Research Report: Manuscript CMCU-95-04, July 1995
A Space-Time Finite Element
Method for the Exterior Structural
Acoustics Problem: Time-Dependent
Radiation Boundary Conditions
in Two Space Dimensions
Lonny L. Thompson
Computational Mechanics at Clemson University
Department of Mechanical Engineering
Clemson, South Carolina 29634-0921
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.
Aborbing boundary conditions are incorporated
as `natural'
boundary conditions in the space-time variational equation, i.e.
they are enforced weakly in both space and 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
nondimensional wavenumber.
In this paper we undertake a brief development of the time-dependent
radiation boundary
conditions, establishing their relationship to the exact
impedance (DtN 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 matrix problem emanating from 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.
Postscript file of Manuscript CMCU-95-04
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