, and conduct several wave simulations. First, we use a monochromatic wave to demonstrate the implementation of embedded wave generation for constructing transparent boundary condition. Second, we show how this method has an effect on the backward and onward shoreline motion of Carrier-Greenspan [2] simulation. Finally, we consider a simulation of wave reduction due to a submerged breakwater with a certain dimension.