Local high-order radiation boundary conditions for the two-dimensional time-dependent structural acoustics problem

Abstract

The time-dependent structural acoustics problem involving solution of the coupled wave equation over an infinite fluid domain is posed as a coupled problem over a finite fluid domain with local time-dependent radiation boundary conditions applied to the fluid truncation boundary. The proposed radiation boundary conditions are based on an asymptotic approximation to the exact solution in the frequency domain expressed in negative powers of a nondimensional wave number. A sequence of differential operators that match the leading terms of the asymptotic expansion provide boundary conditions that are of progressively higher order and increasing accuracy. Time-dependent boundary conditions are obtained through an inverse Fourier transform. The relationship of these approximate local operators to the exact nonlocal Dirichlet-to-Neumann map is examined. To illustrate their effectiveness, the boundary conditions are employed in a finite element formulation for the time-dependent structural acoustics problem. In contrast to nonlocal boundary conditions based on the Dirichlet-to-Neumann map or retarded potential integral formulations, the proposed local boundary conditions preserve the data structure of the standard finite element method and do not require storage of a large pool of historical data during the solution process. Numerical results illustrate the accuracy of the proposed boundary conditions as effected by the operator order, acoustic wave number, radiation directionality, and distance from the acoustic source.