Transparent boundary condition for the momentum conservative scheme of the shallow water equations
Maria Artanta Ginting (a*). Sri Redjeki Pudjaprasetya (a). Didit Adytia (b)
a) Industrial and Financial Mathematics Research Group, Institut Teknologi Bandung, Jalan Ganesha No. 10, Bandung 40132, Indonesia
*mariaaginting[at]s.itb.ac.id
b) School of Computing, Telkom University, Jl. Telekomunikasi No. 01 Terusan Buah Batu, Bandung 40257, Indonesia
Abstract
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 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. [2014]. In this paper, the method is implemented to the momentum conservative scheme of the shallow water equations, and conduct a simulation of wave reduction due to a submerged breakwater with certain dimension. Further, we measured the reflection and transmission coefficients and compare it with the analytical formulas.
Keywords: Transparent boundary condition; Embedded influxing; Momentum conservative scheme; Shallow water equations; Reflection and transmittion coefficients
Topic: Coastal and Ocean Dynamics