A time-discontinuous Galerkin space-time finite element method is formulated for the exterior structural acoustics problem in two space dimensions. The problem is posed over a bounded computational domain with local time-dependent radiation (absorbing) boundary conditions applied to the fluid truncation boundary. Absorbing boundary conditions are incorporated as 'natural' boundary conditions in the space-time variational equation, i.e. they are enforced weakly in both space an time. Following Bayliss and Turkel, time-dependent radiation boundary conditions for the two-dimensional wave equation are developed from an asymptotic approximation to the exact solution in the frequency domain expressed in negative powers of a non-dimensional wavenumber. In this paper, we undertake a brief development of the time- dependent radiation boundary conditons, establishing their relationship to the exact impedance (Dirichlet-to-Neumann map) for the acoustic fluid, and characterize their accuracy when implemented in our space-time finite element formulation for transient structural acoustics. Stability estimates are reported together with an analysis of the positive form of the space time variational equations for the coupled fluid-structure system. Several numerical simulations of transient radiation and scattering in two space dimensions are presented to demonstrate the effectiveness of the space time method.
CITATION STYLE
Thompson, L. L., & Pinsk Y, P. M. (1996). A space-time finite element method for the exterior structural acoustics problem: Time-dependent radiation boundary conditions in two space dimensions. International Journal for Numerical Methods in Engineering, 39(10), 1635–1657. https://doi.org/10.1002/(SICI)1097-0207(19960530)39:10<1635::AID-NME922>3.0.CO;2-T
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