A space-time finite element method for the exterior structural acoustics problem: Time-dependent radiation boundary conditions in two space dimensions

17Citations
Citations of this article
12Readers
Mendeley users who have this article in their library.
Get full text

Abstract

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.

Cite

CITATION STYLE

APA

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

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free