A family of second-order boundary dampers for finite element analysis of two and three-dimensional problems in transient exterior acoustics

Numerical modelling of exterior acoustics problems involving in"nite medium requires truncation of the medium at a "nite distance from the obstacle or the structure and use of non-re#ecting boundary condition at this truncation surface to simulate the asymptotic behaviour of radiated waves at far "eld. In the context of the "nite element method, Bayliss}Gunzburger}Turkel (BGT) boundary conditions are well suited since they are local in both space and time. These conditions involve &damperʹ operators of various orders, which work on acoustic pressure p and they have been used in time harmonic problems widely and in transient problems in a limited way. Alternative forms of second-order BGT operators, which work on pR (time derivative of p) had been suggested in an earlier paper for 3D problems but they were neither implemented nor validated. This paper presents detailed formulations of these second-order dampers both for 2D and 3D problems, implements them in a "nite element code and validates them using appropriate example problems. The developed code is capable of handling exterior acoustics problems involving both Dirichlet and Neumann boundary conditions