In a domain method of solution of exterior scalar wave equation, the radiation condition needs to be imposed on a truncation boundary of the modeling domain. The Bayliss, Gunzberger and Turkel (BGT) boundary dampers (1984) which require a circular cylindrical truncation boundary in the diffraction problem of water waves, have been particularly successful in this task. However, for an elongated body, an elliptic truncation boundary has the potential to reduce the modeling domain and hence the computational effort. Lee et al (1990), based on the pseudo-differential operator approach put forward by Engquist and Majda (1977), derived a second order absorbing boundary condition for elliptic boundary equivalent to the BGT damper and used it in electromagnetic wave scattering problems by finite difference method. In this paper, this boundary condition is implemented in the form of boundary damper approximation in the context of finite element method and used it in water wave diffraction problem. The performance of the damper on elliptic truncation boundary is studied using an example of diffraction by an elliptic cylinder.
Linear diffraction of small amplitude free surface water waves by large bodies is a well understood problem. The boundary value problem associated with this can be solved by various numerical methods like Boundary Element Method (BEM), Finite Difference Method (FDM), Finite Element Method (FEM) etc. In a domain method such as FEM, the infinite fluid domain has to be limited to a finite one in which computations are carried out. This requires setting up of a truncation boundary around the body that demarcates the far field from the near field. Then, a radiation condition in the form of an absorbing boundary condition (ABC) needs to be imposed on this boundary to ensure that the waves are truly outgoing.
